src: Add secp256k1 tests and sign/verify benchmarks

For checking CPU speed/reliability and testing secp256k1 on weird
architectures.

README.md

@@ -47,6 +47,11 @@ serial output in Intel HEX format.
 
 [README](src/dump_otp/README.md)
 
+secp256k1\_{tests,bench}
+------------------------
+
+Run tests and benchmarks for the secp256k1 elliptic curve cryptographic library on this RISC-V CPU.
+
 rust/k210-console
 -----------------
 
@@ -73,7 +78,7 @@ Annotated radare2 config files for the Boot ROM and OTP can be found under [r2](
 Other projects
 ==============
 
-Some other interesting K210-based projects and demos:
+Some interesting K210-based projects and demos by other people:
 
 - [accelerometer](https://github.com/GitJer/Some-Sipeed-MAIX-GO-k210-stuff/tree/master/src/accelerometer) - Example of using the MSA300 accelerometer on the MAIX Go board, by GitJer
 

src/secp256k1_bench/bench.h

@@ -0,0 +1,82 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_BENCH_H
+#define SECP256K1_BENCH_H
+
+#include <stdio.h>
+#include <string.h>
+#include <math.h>
+#include "sys/time.h"
+
+static double gettimedouble(void) {
+    struct timeval tv;
+    gettimeofday(&tv, NULL);
+    return tv.tv_usec * 0.000001 + tv.tv_sec;
+}
+
+void print_number(double x) {
+    double y = x;
+    int c = 0;
+    if (y < 0.0) {
+        y = -y;
+    }
+    while (y > 0 && y < 100.0) {
+        y *= 10.0;
+        c++;
+    }
+    printf("%.*f", c, x);
+}
+
+void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) {
+    int i;
+    double min = HUGE_VAL;
+    double sum = 0.0;
+    double max = 0.0;
+    for (i = 0; i < count; i++) {
+        double begin, total;
+        if (setup != NULL) {
+            setup(data);
+        }
+        begin = gettimedouble();
+        benchmark(data);
+        total = gettimedouble() - begin;
+        if (teardown != NULL) {
+            teardown(data);
+        }
+        if (total < min) {
+            min = total;
+        }
+        if (total > max) {
+            max = total;
+        }
+        sum += total;
+    }
+    printf("%s: min ", name);
+    print_number(min * 1000000.0 / iter);
+    printf("us / avg ");
+    print_number((sum / count) * 1000000.0 / iter);
+    printf("us / max ");
+    print_number(max * 1000000.0 / iter);
+    printf("us\n");
+}
+
+int have_flag(int argc, char** argv, char *flag) {
+    char** argm = argv + argc;
+    argv++;
+    if (argv == argm) {
+        return 1;
+    }
+    while (argv != NULL && argv != argm) {
+        if (strcmp(*argv, flag) == 0) {
+            return 1;
+        }
+        argv++;
+    }
+    return 0;
+}
+
+#endif /* SECP256K1_BENCH_H */

src/secp256k1_bench/main.c

@@ -0,0 +1,179 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+#define HAVE_CONFIG_H
+#define SECP256K1_BUILD
+// Do not define VERIFY for the benchmarks: it makes things run much slower
+
+#if defined HAVE_CONFIG_H
+#include "../secp256k1_tests/libsecp256k1-config.h"
+#endif
+
+#include <stdio.h>
+#include <string.h>
+
+#include "../secp256k1_tests/secp256k1_c.h"
+#include "util.h"
+#include "bench.h"
+
+#include "sysctl.h"
+#include "uarths.h"
+#include "sleep.h"
+
+#define V_RUNS (200)
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+    unsigned char sig[72];
+    size_t siglen;
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+} benchmark_verify_t;
+
+static void benchmark_verify(void* arg) {
+    int i;
+    benchmark_verify_t* data = (benchmark_verify_t*)arg;
+
+    for (i = 0; i < V_RUNS; i++) {
+        secp256k1_pubkey pubkey;
+        secp256k1_ecdsa_signature sig;
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
+        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+    }
+}
+
+int bench_verify_main(void) {
+    int i;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    benchmark_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    for (i = 0; i < 32; i++) {
+        data.msg[i] = 1 + i;
+    }
+    for (i = 0; i < 32; i++) {
+        data.key[i] = 33 + i;
+    }
+    data.siglen = 72;
+    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
+    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
+    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
+    data.pubkeylen = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+
+    run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, V_RUNS);
+
+    secp256k1_context_destroy(data.ctx);
+
+    return 0;
+}
+
+typedef struct {
+    secp256k1_context* ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+} bench_sign;
+
+static void bench_sign_setup(void* arg) {
+    int i;
+    bench_sign *data = (bench_sign*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = i + 1;
+    }
+    for (i = 0; i < 32; i++) {
+        data->key[i] = i + 65;
+    }
+}
+
+static void bench_sign_run(void* arg) {
+    int i;
+    bench_sign *data = (bench_sign*)arg;
+
+    unsigned char sig[74];
+    for (i = 0; i < V_RUNS; i++) {
+        size_t siglen = 74;
+        int j;
+        secp256k1_ecdsa_signature signature;
+        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
+        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
+        for (j = 0; j < 32; j++) {
+            data->msg[j] = sig[j];
+            data->key[j] = sig[j + 32];
+        }
+    }
+}
+
+int bench_sign_main(void) {
+    bench_sign data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+
+    run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+
+    return 0;
+}
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char scalar[32];
+} bench_ecdh_data;
+
+static void bench_ecdh_setup(void* arg) {
+    int i;
+    bench_ecdh_data *data = (bench_ecdh_data*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+
+    /* create a context with no capabilities */
+    data->ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT);
+    for (i = 0; i < 32; i++) {
+        data->scalar[i] = i + 1;
+    }
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+int main(void) {
+    if (current_coreid() != 0) {
+        while (1)
+            asm volatile ("wfi");
+    }
+
+    sysctl_pll_set_freq(SYSCTL_PLL0, 800000000UL);
+
+    uarths_init();
+    usleep(100000);
+
+    printf("Running secp256k1 benchamrks with CPU clock %u\n", sysctl_clock_get_freq(SYSCTL_CLOCK_CPU));
+    printf("see add_compile_flags in cmake/compile-flags.cmake to tweak optimization flags\n");
+    printf("  WINDOW_A is %d\n", WINDOW_A);
+    printf("  WINDOW_G is %d\n", WINDOW_G);
+    bench_verify_main();
+    bench_sign_main();
+    printf("[done]\n");
+
+    while (1)
+        asm volatile ("wfi");
+    return 0;
+}

src/secp256k1_bench/util.h

@@ -0,0 +1,121 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_UTIL_H
+#define SECP256K1_UTIL_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <stdio.h>
+
+typedef struct {
+    void (*fn)(const char *text, void* data);
+    const void* data;
+} secp256k1_callback;
+
+static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
+    cb->fn(text, (void*)cb->data);
+}
+
+#ifdef DETERMINISTIC
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s\n", msg); \
+    abort(); \
+} while(0);
+#else
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \
+    abort(); \
+} while(0)
+#endif
+
+#if SECP256K1_GNUC_PREREQ(3, 0)
+#define EXPECT(x,c) __builtin_expect((x),(c))
+#else
+#define EXPECT(x,c) (x)
+#endif
+
+#ifdef DETERMINISTIC
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed"); \
+    } \
+} while(0)
+#else
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed: " #cond); \
+    } \
+} while(0)
+#endif
+
+/* Like assert(), but when VERIFY is defined, and side-effect safe. */
+#if defined(COVERAGE)
+#define VERIFY_CHECK(check)
+#define VERIFY_SETUP(stmt)
+#elif defined(VERIFY)
+#define VERIFY_CHECK CHECK
+#define VERIFY_SETUP(stmt) do { stmt; } while(0)
+#else
+#define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
+#define VERIFY_SETUP(stmt)
+#endif
+
+static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
+    void *ret = malloc(size);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
+    return ret;
+}
+
+static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) {
+    void *ret = realloc(ptr, size);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
+    return ret;
+}
+
+/* Macro for restrict, when available and not in a VERIFY build. */
+#if defined(SECP256K1_BUILD) && defined(VERIFY)
+# define SECP256K1_RESTRICT
+#else
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(3,0)
+#   define SECP256K1_RESTRICT __restrict__
+#  elif (defined(_MSC_VER) && _MSC_VER >= 1400)
+#   define SECP256K1_RESTRICT __restrict
+#  else
+#   define SECP256K1_RESTRICT
+#  endif
+# else
+#  define SECP256K1_RESTRICT restrict
+# endif
+#endif
+
+#if defined(_WIN32)
+# define I64FORMAT "I64d"
+# define I64uFORMAT "I64u"
+#else
+# define I64FORMAT "lld"
+# define I64uFORMAT "llu"
+#endif
+
+#if defined(HAVE___INT128)
+# if defined(__GNUC__)
+#  define SECP256K1_GNUC_EXT __extension__
+# else
+#  define SECP256K1_GNUC_EXT
+# endif
+SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+#endif
+
+#endif /* SECP256K1_UTIL_H */

src/secp256k1_tests/COPYING

@@ -0,0 +1,19 @@
+Copyright (c) 2013 Pieter Wuille
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.

src/secp256k1_tests/README.md

@@ -0,0 +1,54 @@
+libsecp256k1
+============
+
+Run tests and benchmarks for the secp256k1 elliptic curve cryptographic library on this RISC-V CPU.
+
+Description
+-----------
+
+Optimized C library for EC operations on curve secp256k1.
+
+This library is a work in progress and is being used to research best practices. Use at your own risk.
+
+Features:
+* secp256k1 ECDSA signing/verification and key generation.
+* Adding/multiplying private/public keys.
+* Serialization/parsing of private keys, public keys, signatures.
+* Constant time, constant memory access signing and pubkey generation.
+* Derandomized DSA (via RFC6979 or with a caller provided function.)
+* Very efficient implementation.
+
+Implementation details
+----------------------
+
+* General
+  * No runtime heap allocation.
+  * Extensive testing infrastructure.
+  * Structured to facilitate review and analysis.
+  * Intended to be portable to any system with a C89 compiler and uint64_t support.
+  * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
+* Field operations
+  * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
+    * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
+    * Using 10 26-bit limbs.
+  * Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
+* Scalar operations
+  * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
+    * Using 4 64-bit limbs (relying on __int128 support in the compiler).
+    * Using 8 32-bit limbs.
+* Group operations
+  * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
+  * Use addition between points in Jacobian and affine coordinates where possible.
+  * Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
+  * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
+* Point multiplication for verification (a*P + b*G).
+  * Use wNAF notation for point multiplicands.
+  * Use a much larger window for multiples of G, using precomputed multiples.
+  * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
+  * Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
+* Point multiplication for signing
+  * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
+  * Access the table with branch-free conditional moves so memory access is uniform.
+  * No data-dependent branches
+  * The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally.
+

src/secp256k1_tests/contrib/lax_der_parsing.c.h

@@ -0,0 +1,150 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <include/secp256k1.h>
+
+#include "lax_der_parsing.h"
+
+int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    size_t rpos, rlen, spos, slen;
+    size_t pos = 0;
+    size_t lenbyte;
+    unsigned char tmpsig[64] = {0};
+    int overflow = 0;
+
+    /* Hack to initialize sig with a correctly-parsed but invalid signature. */
+    secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+
+    /* Sequence tag byte */
+    if (pos == inputlen || input[pos] != 0x30) {
+        return 0;
+    }
+    pos++;
+
+    /* Sequence length bytes */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        pos += lenbyte;
+    }
+
+    /* Integer tag byte for R */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for R */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        rlen = 0;
+        while (lenbyte > 0) {
+            rlen = (rlen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        rlen = lenbyte;
+    }
+    if (rlen > inputlen - pos) {
+        return 0;
+    }
+    rpos = pos;
+    pos += rlen;
+
+    /* Integer tag byte for S */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for S */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        slen = 0;
+        while (lenbyte > 0) {
+            slen = (slen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        slen = lenbyte;
+    }
+    if (slen > inputlen - pos) {
+        return 0;
+    }
+    spos = pos;
+    pos += slen;
+
+    /* Ignore leading zeroes in R */
+    while (rlen > 0 && input[rpos] == 0) {
+        rlen--;
+        rpos++;
+    }
+    /* Copy R value */
+    if (rlen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 32 - rlen, input + rpos, rlen);
+    }
+
+    /* Ignore leading zeroes in S */
+    while (slen > 0 && input[spos] == 0) {
+        slen--;
+        spos++;
+    }
+    /* Copy S value */
+    if (slen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 64 - slen, input + spos, slen);
+    }
+
+    if (!overflow) {
+        overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    if (overflow) {
+        memset(tmpsig, 0, 64);
+        secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    return 1;
+}
+

src/secp256k1_tests/contrib/lax_der_parsing.h

@@ -0,0 +1,91 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file defines a function that parses DER with various errors and
+ * violations. This is not a part of the library itself, because the allowed
+ * violations are chosen arbitrarily and do not follow or establish any
+ * standard.
+ *
+ * In many places it matters that different implementations do not only accept
+ * the same set of valid signatures, but also reject the same set of signatures.
+ * The only means to accomplish that is by strictly obeying a standard, and not
+ * accepting anything else.
+ *
+ * Nonetheless, sometimes there is a need for compatibility with systems that
+ * use signatures which do not strictly obey DER. The snippet below shows how
+ * certain violations are easily supported. You may need to adapt it.
+ *
+ * Do not use this for new systems. Use well-defined DER or compact signatures
+ * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and
+ * secp256k1_ecdsa_signature_parse_compact).
+ *
+ * The supported violations are:
+ * - All numbers are parsed as nonnegative integers, even though X.609-0207
+ *   section 8.3.3 specifies that integers are always encoded as two's
+ *   complement.
+ * - Integers can have length 0, even though section 8.3.1 says they can't.
+ * - Integers with overly long padding are accepted, violation section
+ *   8.3.2.
+ * - 127-byte long length descriptors are accepted, even though section
+ *   8.1.3.5.c says that they are not.
+ * - Trailing garbage data inside or after the signature is ignored.
+ * - The length descriptor of the sequence is ignored.
+ *
+ * Compared to for example OpenSSL, many violations are NOT supported:
+ * - Using overly long tag descriptors for the sequence or integers inside,
+ *   violating section 8.1.2.2.
+ * - Encoding primitive integers as constructed values, violating section
+ *   8.3.1.
+ */
+
+#ifndef SECP256K1_CONTRIB_LAX_DER_PARSING_H
+#define SECP256K1_CONTRIB_LAX_DER_PARSING_H
+
+#include <include/secp256k1.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Parse a signature in "lax DER" format
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range. In addition, it will accept signatures
+ *  which violate the DER spec in various ways. Its purpose is to allow
+ *  validation of the Bitcoin blockchain, which includes non-DER signatures
+ *  from before the network rules were updated to enforce DER. Note that
+ *  the set of supported violations is a strict subset of what OpenSSL will
+ *  accept.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+int ecdsa_signature_parse_der_lax(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_CONTRIB_LAX_DER_PARSING_H */

src/secp256k1_tests/contrib/lax_der_privatekey_parsing.c.h

@@ -0,0 +1,113 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <include/secp256k1.h>
+
+#include "lax_der_privatekey_parsing.h"
+
+int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) {
+    const unsigned char *end = privkey + privkeylen;
+    int lenb = 0;
+    int len = 0;
+    memset(out32, 0, 32);
+    /* sequence header */
+    if (end < privkey+1 || *privkey != 0x30) {
+        return 0;
+    }
+    privkey++;
+    /* sequence length constructor */
+    if (end < privkey+1 || !(*privkey & 0x80)) {
+        return 0;
+    }
+    lenb = *privkey & ~0x80; privkey++;
+    if (lenb < 1 || lenb > 2) {
+        return 0;
+    }
+    if (end < privkey+lenb) {
+        return 0;
+    }
+    /* sequence length */
+    len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
+    privkey += lenb;
+    if (end < privkey+len) {
+        return 0;
+    }
+    /* sequence element 0: version number (=1) */
+    if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
+        return 0;
+    }
+    privkey += 3;
+    /* sequence element 1: octet string, up to 32 bytes */
+    if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
+        return 0;
+    }
+    memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]);
+    if (!secp256k1_ec_seckey_verify(ctx, out32)) {
+        memset(out32, 0, 32);
+        return 0;
+    }
+    return 1;
+}
+
+int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) {
+    secp256k1_pubkey pubkey;
+    size_t pubkeylen = 0;
+    if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) {
+        *privkeylen = 0;
+        return 0;
+    }
+    if (compressed) {
+        static const unsigned char begin[] = {
+            0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 33;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    } else {
+        static const unsigned char begin[] = {
+            0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
+            0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
+            0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 65;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    }
+    return 1;
+}

src/secp256k1_tests/contrib/lax_der_privatekey_parsing.h

@@ -0,0 +1,90 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file contains code snippets that parse DER private keys with
+ * various errors and violations.  This is not a part of the library
+ * itself, because the allowed violations are chosen arbitrarily and
+ * do not follow or establish any standard.
+ *
+ * It also contains code to serialize private keys in a compatible
+ * manner.
+ *
+ * These functions are meant for compatibility with applications
+ * that require BER encoded keys. When working with secp256k1-specific
+ * code, the simple 32-byte private keys normally used by the
+ * library are sufficient.
+ */
+
+#ifndef SECP256K1_CONTRIB_BER_PRIVATEKEY_H
+#define SECP256K1_CONTRIB_BER_PRIVATEKEY_H
+
+#include <include/secp256k1.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Export a private key in DER format.
+ *
+ *  Returns: 1 if the private key was valid.
+ *  Args: ctx:        pointer to a context object, initialized for signing (cannot
+ *                    be NULL)
+ *  Out: privkey:     pointer to an array for storing the private key in BER.
+ *                    Should have space for 279 bytes, and cannot be NULL.
+ *       privkeylen:  Pointer to an int where the length of the private key in
+ *                    privkey will be stored.
+ *  In:  seckey:      pointer to a 32-byte secret key to export.
+ *       compressed:  1 if the key should be exported in
+ *                    compressed format, 0 otherwise
+ *
+ *  This function is purely meant for compatibility with applications that
+ *  require BER encoded keys. When working with secp256k1-specific code, the
+ *  simple 32-byte private keys are sufficient.
+ *
+ *  Note that this function does not guarantee correct DER output. It is
+ *  guaranteed to be parsable by secp256k1_ec_privkey_import_der
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der(
+    const secp256k1_context* ctx,
+    unsigned char *privkey,
+    size_t *privkeylen,
+    const unsigned char *seckey,
+    int compressed
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Import a private key in DER format.
+ * Returns: 1 if a private key was extracted.
+ * Args: ctx:        pointer to a context object (cannot be NULL).
+ * Out:  seckey:     pointer to a 32-byte array for storing the private key.
+ *                   (cannot be NULL).
+ * In:   privkey:    pointer to a private key in DER format (cannot be NULL).
+ *       privkeylen: length of the DER private key pointed to be privkey.
+ *
+ * This function will accept more than just strict DER, and even allow some BER
+ * violations. The public key stored inside the DER-encoded private key is not
+ * verified for correctness, nor are the curve parameters. Use this function
+ * only if you know in advance it is supposed to contain a secp256k1 private
+ * key.
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *privkey,
+    size_t privkeylen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_CONTRIB_BER_PRIVATEKEY_H */

src/secp256k1_tests/ecdsa.h

@@ -0,0 +1,21 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECDSA_H
+#define SECP256K1_ECDSA_H
+
+#include <stddef.h>
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult.h"
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
+
+#endif /* SECP256K1_ECDSA_H */

src/secp256k1_tests/ecdsa_impl.h

@@ -0,0 +1,313 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+
+#ifndef SECP256K1_ECDSA_IMPL_H
+#define SECP256K1_ECDSA_IMPL_H
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+#include "ecdsa.h"
+
+/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
+ *  sage: for t in xrange(1023, -1, -1):
+ *     ..   p = 2**256 - 2**32 - t
+ *     ..   if p.is_prime():
+ *     ..     print '%x'%p
+ *     ..     break
+ *   'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
+ *  sage: a = 0
+ *  sage: b = 7
+ *  sage: F = FiniteField (p)
+ *  sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
+ *   'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+    0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+    0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
+);
+
+/** Difference between field and order, values 'p' and 'n' values defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ *  sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+ *  sage: a = 0
+ *  sage: b = 7
+ *  sage: F = FiniteField (p)
+ *  sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
+ *   '14551231950b75fc4402da1722fc9baee'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
+);
+
+static int secp256k1_der_read_len(const unsigned char **sigp, const unsigned char *sigend) {
+    int lenleft, b1;
+    size_t ret = 0;
+    if (*sigp >= sigend) {
+        return -1;
+    }
+    b1 = *((*sigp)++);
+    if (b1 == 0xFF) {
+        /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */
+        return -1;
+    }
+    if ((b1 & 0x80) == 0) {
+        /* X.690-0207 8.1.3.4 short form length octets */
+        return b1;
+    }
+    if (b1 == 0x80) {
+        /* Indefinite length is not allowed in DER. */
+        return -1;
+    }
+    /* X.690-207 8.1.3.5 long form length octets */
+    lenleft = b1 & 0x7F;
+    if (lenleft > sigend - *sigp) {
+        return -1;
+    }
+    if (**sigp == 0) {
+        /* Not the shortest possible length encoding. */
+        return -1;
+    }
+    if ((size_t)lenleft > sizeof(size_t)) {
+        /* The resulting length would exceed the range of a size_t, so
+         * certainly longer than the passed array size.
+         */
+        return -1;
+    }
+    while (lenleft > 0) {
+        ret = (ret << 8) | **sigp;
+        if (ret + lenleft > (size_t)(sigend - *sigp)) {
+            /* Result exceeds the length of the passed array. */
+            return -1;
+        }
+        (*sigp)++;
+        lenleft--;
+    }
+    if (ret < 128) {
+        /* Not the shortest possible length encoding. */
+        return -1;
+    }
+    return ret;
+}
+
+static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) {
+    int overflow = 0;
+    unsigned char ra[32] = {0};
+    int rlen;
+
+    if (*sig == sigend || **sig != 0x02) {
+        /* Not a primitive integer (X.690-0207 8.3.1). */
+        return 0;
+    }
+    (*sig)++;
+    rlen = secp256k1_der_read_len(sig, sigend);
+    if (rlen <= 0 || (*sig) + rlen > sigend) {
+        /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1).  */
+        return 0;
+    }
+    if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) {
+        /* Excessive 0x00 padding. */
+        return 0;
+    }
+    if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) {
+        /* Excessive 0xFF padding. */
+        return 0;
+    }
+    if ((**sig & 0x80) == 0x80) {
+        /* Negative. */
+        overflow = 1;
+    }
+    while (rlen > 0 && **sig == 0) {
+        /* Skip leading zero bytes */
+        rlen--;
+        (*sig)++;
+    }
+    if (rlen > 32) {
+        overflow = 1;
+    }
+    if (!overflow) {
+        memcpy(ra + 32 - rlen, *sig, rlen);
+        secp256k1_scalar_set_b32(r, ra, &overflow);
+    }
+    if (overflow) {
+        secp256k1_scalar_set_int(r, 0);
+    }
+    (*sig) += rlen;
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
+    const unsigned char *sigend = sig + size;
+    int rlen;
+    if (sig == sigend || *(sig++) != 0x30) {
+        /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */
+        return 0;
+    }
+    rlen = secp256k1_der_read_len(&sig, sigend);
+    if (rlen < 0 || sig + rlen > sigend) {
+        /* Tuple exceeds bounds */
+        return 0;
+    }
+    if (sig + rlen != sigend) {
+        /* Garbage after tuple. */
+        return 0;
+    }
+
+    if (!secp256k1_der_parse_integer(rr, &sig, sigend)) {
+        return 0;
+    }
+    if (!secp256k1_der_parse_integer(rs, &sig, sigend)) {
+        return 0;
+    }
+
+    if (sig != sigend) {
+        /* Trailing garbage inside tuple. */
+        return 0;
+    }
+
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
+    unsigned char r[33] = {0}, s[33] = {0};
+    unsigned char *rp = r, *sp = s;
+    size_t lenR = 33, lenS = 33;
+    secp256k1_scalar_get_b32(&r[1], ar);
+    secp256k1_scalar_get_b32(&s[1], as);
+    while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
+    while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
+    if (*size < 6+lenS+lenR) {
+        *size = 6 + lenS + lenR;
+        return 0;
+    }
+    *size = 6 + lenS + lenR;
+    sig[0] = 0x30;
+    sig[1] = 4 + lenS + lenR;
+    sig[2] = 0x02;
+    sig[3] = lenR;
+    memcpy(sig+4, rp, lenR);
+    sig[4+lenR] = 0x02;
+    sig[5+lenR] = lenS;
+    memcpy(sig+lenR+6, sp, lenS);
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
+    unsigned char c[32];
+    secp256k1_scalar sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
+    secp256k1_fe xr;
+#endif
+    secp256k1_gej pubkeyj;
+    secp256k1_gej pr;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_inverse_var(&sn, sigs);
+    secp256k1_scalar_mul(&u1, &sn, message);
+    secp256k1_scalar_mul(&u2, &sn, sigr);
+    secp256k1_gej_set_ge(&pubkeyj, pubkey);
+    secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
+    if (secp256k1_gej_is_infinity(&pr)) {
+        return 0;
+    }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+    secp256k1_scalar computed_r;
+    secp256k1_ge pr_ge;
+    secp256k1_ge_set_gej(&pr_ge, &pr);
+    secp256k1_fe_normalize(&pr_ge.x);
+
+    secp256k1_fe_get_b32(c, &pr_ge.x);
+    secp256k1_scalar_set_b32(&computed_r, c, NULL);
+    return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
+    secp256k1_scalar_get_b32(c, sigr);
+    secp256k1_fe_set_b32(&xr, c);
+
+    /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
+     *  in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
+     *  compute the remainder modulo n, and compare it to xr. However:
+     *
+     *        xr == X(pr) mod n
+     *    <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
+     *    [Since 2 * n > p, h can only be 0 or 1]
+     *    <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
+     *    [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
+     *    <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
+     *    [Multiplying both sides of the equations by pr.z^2 mod p]
+     *    <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
+     *
+     *  Thus, we can avoid the inversion, but we have to check both cases separately.
+     *  secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
+     */
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+        /* xr + n >= p, so we can skip testing the second case. */
+        return 0;
+    }
+    secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    return 0;
+#endif
+}
+
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
+    unsigned char b[32];
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    secp256k1_scalar n;
+    int overflow = 0;
+
+    secp256k1_ecmult_gen(ctx, &rp, nonce);
+    secp256k1_ge_set_gej(&r, &rp);
+    secp256k1_fe_normalize(&r.x);
+    secp256k1_fe_normalize(&r.y);
+    secp256k1_fe_get_b32(b, &r.x);
+    secp256k1_scalar_set_b32(sigr, b, &overflow);
+    /* These two conditions should be checked before calling */
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr));
+    VERIFY_CHECK(overflow == 0);
+
+    if (recid) {
+        /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
+         * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
+         */
+        *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
+    }
+    secp256k1_scalar_mul(&n, sigr, seckey);
+    secp256k1_scalar_add(&n, &n, message);
+    secp256k1_scalar_inverse(sigs, nonce);
+    secp256k1_scalar_mul(sigs, sigs, &n);
+    secp256k1_scalar_clear(&n);
+    secp256k1_gej_clear(&rp);
+    secp256k1_ge_clear(&r);
+    if (secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+    if (secp256k1_scalar_is_high(sigs)) {
+        secp256k1_scalar_negate(sigs, sigs);
+        if (recid) {
+            *recid ^= 1;
+        }
+    }
+    return 1;
+}
+
+#endif /* SECP256K1_ECDSA_IMPL_H */

src/secp256k1_tests/eckey.h

@@ -0,0 +1,25 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECKEY_H
+#define SECP256K1_ECKEY_H
+
+#include <stddef.h>
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed);
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+
+#endif /* SECP256K1_ECKEY_H */

src/secp256k1_tests/eckey_impl.h

@@ -0,0 +1,100 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECKEY_IMPL_H
+#define SECP256K1_ECKEY_IMPL_H
+
+#include "eckey.h"
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
+    if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) {
+        secp256k1_fe x;
+        return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD);
+    } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) {
+        secp256k1_fe x, y;
+        if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
+            return 0;
+        }
+        secp256k1_ge_set_xy(elem, &x, &y);
+        if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) &&
+            secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) {
+            return 0;
+        }
+        return secp256k1_ge_is_valid_var(elem);
+    } else {
+        return 0;
+    }
+}
+
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) {
+    if (secp256k1_ge_is_infinity(elem)) {
+        return 0;
+    }
+    secp256k1_fe_normalize_var(&elem->x);
+    secp256k1_fe_normalize_var(&elem->y);
+    secp256k1_fe_get_b32(&pub[1], &elem->x);
+    if (compressed) {
+        *size = 33;
+        pub[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN;
+    } else {
+        *size = 65;
+        pub[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED;
+        secp256k1_fe_get_b32(&pub[33], &elem->y);
+    }
+    return 1;
+}
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar_add(key, key, tweak);
+    if (secp256k1_scalar_is_zero(key)) {
+        return 0;
+    }
+    return 1;
+}
+
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    secp256k1_scalar one;
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_scalar_set_int(&one, 1);
+    secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
+
+    if (secp256k1_gej_is_infinity(&pt)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    if (secp256k1_scalar_is_zero(tweak)) {
+        return 0;
+    }
+
+    secp256k1_scalar_mul(key, key, tweak);
+    return 1;
+}
+
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar zero;
+    secp256k1_gej pt;
+    if (secp256k1_scalar_is_zero(tweak)) {
+        return 0;
+    }
+
+    secp256k1_scalar_set_int(&zero, 0);
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero);
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+#endif /* SECP256K1_ECKEY_IMPL_H */

src/secp256k1_tests/ecmult.h

@@ -0,0 +1,48 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_H
+#define SECP256K1_ECMULT_H
+
+#include "num.h"
+#include "group.h"
+#include "scalar.h"
+#include "scratch.h"
+
+typedef struct {
+    /* For accelerating the computation of a*P + b*G: */
+    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
+#endif
+} secp256k1_ecmult_context;
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
+
+/** Double multiply: R = na*A + ng*G */
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+
+typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data);
+
+/**
+ * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai.
+ * Chooses the right algorithm for a given number of points and scratch space
+ * size. Resets and overwrites the given scratch space. If the points do not
+ * fit in the scratch space the algorithm is repeatedly run with batches of
+ * points. If no scratch space is given then a simple algorithm is used that
+ * simply multiplies the points with the corresponding scalars and adds them up.
+ * Returns: 1 on success (including when inp_g_sc is NULL and n is 0)
+ *          0 if there is not enough scratch space for a single point or
+ *          callback returns 0
+ */
+static int secp256k1_ecmult_multi_var(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n);
+
+#endif /* SECP256K1_ECMULT_H */

src/secp256k1_tests/ecmult_const.h

@@ -0,0 +1,17 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_H
+#define SECP256K1_ECMULT_CONST_H
+
+#include "scalar.h"
+#include "group.h"
+
+/* Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
+ * one because we internally sometimes add 2 to the number during the WNAF conversion. */
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
+
+#endif /* SECP256K1_ECMULT_CONST_H */

src/secp256k1_tests/ecmult_const_impl.h

@@ -0,0 +1,257 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_IMPL_H
+#define SECP256K1_ECMULT_CONST_IMPL_H
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+    int m; \
+    int abs_n = (n) * (((n) > 0) * 2 - 1); \
+    int idx_n = abs_n / 2; \
+    secp256k1_fe neg_y; \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+    for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+        /* This loop is used to avoid secret data in array indices. See
+         * the comment in ecmult_gen_impl.h for rationale. */ \
+        secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+        secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+    } \
+    (r)->infinity = 0; \
+    secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+    secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation.
+ *  The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
+ *  It has the following guarantees:
+ *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ *  - each wnaf[i] is nonzero
+ *  - the number of words set is always WNAF_SIZE(w) + 1
+ *
+ *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {
+    int global_sign;
+    int skew = 0;
+    int word = 0;
+
+    /* 1 2 3 */
+    int u_last;
+    int u;
+
+    int flip;
+    int bit;
+    secp256k1_scalar neg_s;
+    int not_neg_one;
+    /* Note that we cannot handle even numbers by negating them to be odd, as is
+     * done in other implementations, since if our scalars were specified to have
+     * width < 256 for performance reasons, their negations would have width 256
+     * and we'd lose any performance benefit. Instead, we use a technique from
+     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+     * or 2 (for odd) to the number we are encoding, returning a skew value indicating
+     * this, and having the caller compensate after doing the multiplication.
+     *
+     * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
+     * particular, to ensure that the outputs from the endomorphism-split fit into
+     * 128 bits). If we negate, the parity of our number flips, inverting which of
+     * {1, 2} we want to add to the scalar when ensuring that it's odd. Further
+     * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and
+     * we need to special-case it in this logic. */
+    flip = secp256k1_scalar_is_high(&s);
+    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+    bit = flip ^ !secp256k1_scalar_is_even(&s);
+    /* We check for negative one, since adding 2 to it will cause an overflow */
+    secp256k1_scalar_negate(&neg_s, &s);
+    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+     * that we added two to it and flipped it. In fact for -1 these operations are
+     * identical. We only flipped, but since skewing is required (in the sense that
+     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+     * our flags to claim that we only skewed. */
+    global_sign = secp256k1_scalar_cond_negate(&s, flip);
+    global_sign *= not_neg_one * 2 - 1;
+    skew = 1 << bit;
+
+    /* 4 */
+    u_last = secp256k1_scalar_shr_int(&s, w);
+    while (word * w < size) {
+        int sign;
+        int even;
+
+        /* 4.1 4.4 */
+        u = secp256k1_scalar_shr_int(&s, w);
+        /* 4.2 */
+        even = ((u & 1) == 0);
+        sign = 2 * (u_last > 0) - 1;
+        u += sign * even;
+        u_last -= sign * even * (1 << w);
+
+        /* 4.3, adapted for global sign change */
+        wnaf[word++] = u_last * global_sign;
+
+        u_last = u;
+    }
+    wnaf[word] = u * global_sign;
+
+    VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+    VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
+    return skew;
+}
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+
+    int skew_1;
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int skew_lam;
+    secp256k1_scalar q_1, q_lam;
+#endif
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+
+    int i;
+    secp256k1_scalar sc = *scalar;
+
+    /* build wnaf representation for q. */
+    int rsize = size;
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        rsize = 128;
+        /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+        secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+        skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1, 128);
+        skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128);
+    } else
+#endif
+    {
+        skew_1   = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size);
+#ifdef USE_ENDOMORPHISM
+        skew_lam = 0;
+#endif
+    }
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_fe_normalize_weak(&pre_a[i].y);
+    }
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+            secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+        }
+    }
+#endif
+
+    /* first loop iteration (separated out so we can directly set r, rather
+     * than having it start at infinity, get doubled several times, then have
+     * its new value added to it) */
+    i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
+        VERIFY_CHECK(i != 0);
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+    }
+#endif
+    /* remaining loop iterations */
+    for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
+        int n;
+        int j;
+        for (j = 0; j < WINDOW_A - 1; ++j) {
+            secp256k1_gej_double_nonzero(r, r, NULL);
+        }
+
+        n = wnaf_1[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            n = wnaf_lam[i];
+            ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+            VERIFY_CHECK(n != 0);
+            secp256k1_gej_add_ge(r, r, &tmpa);
+        }
+#endif
+    }
+
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
+
+    {
+        /* Correct for wNAF skew */
+        secp256k1_ge correction = *a;
+        secp256k1_ge_storage correction_1_stor;
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_storage correction_lam_stor;
+#endif
+        secp256k1_ge_storage a2_stor;
+        secp256k1_gej tmpj;
+        secp256k1_gej_set_ge(&tmpj, &correction);
+        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+        secp256k1_ge_set_gej(&correction, &tmpj);
+        secp256k1_ge_to_storage(&correction_1_stor, a);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_to_storage(&correction_lam_stor, a);
+        }
+#endif
+        secp256k1_ge_to_storage(&a2_stor, &correction);
+
+        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+        }
+#endif
+
+        /* Apply the correction */
+        secp256k1_ge_from_storage(&correction, &correction_1_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+            secp256k1_ge_neg(&correction, &correction);
+            secp256k1_ge_mul_lambda(&correction, &correction);
+            secp256k1_gej_add_ge(r, r, &correction);
+        }
+#endif
+    }
+}
+
+#endif /* SECP256K1_ECMULT_CONST_IMPL_H */

src/secp256k1_tests/ecmult_gen.h

@@ -0,0 +1,43 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_H
+#define SECP256K1_ECMULT_GEN_H
+
+#include "scalar.h"
+#include "group.h"
+
+typedef struct {
+    /* For accelerating the computation of a*G:
+     * To harden against timing attacks, use the following mechanism:
+     * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
+     * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
+     *   * U_i = U * 2^i (for i=0..62)
+     *   * U_i = U * (1-2^63) (for i=63)
+     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
+     * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
+     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
+     * None of the resulting prec group elements have a known scalar, and neither do any of
+     * the intermediate sums while computing a*G.
+     */
+    secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
+    secp256k1_scalar blind;
+    secp256k1_gej initial;
+} secp256k1_ecmult_gen_context;
+
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
+
+/** Multiply with the generator: R = a*G */
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
+
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
+
+#endif /* SECP256K1_ECMULT_GEN_H */

src/secp256k1_tests/ecmult_gen_impl.h

@@ -0,0 +1,210 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_IMPL_H
+#define SECP256K1_ECMULT_GEN_IMPL_H
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_gen.h"
+#include "hash_impl.h"
+#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
+#include "ecmult_static_context.h"
+#endif
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    secp256k1_ge prec[1024];
+    secp256k1_gej gj;
+    secp256k1_gej nums_gej;
+    int i, j;
+#endif
+
+    if (ctx->prec != NULL) {
+        return;
+    }
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+
+    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
+    {
+        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
+        secp256k1_fe nums_x;
+        secp256k1_ge nums_ge;
+        int r;
+        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+        (void)r;
+        VERIFY_CHECK(r);
+        r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
+        (void)r;
+        VERIFY_CHECK(r);
+        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
+        /* Add G to make the bits in x uniformly distributed. */
+        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
+    }
+
+    /* compute prec. */
+    {
+        secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
+        secp256k1_gej gbase;
+        secp256k1_gej numsbase;
+        gbase = gj; /* 16^j * G */
+        numsbase = nums_gej; /* 2^j * nums. */
+        for (j = 0; j < 64; j++) {
+            /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
+            precj[j*16] = numsbase;
+            for (i = 1; i < 16; i++) {
+                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
+            }
+            /* Multiply gbase by 16. */
+            for (i = 0; i < 4; i++) {
+                secp256k1_gej_double_var(&gbase, &gbase, NULL);
+            }
+            /* Multiply numbase by 2. */
+            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
+            if (j == 62) {
+                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
+                secp256k1_gej_neg(&numsbase, &numsbase);
+                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
+            }
+        }
+        secp256k1_ge_set_all_gej_var(prec, precj, 1024);
+    }
+    for (j = 0; j < 64; j++) {
+        for (i = 0; i < 16; i++) {
+            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
+        }
+    }
+#else
+    (void)cb;
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
+#endif
+    secp256k1_ecmult_gen_blind(ctx, NULL);
+}
+
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
+    return ctx->prec != NULL;
+}
+
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
+    if (src->prec == NULL) {
+        dst->prec = NULL;
+    } else {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+        dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
+        memcpy(dst->prec, src->prec, sizeof(*dst->prec));
+#else
+        (void)cb;
+        dst->prec = src->prec;
+#endif
+        dst->initial = src->initial;
+        dst->blind = src->blind;
+    }
+}
+
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    free(ctx->prec);
+#endif
+    secp256k1_scalar_clear(&ctx->blind);
+    secp256k1_gej_clear(&ctx->initial);
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    secp256k1_ge add;
+    secp256k1_ge_storage adds;
+    secp256k1_scalar gnb;
+    int bits;
+    int i, j;
+    memset(&adds, 0, sizeof(adds));
+    *r = ctx->initial;
+    /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
+    secp256k1_scalar_add(&gnb, gn, &ctx->blind);
+    add.infinity = 0;
+    for (j = 0; j < 64; j++) {
+        bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
+        for (i = 0; i < 16; i++) {
+            /** This uses a conditional move to avoid any secret data in array indexes.
+             *   _Any_ use of secret indexes has been demonstrated to result in timing
+             *   sidechannels, even when the cache-line access patterns are uniform.
+             *  See also:
+             *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
+             *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
+             *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
+             *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
+             *    (http://www.tau.ac.il/~tromer/papers/cache.pdf)
+             */
+            secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
+        }
+        secp256k1_ge_from_storage(&add, &adds);
+        secp256k1_gej_add_ge(r, r, &add);
+    }
+    bits = 0;
+    secp256k1_ge_clear(&add);
+    secp256k1_scalar_clear(&gnb);
+}
+
+/* Setup blinding values for secp256k1_ecmult_gen. */
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+    secp256k1_scalar b;
+    secp256k1_gej gb;
+    secp256k1_fe s;
+    unsigned char nonce32[32];
+    secp256k1_rfc6979_hmac_sha256 rng;
+    int retry;
+    unsigned char keydata[64] = {0};
+    if (seed32 == NULL) {
+        /* When seed is NULL, reset the initial point and blinding value. */
+        secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
+        secp256k1_gej_neg(&ctx->initial, &ctx->initial);
+        secp256k1_scalar_set_int(&ctx->blind, 1);
+    }
+    /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
+    secp256k1_scalar_get_b32(nonce32, &ctx->blind);
+    /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
+     *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
+     *   asking the caller for blinding values directly and expecting them to retry on failure.
+     */
+    memcpy(keydata, nonce32, 32);
+    if (seed32 != NULL) {
+        memcpy(keydata + 32, seed32, 32);
+    }
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+    memset(keydata, 0, sizeof(keydata));
+    /* Retry for out of range results to achieve uniformity. */
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        retry = !secp256k1_fe_set_b32(&s, nonce32);
+        retry |= secp256k1_fe_is_zero(&s);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
+    /* Randomize the projection to defend against multiplier sidechannels. */
+    secp256k1_gej_rescale(&ctx->initial, &s);
+    secp256k1_fe_clear(&s);
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        secp256k1_scalar_set_b32(&b, nonce32, &retry);
+        /* A blinding value of 0 works, but would undermine the projection hardening. */
+        retry |= secp256k1_scalar_is_zero(&b);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+    memset(nonce32, 0, 32);
+    secp256k1_ecmult_gen(ctx, &gb, &b);
+    secp256k1_scalar_negate(&b, &b);
+    ctx->blind = b;
+    ctx->initial = gb;
+    secp256k1_scalar_clear(&b);
+    secp256k1_gej_clear(&gb);
+}
+
+#endif /* SECP256K1_ECMULT_GEN_IMPL_H */

src/secp256k1_tests/field.h

@@ -0,0 +1,132 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_FIELD_H
+#define SECP256K1_FIELD_H
+
+/** Field element module.
+ *
+ *  Field elements can be represented in several ways, but code accessing
+ *  it (and implementations) need to take certain properties into account:
+ *  - Each field element can be normalized or not.
+ *  - Each field element has a magnitude, which represents how far away
+ *    its representation is away from normalization. Normalized elements
+ *    always have a magnitude of 1, but a magnitude of 1 doesn't imply
+ *    normality.
+ */
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(USE_FIELD_10X26)
+#include "field_10x26.h"
+#elif defined(USE_FIELD_5X52)
+#include "field_5x52.h"
+#else
+#error "Please select field implementation"
+#endif
+
+#include "util.h"
+
+/** Normalize a field element. */
+static void secp256k1_fe_normalize(secp256k1_fe *r);
+
+/** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
+
+/** Normalize a field element, without constant-time guarantee. */
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
+
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ *  implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
+
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ *  implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
+
+/** Set a field element equal to a small integer. Resulting field element is normalized. */
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
+
+/** Sets a field element equal to zero, initializing all fields. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
+
+/** Verify whether a field element is zero. Requires the input to be normalized. */
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
+
+/** Check the "oddness" of a field element. Requires the input to be normalized. */
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
+
+/** Compare two field elements. Requires magnitude-1 inputs. */
+static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Same as secp256k1_fe_equal, but may be variable time. */
+static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Compare two field elements. Requires both inputs to be normalized */
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
+
+/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
+ *  as an argument. The magnitude of the output is one higher. */
+static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
+
+/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
+ *  small integer. */
+static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
+
+/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
+ *  The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
+
+/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
+ *  The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** If a has a square root, it is computed in r and 1 is returned. If a does not
+ *  have a square root, the root of its negation is computed and 0 is returned.
+ *  The input's magnitude can be at most 8. The output magnitude is 1 (but not
+ *  guaranteed to be normalized). The result in r will always be a square
+ *  itself. */
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Checks whether a field element is a quadratic residue. */
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a);
+
+/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
+ *  at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
+ *  at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
+ *  outputs must not overlap in memory. */
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len);
+
+/** Convert a field element to the storage type. */
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
+
+/** Convert a field element back from the storage type. */
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
+
+#endif /* SECP256K1_FIELD_H */

src/secp256k1_tests/field_5x52.h

@@ -0,0 +1,49 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_FIELD_REPR_H
+#define SECP256K1_FIELD_REPR_H
+
+#include <stdint.h>
+
+typedef struct {
+    /* X = sum(i=0..4, n[i]*2^(i*52)) mod p
+     * where p = 2^256 - 0x1000003D1
+     */
+    uint64_t n[5];
+#ifdef VERIFY
+    int magnitude;
+    int normalized;
+#endif
+} secp256k1_fe;
+
+/* Unpacks a constant into a overlapping multi-limbed FE element. */
+#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
+    (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
+    ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
+    ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
+    ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
+    ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
+}
+
+#ifdef VERIFY
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
+#else
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
+#endif
+
+typedef struct {
+    uint64_t n[4];
+} secp256k1_fe_storage;
+
+#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
+    (d0) | (((uint64_t)(d1)) << 32), \
+    (d2) | (((uint64_t)(d3)) << 32), \
+    (d4) | (((uint64_t)(d5)) << 32), \
+    (d6) | (((uint64_t)(d7)) << 32) \
+}}
+
+#endif /* SECP256K1_FIELD_REPR_H */

src/secp256k1_tests/field_5x52_impl.h

@@ -0,0 +1,496 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_FIELD_REPR_IMPL_H
+#define SECP256K1_FIELD_REPR_IMPL_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "util.h"
+#include "field.h"
+
+#if defined(USE_ASM_X86_64)
+#include "field_5x52_asm_impl.h"
+#else
+#include "field_5x52_int128_impl.h"
+#endif
+
+/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
+ *  represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
+ *  each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
+ *  is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
+ *  accept any input with magnitude at most M, and have different rules for propagating magnitude to their
+ *  output.
+ */
+
+#ifdef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
+    const uint64_t *d = a->n;
+    int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
+   /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
+    r &= (a->magnitude >= 0);
+    r &= (a->magnitude <= 2048);
+    if (a->normalized) {
+        r &= (a->magnitude <= 1);
+        if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+            r &= (d[0] < 0xFFFFEFFFFFC2FULL);
+        }
+    }
+    VERIFY_CHECK(r == 1);
+}
+#endif
+
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    /* Apply the final reduction (for constant-time behaviour, we do it always) */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+    VERIFY_CHECK(t4 >> 48 == x);
+
+    /* Mask off the possible multiple of 2^256 from the final reduction */
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    if (x) {
+        t0 += 0x1000003D1ULL;
+        t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+        t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+        t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+        t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+        /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+        VERIFY_CHECK(t4 >> 48 == x);
+
+        /* Mask off the possible multiple of 2^256 from the final reduction */
+        t4 &= 0x0FFFFFFFFFFFFULL;
+    }
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint64_t z0, z1;
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0  = t0; z1  = t0 ^ 0x1000003D0ULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
+    uint64_t t0, t1, t2, t3, t4;
+    uint64_t z0, z1;
+    uint64_t x;
+
+    t0 = r->n[0];
+    t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    x = t4 >> 48;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    z0 = t0 & 0xFFFFFFFFFFFFFULL;
+    z1 = z0 ^ 0x1000003D0ULL;
+
+    /* Fast return path should catch the majority of cases */
+    if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
+        return 0;
+    }
+
+    t1 = r->n[1];
+    t2 = r->n[2];
+    t3 = r->n[3];
+
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    t1 += (t0 >> 52);
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    r->n[0] = a;
+    r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+    const uint64_t *t = a->n;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return a->n[0] & 1;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+    int i;
+#ifdef VERIFY
+    a->magnitude = 0;
+    a->normalized = 1;
+#endif
+    for (i=0; i<5; i++) {
+        a->n[i] = 0;
+    }
+}
+
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    int i;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    VERIFY_CHECK(b->normalized);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+#endif
+    for (i = 4; i >= 0; i--) {
+        if (a->n[i] > b->n[i]) {
+            return 1;
+        }
+        if (a->n[i] < b->n[i]) {
+            return -1;
+        }
+    }
+    return 0;
+}
+
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
+    r->n[0] = (uint64_t)a[31]
+            | ((uint64_t)a[30] << 8)
+            | ((uint64_t)a[29] << 16)
+            | ((uint64_t)a[28] << 24)
+            | ((uint64_t)a[27] << 32)
+            | ((uint64_t)a[26] << 40)
+            | ((uint64_t)(a[25] & 0xF)  << 48);
+    r->n[1] = (uint64_t)((a[25] >> 4) & 0xF)
+            | ((uint64_t)a[24] << 4)
+            | ((uint64_t)a[23] << 12)
+            | ((uint64_t)a[22] << 20)
+            | ((uint64_t)a[21] << 28)
+            | ((uint64_t)a[20] << 36)
+            | ((uint64_t)a[19] << 44);
+    r->n[2] = (uint64_t)a[18]
+            | ((uint64_t)a[17] << 8)
+            | ((uint64_t)a[16] << 16)
+            | ((uint64_t)a[15] << 24)
+            | ((uint64_t)a[14] << 32)
+            | ((uint64_t)a[13] << 40)
+            | ((uint64_t)(a[12] & 0xF) << 48);
+    r->n[3] = (uint64_t)((a[12] >> 4) & 0xF)
+            | ((uint64_t)a[11] << 4)
+            | ((uint64_t)a[10] << 12)
+            | ((uint64_t)a[9]  << 20)
+            | ((uint64_t)a[8]  << 28)
+            | ((uint64_t)a[7]  << 36)
+            | ((uint64_t)a[6]  << 44);
+    r->n[4] = (uint64_t)a[5]
+            | ((uint64_t)a[4] << 8)
+            | ((uint64_t)a[3] << 16)
+            | ((uint64_t)a[2] << 24)
+            | ((uint64_t)a[1] << 32)
+            | ((uint64_t)a[0] << 40);
+    if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
+        return 0;
+    }
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+    return 1;
+}
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    r[0] = (a->n[4] >> 40) & 0xFF;
+    r[1] = (a->n[4] >> 32) & 0xFF;
+    r[2] = (a->n[4] >> 24) & 0xFF;
+    r[3] = (a->n[4] >> 16) & 0xFF;
+    r[4] = (a->n[4] >> 8) & 0xFF;
+    r[5] = a->n[4] & 0xFF;
+    r[6] = (a->n[3] >> 44) & 0xFF;
+    r[7] = (a->n[3] >> 36) & 0xFF;
+    r[8] = (a->n[3] >> 28) & 0xFF;
+    r[9] = (a->n[3] >> 20) & 0xFF;
+    r[10] = (a->n[3] >> 12) & 0xFF;
+    r[11] = (a->n[3] >> 4) & 0xFF;
+    r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4);
+    r[13] = (a->n[2] >> 40) & 0xFF;
+    r[14] = (a->n[2] >> 32) & 0xFF;
+    r[15] = (a->n[2] >> 24) & 0xFF;
+    r[16] = (a->n[2] >> 16) & 0xFF;
+    r[17] = (a->n[2] >> 8) & 0xFF;
+    r[18] = a->n[2] & 0xFF;
+    r[19] = (a->n[1] >> 44) & 0xFF;
+    r[20] = (a->n[1] >> 36) & 0xFF;
+    r[21] = (a->n[1] >> 28) & 0xFF;
+    r[22] = (a->n[1] >> 20) & 0xFF;
+    r[23] = (a->n[1] >> 12) & 0xFF;
+    r[24] = (a->n[1] >> 4) & 0xFF;
+    r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4);
+    r[26] = (a->n[0] >> 40) & 0xFF;
+    r[27] = (a->n[0] >> 32) & 0xFF;
+    r[28] = (a->n[0] >> 24) & 0xFF;
+    r[29] = (a->n[0] >> 16) & 0xFF;
+    r[30] = (a->n[0] >> 8) & 0xFF;
+    r[31] = a->n[0] & 0xFF;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= m);
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
+    r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
+    r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
+    r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
+    r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
+#ifdef VERIFY
+    r->magnitude = m + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+    r->n[0] *= a;
+    r->n[1] *= a;
+    r->n[2] *= a;
+    r->n[3] *= a;
+    r->n[4] *= a;
+#ifdef VERIFY
+    r->magnitude *= a;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] += a->n[0];
+    r->n[1] += a->n[1];
+    r->n[2] += a->n[2];
+    r->n[3] += a->n[3];
+    r->n[4] += a->n[4];
+#ifdef VERIFY
+    r->magnitude += a->magnitude;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    VERIFY_CHECK(b->magnitude <= 8);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
+#endif
+    secp256k1_fe_mul_inner(r->n, a->n, b->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    secp256k1_fe_verify(a);
+#endif
+    secp256k1_fe_sqr_inner(r->n, a->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint64_t mask0, mask1;
+    mask0 = flag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+#ifdef VERIFY
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
+    uint64_t mask0, mask1;
+    mask0 = flag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+}
+
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+#endif
+    r->n[0] = a->n[0] | a->n[1] << 52;
+    r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
+    r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
+    r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
+}
+
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
+    r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
+    r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
+    r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
+    r->n[4] = a->n[3] >> 16;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+#endif
+}
+
+#endif /* SECP256K1_FIELD_REPR_IMPL_H */

src/secp256k1_tests/field_5x52_int128_impl.h

@@ -0,0 +1,279 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H
+#define SECP256K1_FIELD_INNER5X52_IMPL_H
+
+#include <stdint.h>
+
+#ifdef VERIFY
+#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
+#else
+#define VERIFY_BITS(x, n) do { } while(0)
+#endif
+
+SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
+    uint128_t c, d;
+    uint64_t t3, t4, tx, u0;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+    VERIFY_BITS(b[0], 56);
+    VERIFY_BITS(b[1], 56);
+    VERIFY_BITS(b[2], 56);
+    VERIFY_BITS(b[3], 56);
+    VERIFY_BITS(b[4], 52);
+    VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
+
+    /*  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4)
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    d  = (uint128_t)a0 * b[3]
+       + (uint128_t)a1 * b[2]
+       + (uint128_t)a2 * b[1]
+       + (uint128_t)a3 * b[0];
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    c  = (uint128_t)a4 * b[4];
+    VERIFY_BITS(c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    d += (c & M) * R; c >>= 52;
+    VERIFY_BITS(d, 115);
+    VERIFY_BITS(c, 60);
+    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = d & M; d >>= 52;
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS(d, 63);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    d += (uint128_t)a0 * b[4]
+       + (uint128_t)a1 * b[3]
+       + (uint128_t)a2 * b[2]
+       + (uint128_t)a3 * b[1]
+       + (uint128_t)a4 * b[0];
+    VERIFY_BITS(d, 115);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    d += c * R;
+    VERIFY_BITS(d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = d & M; d >>= 52;
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS(d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    c  = (uint128_t)a0 * b[0];
+    VERIFY_BITS(c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    d += (uint128_t)a1 * b[4]
+       + (uint128_t)a2 * b[3]
+       + (uint128_t)a3 * b[2]
+       + (uint128_t)a4 * b[1];
+    VERIFY_BITS(d, 115);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = d & M; d >>= 52;
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS(d, 63);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    c += (uint128_t)u0 * (R >> 4);
+    VERIFY_BITS(c, 115);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = c & M; c >>= 52;
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS(c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    c += (uint128_t)a0 * b[1]
+       + (uint128_t)a1 * b[0];
+    VERIFY_BITS(c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    d += (uint128_t)a2 * b[4]
+       + (uint128_t)a3 * b[3]
+       + (uint128_t)a4 * b[2];
+    VERIFY_BITS(d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = c & M; c >>= 52;
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    c += (uint128_t)a0 * b[2]
+       + (uint128_t)a1 * b[1]
+       + (uint128_t)a2 * b[0];
+    VERIFY_BITS(c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint128_t)a3 * b[4]
+       + (uint128_t)a4 * b[3];
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = c & M; c >>= 52;
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += d * R + t3;
+    VERIFY_BITS(c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = c & M; c >>= 52;
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS(c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += t4;
+    VERIFY_BITS(c, 49);
+    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = c;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
+    uint128_t c, d;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    int64_t t3, t4, tx, u0;
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+
+    /**  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*a[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    d  = (uint128_t)(a0*2) * a3
+       + (uint128_t)(a1*2) * a2;
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    c  = (uint128_t)a4 * a4;
+    VERIFY_BITS(c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    d += (c & M) * R; c >>= 52;
+    VERIFY_BITS(d, 115);
+    VERIFY_BITS(c, 60);
+    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = d & M; d >>= 52;
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS(d, 63);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    a4 *= 2;
+    d += (uint128_t)a0 * a4
+       + (uint128_t)(a1*2) * a3
+       + (uint128_t)a2 * a2;
+    VERIFY_BITS(d, 115);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    d += c * R;
+    VERIFY_BITS(d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = d & M; d >>= 52;
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS(d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    c  = (uint128_t)a0 * a0;
+    VERIFY_BITS(c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    d += (uint128_t)a1 * a4
+       + (uint128_t)(a2*2) * a3;
+    VERIFY_BITS(d, 114);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = d & M; d >>= 52;
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS(d, 62);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    c += (uint128_t)u0 * (R >> 4);
+    VERIFY_BITS(c, 113);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = c & M; c >>= 52;
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS(c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    a0 *= 2;
+    c += (uint128_t)a0 * a1;
+    VERIFY_BITS(c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    d += (uint128_t)a2 * a4
+       + (uint128_t)a3 * a3;
+    VERIFY_BITS(d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = c & M; c >>= 52;
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    c += (uint128_t)a0 * a2
+       + (uint128_t)a1 * a1;
+    VERIFY_BITS(c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint128_t)a3 * a4;
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = c & M; c >>= 52;
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    c   += d * R + t3;
+    VERIFY_BITS(c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = c & M; c >>= 52;
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS(c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += t4;
+    VERIFY_BITS(c, 49);
+    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = c;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */

src/secp256k1_tests/field_impl.h

@@ -0,0 +1,318 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_FIELD_IMPL_H
+#define SECP256K1_FIELD_IMPL_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "util.h"
+#include "num.h"
+
+#if defined(USE_FIELD_10X26)
+#include "field_10x26_impl.h"
+#elif defined(USE_FIELD_5X52)
+#include "field_5x52_impl.h"
+#else
+#error "Please select field implementation"
+#endif
+
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero(&na);
+}
+
+SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero_var(&na);
+}
+
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
+    /** Given that p is congruent to 3 mod 4, we can compute the square root of
+     *  a mod p as the (p+1)/4'th power of a.
+     *
+     *  As (p+1)/4 is an even number, it will have the same result for a and for
+     *  (-a). Only one of these two numbers actually has a square root however,
+     *  so we test at the end by squaring and comparing to the input.
+     *  Also because (p+1)/4 is an even number, the computed square root is
+     *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
+     */
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+    int j;
+
+    VERIFY_CHECK(r != a);
+
+    /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
+     *  { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+     *  1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+     */
+
+    secp256k1_fe_sqr(&x2, a);
+    secp256k1_fe_mul(&x2, &x2, a);
+
+    secp256k1_fe_sqr(&x3, &x2);
+    secp256k1_fe_mul(&x3, &x3, a);
+
+    x6 = x3;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x6, &x6);
+    }
+    secp256k1_fe_mul(&x6, &x6, &x3);
+
+    x9 = x6;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x9, &x9);
+    }
+    secp256k1_fe_mul(&x9, &x9, &x3);
+
+    x11 = x9;
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&x11, &x11);
+    }
+    secp256k1_fe_mul(&x11, &x11, &x2);
+
+    x22 = x11;
+    for (j=0; j<11; j++) {
+        secp256k1_fe_sqr(&x22, &x22);
+    }
+    secp256k1_fe_mul(&x22, &x22, &x11);
+
+    x44 = x22;
+    for (j=0; j<22; j++) {
+        secp256k1_fe_sqr(&x44, &x44);
+    }
+    secp256k1_fe_mul(&x44, &x44, &x22);
+
+    x88 = x44;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x88, &x88);
+    }
+    secp256k1_fe_mul(&x88, &x88, &x44);
+
+    x176 = x88;
+    for (j=0; j<88; j++) {
+        secp256k1_fe_sqr(&x176, &x176);
+    }
+    secp256k1_fe_mul(&x176, &x176, &x88);
+
+    x220 = x176;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x220, &x220);
+    }
+    secp256k1_fe_mul(&x220, &x220, &x44);
+
+    x223 = x220;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x223, &x223);
+    }
+    secp256k1_fe_mul(&x223, &x223, &x3);
+
+    /* The final result is then assembled using a sliding window over the blocks. */
+
+    t1 = x223;
+    for (j=0; j<23; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x22);
+    for (j=0; j<6; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x2);
+    secp256k1_fe_sqr(&t1, &t1);
+    secp256k1_fe_sqr(r, &t1);
+
+    /* Check that a square root was actually calculated */
+
+    secp256k1_fe_sqr(&t1, r);
+    return secp256k1_fe_equal(&t1, a);
+}
+
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+    int j;
+
+    /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
+     *  { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+     *  [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+     */
+
+    secp256k1_fe_sqr(&x2, a);
+    secp256k1_fe_mul(&x2, &x2, a);
+
+    secp256k1_fe_sqr(&x3, &x2);
+    secp256k1_fe_mul(&x3, &x3, a);
+
+    x6 = x3;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x6, &x6);
+    }
+    secp256k1_fe_mul(&x6, &x6, &x3);
+
+    x9 = x6;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x9, &x9);
+    }
+    secp256k1_fe_mul(&x9, &x9, &x3);
+
+    x11 = x9;
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&x11, &x11);
+    }
+    secp256k1_fe_mul(&x11, &x11, &x2);
+
+    x22 = x11;
+    for (j=0; j<11; j++) {
+        secp256k1_fe_sqr(&x22, &x22);
+    }
+    secp256k1_fe_mul(&x22, &x22, &x11);
+
+    x44 = x22;
+    for (j=0; j<22; j++) {
+        secp256k1_fe_sqr(&x44, &x44);
+    }
+    secp256k1_fe_mul(&x44, &x44, &x22);
+
+    x88 = x44;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x88, &x88);
+    }
+    secp256k1_fe_mul(&x88, &x88, &x44);
+
+    x176 = x88;
+    for (j=0; j<88; j++) {
+        secp256k1_fe_sqr(&x176, &x176);
+    }
+    secp256k1_fe_mul(&x176, &x176, &x88);
+
+    x220 = x176;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x220, &x220);
+    }
+    secp256k1_fe_mul(&x220, &x220, &x44);
+
+    x223 = x220;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x223, &x223);
+    }
+    secp256k1_fe_mul(&x223, &x223, &x3);
+
+    /* The final result is then assembled using a sliding window over the blocks. */
+
+    t1 = x223;
+    for (j=0; j<23; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x22);
+    for (j=0; j<5; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, a);
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x2);
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(r, a, &t1);
+}
+
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
+#if defined(USE_FIELD_INV_BUILTIN)
+    secp256k1_fe_inv(r, a);
+#elif defined(USE_FIELD_INV_NUM)
+    secp256k1_num n, m;
+    static const secp256k1_fe negone = SECP256K1_FE_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
+    );
+    /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    static const unsigned char prime[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+    };
+    unsigned char b[32];
+    int res;
+    secp256k1_fe c = *a;
+    secp256k1_fe_normalize_var(&c);
+    secp256k1_fe_get_b32(b, &c);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_num_set_bin(&m, prime, 32);
+    secp256k1_num_mod_inverse(&n, &n, &m);
+    secp256k1_num_get_bin(b, 32, &n);
+    res = secp256k1_fe_set_b32(r, b);
+    (void)res;
+    VERIFY_CHECK(res);
+    /* Verify the result is the (unique) valid inverse using non-GMP code. */
+    secp256k1_fe_mul(&c, &c, r);
+    secp256k1_fe_add(&c, &negone);
+    CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
+#else
+#error "Please select field inverse implementation"
+#endif
+}
+
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
+    secp256k1_fe u;
+    size_t i;
+    if (len < 1) {
+        return;
+    }
+
+    VERIFY_CHECK((r + len <= a) || (a + len <= r));
+
+    r[0] = a[0];
+
+    i = 0;
+    while (++i < len) {
+        secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]);
+    }
+
+    secp256k1_fe_inv_var(&u, &r[--i]);
+
+    while (i > 0) {
+        size_t j = i--;
+        secp256k1_fe_mul(&r[j], &r[i], &u);
+        secp256k1_fe_mul(&u, &u, &a[j]);
+    }
+
+    r[0] = u;
+}
+
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
+#ifndef USE_NUM_NONE
+    unsigned char b[32];
+    secp256k1_num n;
+    secp256k1_num m;
+    /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    static const unsigned char prime[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+    };
+
+    secp256k1_fe c = *a;
+    secp256k1_fe_normalize_var(&c);
+    secp256k1_fe_get_b32(b, &c);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_num_set_bin(&m, prime, 32);
+    return secp256k1_num_jacobi(&n, &m) >= 0;
+#else
+    secp256k1_fe r;
+    return secp256k1_fe_sqrt(&r, a);
+#endif
+}
+
+#endif /* SECP256K1_FIELD_IMPL_H */

src/secp256k1_tests/group.h

@@ -0,0 +1,142 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_GROUP_H
+#define SECP256K1_GROUP_H
+
+#include "num.h"
+#include "field.h"
+
+/** A group element of the secp256k1 curve, in affine coordinates. */
+typedef struct {
+    secp256k1_fe x;
+    secp256k1_fe y;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_ge;
+
+#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
+#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+/** A group element of the secp256k1 curve, in jacobian coordinates. */
+typedef struct {
+    secp256k1_fe x; /* actual X: x/z^2 */
+    secp256k1_fe y; /* actual Y: y/z^3 */
+    secp256k1_fe z;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_gej;
+
+#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
+#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+typedef struct {
+    secp256k1_fe_storage x;
+    secp256k1_fe_storage y;
+} secp256k1_ge_storage;
+
+#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
+
+#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
+
+/** Set a group element equal to the point with given X and Y coordinates */
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (affine) equal to the point with the given X coordinate
+ *  and a Y coordinate that is a quadratic residue modulo p. The return value
+ *  is true iff a coordinate with the given X coordinate exists.
+ */
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x);
+
+/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
+ *  for Y. Return value indicates whether the result is valid. */
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
+
+/** Check whether a group element is valid (i.e., on the curve). */
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates */
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
+
+/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len);
+
+/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
+ *  the same global z "denominator". zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
+ *  coordinates of the result are stored in r, the common z coordinate is
+ *  stored in globalz. */
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
+
+/** Set a group element (affine) equal to the point at infinity. */
+static void secp256k1_ge_set_infinity(secp256k1_ge *r);
+
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej *r);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
+
+/** Compare the X coordinate of a group element (jacobian). */
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
+
+/** Check whether a group element's y coordinate is a quadratic residue. */
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
+ * a may not be zero. Constant time. */
+static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
+    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
+    guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
+
+#ifdef USE_ENDOMORPHISM
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
+#endif
+
+/** Clear a secp256k1_gej to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej *r);
+
+/** Clear a secp256k1_ge to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge *r);
+
+/** Convert a group element to the storage type. */
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
+
+/** Convert a group element back from the storage type. */
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
+
+/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
+
+#endif /* SECP256K1_GROUP_H */

src/secp256k1_tests/group_impl.h

@@ -0,0 +1,705 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_GROUP_IMPL_H
+#define SECP256K1_GROUP_IMPL_H
+
+#include "num.h"
+#include "field.h"
+#include "group.h"
+
+/* These points can be generated in sage as follows:
+ *
+ * 0. Setup a worksheet with the following parameters.
+ *   b = 4  # whatever CURVE_B will be set to
+ *   F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+ *   C = EllipticCurve ([F (0), F (b)])
+ *
+ * 1. Determine all the small orders available to you. (If there are
+ *    no satisfactory ones, go back and change b.)
+ *   print C.order().factor(limit=1000)
+ *
+ * 2. Choose an order as one of the prime factors listed in the above step.
+ *    (You can also multiply some to get a composite order, though the
+ *    tests will crash trying to invert scalars during signing.) We take a
+ *    random point and scale it to drop its order to the desired value.
+ *    There is some probability this won't work; just try again.
+ *   order = 199
+ *   P = C.random_point()
+ *   P = (int(P.order()) / int(order)) * P
+ *   assert(P.order() == order)
+ *
+ * 3. Print the values. You'll need to use a vim macro or something to
+ *    split the hex output into 4-byte chunks.
+ *   print "%x %x" % P.xy()
+ */
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#  if EXHAUSTIVE_TEST_ORDER == 199
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
+    0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
+    0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
+    0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
+);
+
+static const int CURVE_B = 4;
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
+    0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
+    0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
+    0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
+);
+static const int CURVE_B = 2;
+#  else
+#    error No known generator for the specified exhaustive test group order.
+#  endif
+#else
+/** Generator for secp256k1, value 'g' defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ */
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
+    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
+    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
+    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
+);
+
+static const int CURVE_B = 7;
+#endif
+
+static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
+    secp256k1_fe zi2;
+    secp256k1_fe zi3;
+    secp256k1_fe_sqr(&zi2, zi);
+    secp256k1_fe_mul(&zi3, &zi2, zi);
+    secp256k1_fe_mul(&r->x, &a->x, &zi2);
+    secp256k1_fe_mul(&r->y, &a->y, &zi3);
+    r->infinity = a->infinity;
+}
+
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
+    r->infinity = 0;
+    r->x = *x;
+    r->y = *y;
+}
+
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
+    return a->infinity;
+}
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
+    *r = *a;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    secp256k1_fe_inv(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    if (a->infinity) {
+        return;
+    }
+    secp256k1_fe_inv_var(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) {
+    secp256k1_fe u;
+    size_t i;
+    size_t last_i = SIZE_MAX;
+
+    for (i = 0; i < len; i++) {
+        if (!a[i].infinity) {
+            /* Use destination's x coordinates as scratch space */
+            if (last_i == SIZE_MAX) {
+                r[i].x = a[i].z;
+            } else {
+                secp256k1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z);
+            }
+            last_i = i;
+        }
+    }
+    if (last_i == SIZE_MAX) {
+        return;
+    }
+    secp256k1_fe_inv_var(&u, &r[last_i].x);
+
+    i = last_i;
+    while (i > 0) {
+        i--;
+        if (!a[i].infinity) {
+            secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u);
+            secp256k1_fe_mul(&u, &u, &a[last_i].z);
+            last_i = i;
+        }
+    }
+    VERIFY_CHECK(!a[last_i].infinity);
+    r[last_i].x = u;
+
+    for (i = 0; i < len; i++) {
+        r[i].infinity = a[i].infinity;
+        if (!a[i].infinity) {
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x);
+        }
+    }
+}
+
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zs;
+
+    if (len > 0) {
+        /* The z of the final point gives us the "global Z" for the table. */
+        r[i].x = a[i].x;
+        r[i].y = a[i].y;
+        /* Ensure all y values are in weak normal form for fast negation of points */
+        secp256k1_fe_normalize_weak(&r[i].y);
+        *globalz = a[i].z;
+        r[i].infinity = 0;
+        zs = zr[i];
+
+        /* Work our way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            if (i != len - 1) {
+                secp256k1_fe_mul(&zs, &zs, &zr[i]);
+            }
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
+        }
+    }
+}
+
+static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
+    r->infinity = 1;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
+    r->infinity = 1;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+}
+
+static void secp256k1_gej_clear(secp256k1_gej *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_clear(secp256k1_ge *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+}
+
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
+    secp256k1_fe x2, x3, c;
+    r->x = *x;
+    secp256k1_fe_sqr(&x2, x);
+    secp256k1_fe_mul(&x3, x, &x2);
+    r->infinity = 0;
+    secp256k1_fe_set_int(&c, CURVE_B);
+    secp256k1_fe_add(&c, &x3);
+    return secp256k1_fe_sqrt(&r->y, &c);
+}
+
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
+    if (!secp256k1_ge_set_xquad(r, x)) {
+        return 0;
+    }
+    secp256k1_fe_normalize_var(&r->y);
+    if (secp256k1_fe_is_odd(&r->y) != odd) {
+        secp256k1_fe_negate(&r->y, &r->y, 1);
+    }
+    return 1;
+
+}
+
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
+   r->infinity = a->infinity;
+   r->x = a->x;
+   r->y = a->y;
+   secp256k1_fe_set_int(&r->z, 1);
+}
+
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
+    secp256k1_fe r, r2;
+    VERIFY_CHECK(!a->infinity);
+    secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
+    r2 = a->x; secp256k1_fe_normalize_weak(&r2);
+    return secp256k1_fe_equal_var(&r, &r2);
+}
+
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
+    r->infinity = a->infinity;
+    r->x = a->x;
+    r->y = a->y;
+    r->z = a->z;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
+    return a->infinity;
+}
+
+static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
+    secp256k1_fe y2, x3, z2, z6;
+    if (a->infinity) {
+        return 0;
+    }
+    /** y^2 = x^3 + 7
+     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
+     *  Y^2 / Z^6 = X^3 / Z^6 + 7
+     *  Y^2 = X^3 + 7*Z^6
+     */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
+    secp256k1_fe_mul_int(&z6, CURVE_B);
+    secp256k1_fe_add(&x3, &z6);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
+    secp256k1_fe y2, x3, c;
+    if (a->infinity) {
+        return 0;
+    }
+    /* y^2 = x^3 + 7 */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_set_int(&c, CURVE_B);
+    secp256k1_fe_add(&x3, &c);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
+     *
+     * Note that there is an implementation described at
+     *     https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+     * which trades a multiply for a square, but in practice this is actually slower,
+     * mainly because it requires more normalizations.
+     */
+    secp256k1_fe t1,t2,t3,t4;
+    /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
+     *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
+     *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
+     *
+     *  Having said this, if this function receives a point on a sextic twist, e.g. by
+     *  a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
+     *  since -6 does have a cube root mod p. For this point, this function will not set
+     *  the infinity flag even though the point doubles to infinity, and the result
+     *  point will be gibberish (z = 0 but infinity = 0).
+     */
+    r->infinity = a->infinity;
+    if (r->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        return;
+    }
+
+    if (rzr != NULL) {
+        *rzr = a->y;
+        secp256k1_fe_normalize_weak(rzr);
+        secp256k1_fe_mul_int(rzr, 2);
+    }
+
+    secp256k1_fe_mul(&r->z, &a->z, &a->y);
+    secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
+    secp256k1_fe_sqr(&t1, &a->x);
+    secp256k1_fe_mul_int(&t1, 3);         /* T1 = 3*X^2 (3) */
+    secp256k1_fe_sqr(&t2, &t1);           /* T2 = 9*X^4 (1) */
+    secp256k1_fe_sqr(&t3, &a->y);
+    secp256k1_fe_mul_int(&t3, 2);         /* T3 = 2*Y^2 (2) */
+    secp256k1_fe_sqr(&t4, &t3);
+    secp256k1_fe_mul_int(&t4, 2);         /* T4 = 8*Y^4 (2) */
+    secp256k1_fe_mul(&t3, &t3, &a->x);    /* T3 = 2*X*Y^2 (1) */
+    r->x = t3;
+    secp256k1_fe_mul_int(&r->x, 4);       /* X' = 8*X*Y^2 (4) */
+    secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
+    secp256k1_fe_add(&r->x, &t2);         /* X' = 9*X^4 - 8*X*Y^2 (6) */
+    secp256k1_fe_negate(&t2, &t2, 1);     /* T2 = -9*X^4 (2) */
+    secp256k1_fe_mul_int(&t3, 6);         /* T3 = 12*X*Y^2 (6) */
+    secp256k1_fe_add(&t3, &t2);           /* T3 = 12*X*Y^2 - 9*X^4 (8) */
+    secp256k1_fe_mul(&r->y, &t1, &t3);    /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
+    secp256k1_fe_negate(&t2, &t4, 2);     /* T2 = -8*Y^4 (3) */
+    secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
+}
+
+static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
+    secp256k1_gej_double_var(r, a, rzr);
+}
+
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
+    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        *r = *b;
+        return;
+    }
+
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+
+    r->infinity = 0;
+    secp256k1_fe_sqr(&z22, &b->z);
+    secp256k1_fe_sqr(&z12, &a->z);
+    secp256k1_fe_mul(&u1, &a->x, &z22);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    secp256k1_fe_mul(&h, &h, &b->z);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
+    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        secp256k1_gej_set_ge(r, b);
+        return;
+    }
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+    r->infinity = 0;
+
+    secp256k1_fe_sqr(&z12, &a->z);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
+    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
+    if (a->infinity) {
+        secp256k1_fe bzinv2, bzinv3;
+        r->infinity = b->infinity;
+        secp256k1_fe_sqr(&bzinv2, bzinv);
+        secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
+        secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
+        secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
+        secp256k1_fe_set_int(&r->z, 1);
+        return;
+    }
+    r->infinity = 0;
+
+    /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
+     *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
+     *  by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
+     *  This means that (rx,ry,rz) can be calculated as
+     *  (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
+     *  The variable az below holds the modified Z coordinate for a, which is used
+     *  for the computation of rx and ry, but not for rz.
+     */
+    secp256k1_fe_mul(&az, &a->z, bzinv);
+
+    secp256k1_fe_sqr(&z12, &az);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, NULL);
+        } else {
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
+    /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
+    static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
+    secp256k1_fe m_alt, rr_alt;
+    int infinity, degenerate;
+    VERIFY_CHECK(!b->infinity);
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+
+    /** In:
+     *    Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
+     *    In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
+     *  we find as solution for a unified addition/doubling formula:
+     *    lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
+     *    x3 = lambda^2 - (x1 + x2)
+     *    2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
+     *
+     *  Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
+     *    U1 = X1*Z2^2, U2 = X2*Z1^2
+     *    S1 = Y1*Z2^3, S2 = Y2*Z1^3
+     *    Z = Z1*Z2
+     *    T = U1+U2
+     *    M = S1+S2
+     *    Q = T*M^2
+     *    R = T^2-U1*U2
+     *    X3 = 4*(R^2-Q)
+     *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
+     *    Z3 = 2*M*Z
+     *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
+     *
+     *  This formula has the benefit of being the same for both addition
+     *  of distinct points and doubling. However, it breaks down in the
+     *  case that either point is infinity, or that y1 = -y2. We handle
+     *  these cases in the following ways:
+     *
+     *    - If b is infinity we simply bail by means of a VERIFY_CHECK.
+     *
+     *    - If a is infinity, we detect this, and at the end of the
+     *      computation replace the result (which will be meaningless,
+     *      but we compute to be constant-time) with b.x : b.y : 1.
+     *
+     *    - If a = -b, we have y1 = -y2, which is a degenerate case.
+     *      But here the answer is infinity, so we simply set the
+     *      infinity flag of the result, overriding the computed values
+     *      without even needing to cmov.
+     *
+     *    - If y1 = -y2 but x1 != x2, which does occur thanks to certain
+     *      properties of our curve (specifically, 1 has nontrivial cube
+     *      roots in our field, and the curve equation has no x coefficient)
+     *      then the answer is not infinity but also not given by the above
+     *      equation. In this case, we cmov in place an alternate expression
+     *      for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
+     *      expressions for lambda are defined, they are equal, and can be
+     *      obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
+     *      then substitution of x^3 + 7 for y^2 (using the curve equation).
+     *      For all pairs of nonzero points (a, b) at least one is defined,
+     *      so this covers everything.
+     */
+
+    secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
+    secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
+    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z1^2 (1) */
+    secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
+    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
+    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
+    secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
+    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 */
+    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (2) */
+    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (3) */
+    /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
+     *  case that Z = z1z2 = 0, and this is special-cased later on). */
+    degenerate = secp256k1_fe_normalizes_to_zero(&m) &
+                 secp256k1_fe_normalizes_to_zero(&rr);
+    /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
+     * This means either x1 == beta*x2 or beta*x1 == x2, where beta is
+     * a nontrivial cube root of one. In either case, an alternate
+     * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
+     * so we set R/M equal to this. */
+    rr_alt = s1;
+    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
+    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 */
+
+    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
+    secp256k1_fe_cmov(&m_alt, &m, !degenerate);
+    /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
+     * From here on out Ralt and Malt represent the numerator
+     * and denominator of lambda; R and M represent the explicit
+     * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
+    secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
+    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*Malt^2 (1) */
+    /* These two lines use the observation that either M == Malt or M == 0,
+     * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
+     * zero (which is "computed" by cmov). So the cost is one squaring
+     * versus two multiplications. */
+    secp256k1_fe_sqr(&n, &n);
+    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
+    secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
+    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Malt*Z (1) */
+    infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
+    secp256k1_fe_mul_int(&r->z, 2);                     /* r->z = Z3 = 2*Malt*Z (2) */
+    secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2-Q (3) */
+    secp256k1_fe_normalize_weak(&t);
+    r->x = t;                                           /* r->x = Ralt^2-Q (1) */
+    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*x3 (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = 2*x3 - Q: (4) */
+    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*x3 - Q) (1) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
+    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_mul_int(&r->x, 4);                     /* r->x = X3 = 4*(Ralt^2-Q) */
+    secp256k1_fe_mul_int(&r->y, 4);                     /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
+
+    /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
+    secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
+    secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
+    secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
+    r->infinity = infinity;
+}
+
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
+    /* Operations: 4 mul, 1 sqr */
+    secp256k1_fe zz;
+    VERIFY_CHECK(!secp256k1_fe_is_zero(s));
+    secp256k1_fe_sqr(&zz, s);
+    secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
+    secp256k1_fe_mul(&r->y, &r->y, &zz);
+    secp256k1_fe_mul(&r->y, &r->y, s);                  /* r->y *= s^3 */
+    secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
+}
+
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
+    secp256k1_fe x, y;
+    VERIFY_CHECK(!a->infinity);
+    x = a->x;
+    secp256k1_fe_normalize(&x);
+    y = a->y;
+    secp256k1_fe_normalize(&y);
+    secp256k1_fe_to_storage(&r->x, &x);
+    secp256k1_fe_to_storage(&r->y, &y);
+}
+
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
+    secp256k1_fe_from_storage(&r->x, &a->x);
+    secp256k1_fe_from_storage(&r->y, &a->y);
+    r->infinity = 0;
+}
+
+static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
+    secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
+    secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
+    static const secp256k1_fe beta = SECP256K1_FE_CONST(
+        0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
+        0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
+    );
+    *r = *a;
+    secp256k1_fe_mul(&r->x, &r->x, &beta);
+}
+#endif
+
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
+    secp256k1_fe yz;
+
+    if (a->infinity) {
+        return 0;
+    }
+
+    /* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as
+     * that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z
+       is */
+    secp256k1_fe_mul(&yz, &a->y, &a->z);
+    return secp256k1_fe_is_quad_var(&yz);
+}
+
+#endif /* SECP256K1_GROUP_IMPL_H */

src/secp256k1_tests/hash.h

@@ -0,0 +1,41 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_HASH_H
+#define SECP256K1_HASH_H
+
+#include <stdlib.h>
+#include <stdint.h>
+
+typedef struct {
+    uint32_t s[8];
+    uint32_t buf[16]; /* In big endian */
+    size_t bytes;
+} secp256k1_sha256;
+
+static void secp256k1_sha256_initialize(secp256k1_sha256 *hash);
+static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32);
+
+typedef struct {
+    secp256k1_sha256 inner, outer;
+} secp256k1_hmac_sha256;
+
+static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size);
+static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32);
+
+typedef struct {
+    unsigned char v[32];
+    unsigned char k[32];
+    int retry;
+} secp256k1_rfc6979_hmac_sha256;
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen);
+static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen);
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng);
+
+#endif /* SECP256K1_HASH_H */

src/secp256k1_tests/hash_impl.h

@@ -0,0 +1,282 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_HASH_IMPL_H
+#define SECP256K1_HASH_IMPL_H
+
+#include "hash.h"
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+
+#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z))))
+#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y))))
+#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10))
+#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7))
+#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3))
+#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10))
+
+#define Round(a,b,c,d,e,f,g,h,k,w) do { \
+    uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \
+    uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \
+    (d) += t1; \
+    (h) = t1 + t2; \
+} while(0)
+
+#ifdef WORDS_BIGENDIAN
+#define BE32(x) (x)
+#else
+#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
+#endif
+
+static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) {
+    hash->s[0] = 0x6a09e667ul;
+    hash->s[1] = 0xbb67ae85ul;
+    hash->s[2] = 0x3c6ef372ul;
+    hash->s[3] = 0xa54ff53aul;
+    hash->s[4] = 0x510e527ful;
+    hash->s[5] = 0x9b05688cul;
+    hash->s[6] = 0x1f83d9abul;
+    hash->s[7] = 0x5be0cd19ul;
+    hash->bytes = 0;
+}
+
+/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
+static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) {
+    uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
+    uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
+
+    Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0]));
+    Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1]));
+    Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2]));
+    Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3]));
+    Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4]));
+    Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5]));
+    Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6]));
+    Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7]));
+    Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8]));
+    Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9]));
+    Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10]));
+    Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11]));
+    Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12]));
+    Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13]));
+    Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14]));
+    Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15]));
+
+    Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0));
+
+    s[0] += a;
+    s[1] += b;
+    s[2] += c;
+    s[3] += d;
+    s[4] += e;
+    s[5] += f;
+    s[6] += g;
+    s[7] += h;
+}
+
+static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t len) {
+    size_t bufsize = hash->bytes & 0x3F;
+    hash->bytes += len;
+    while (bufsize + len >= 64) {
+        /* Fill the buffer, and process it. */
+        size_t chunk_len = 64 - bufsize;
+        memcpy(((unsigned char*)hash->buf) + bufsize, data, chunk_len);
+        data += chunk_len;
+        len -= chunk_len;
+        secp256k1_sha256_transform(hash->s, hash->buf);
+        bufsize = 0;
+    }
+    if (len) {
+        /* Fill the buffer with what remains. */
+        memcpy(((unsigned char*)hash->buf) + bufsize, data, len);
+    }
+}
+
+static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) {
+    static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
+    uint32_t sizedesc[2];
+    uint32_t out[8];
+    int i = 0;
+    sizedesc[0] = BE32(hash->bytes >> 29);
+    sizedesc[1] = BE32(hash->bytes << 3);
+    secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
+    secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8);
+    for (i = 0; i < 8; i++) {
+        out[i] = BE32(hash->s[i]);
+        hash->s[i] = 0;
+    }
+    memcpy(out32, (const unsigned char*)out, 32);
+}
+
+static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) {
+    size_t n;
+    unsigned char rkey[64];
+    if (keylen <= sizeof(rkey)) {
+        memcpy(rkey, key, keylen);
+        memset(rkey + keylen, 0, sizeof(rkey) - keylen);
+    } else {
+        secp256k1_sha256 sha256;
+        secp256k1_sha256_initialize(&sha256);
+        secp256k1_sha256_write(&sha256, key, keylen);
+        secp256k1_sha256_finalize(&sha256, rkey);
+        memset(rkey + 32, 0, 32);
+    }
+
+    secp256k1_sha256_initialize(&hash->outer);
+    for (n = 0; n < sizeof(rkey); n++) {
+        rkey[n] ^= 0x5c;
+    }
+    secp256k1_sha256_write(&hash->outer, rkey, sizeof(rkey));
+
+    secp256k1_sha256_initialize(&hash->inner);
+    for (n = 0; n < sizeof(rkey); n++) {
+        rkey[n] ^= 0x5c ^ 0x36;
+    }
+    secp256k1_sha256_write(&hash->inner, rkey, sizeof(rkey));
+    memset(rkey, 0, sizeof(rkey));
+}
+
+static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) {
+    secp256k1_sha256_write(&hash->inner, data, size);
+}
+
+static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32) {
+    unsigned char temp[32];
+    secp256k1_sha256_finalize(&hash->inner, temp);
+    secp256k1_sha256_write(&hash->outer, temp, 32);
+    memset(temp, 0, 32);
+    secp256k1_sha256_finalize(&hash->outer, out32);
+}
+
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) {
+    secp256k1_hmac_sha256 hmac;
+    static const unsigned char zero[1] = {0x00};
+    static const unsigned char one[1] = {0x01};
+
+    memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */
+    memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
+
+    /* RFC6979 3.2.d. */
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(&hmac, zero, 1);
+    secp256k1_hmac_sha256_write(&hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+
+    /* RFC6979 3.2.f. */
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(&hmac, one, 1);
+    secp256k1_hmac_sha256_write(&hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    rng->retry = 0;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) {
+    /* RFC6979 3.2.h. */
+    static const unsigned char zero[1] = {0x00};
+    if (rng->retry) {
+        secp256k1_hmac_sha256 hmac;
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_write(&hmac, zero, 1);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    }
+
+    while (outlen > 0) {
+        secp256k1_hmac_sha256 hmac;
+        int now = outlen;
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+        if (now > 32) {
+            now = 32;
+        }
+        memcpy(out, rng->v, now);
+        out += now;
+        outlen -= now;
+    }
+
+    rng->retry = 1;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng) {
+    memset(rng->k, 0, 32);
+    memset(rng->v, 0, 32);
+    rng->retry = 0;
+}
+
+#undef BE32
+#undef Round
+#undef sigma1
+#undef sigma0
+#undef Sigma1
+#undef Sigma0
+#undef Maj
+#undef Ch
+
+#endif /* SECP256K1_HASH_IMPL_H */

src/secp256k1_tests/include/secp256k1.h

@@ -0,0 +1,666 @@
+#ifndef SECP256K1_H
+#define SECP256K1_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stddef.h>
+
+/* These rules specify the order of arguments in API calls:
+ *
+ * 1. Context pointers go first, followed by output arguments, combined
+ *    output/input arguments, and finally input-only arguments.
+ * 2. Array lengths always immediately the follow the argument whose length
+ *    they describe, even if this violates rule 1.
+ * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated
+ *    later go first. This means: signatures, public nonces, private nonces,
+ *    messages, public keys, secret keys, tweaks.
+ * 4. Arguments that are not data pointers go last, from more complex to less
+ *    complex: function pointers, algorithm names, messages, void pointers,
+ *    counts, flags, booleans.
+ * 5. Opaque data pointers follow the function pointer they are to be passed to.
+ */
+
+/** Opaque data structure that holds context information (precomputed tables etc.).
+ *
+ *  The purpose of context structures is to cache large precomputed data tables
+ *  that are expensive to construct, and also to maintain the randomization data
+ *  for blinding.
+ *
+ *  Do not create a new context object for each operation, as construction is
+ *  far slower than all other API calls (~100 times slower than an ECDSA
+ *  verification).
+ *
+ *  A constructed context can safely be used from multiple threads
+ *  simultaneously, but API call that take a non-const pointer to a context
+ *  need exclusive access to it. In particular this is the case for
+ *  secp256k1_context_destroy and secp256k1_context_randomize.
+ *
+ *  Regarding randomization, either do it once at creation time (in which case
+ *  you do not need any locking for the other calls), or use a read-write lock.
+ */
+typedef struct secp256k1_context_struct secp256k1_context;
+
+/** Opaque data structure that holds rewriteable "scratch space"
+ *
+ *  The purpose of this structure is to replace dynamic memory allocations,
+ *  because we target architectures where this may not be available. It is
+ *  essentially a resizable (within specified parameters) block of bytes,
+ *  which is initially created either by memory allocation or TODO as a pointer
+ *  into some fixed rewritable space.
+ *
+ *  Unlike the context object, this cannot safely be shared between threads
+ *  without additional synchronization logic.
+ */
+typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space;
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_pubkey;
+
+/** Opaque data structured that holds a parsed ECDSA signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_ecdsa_signature;
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
+ * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
+ * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
+ *          key32:     pointer to a 32-byte secret key (will not be NULL)
+ *          algo16:    pointer to a 16-byte array describing the signature
+ *                     algorithm (will be NULL for ECDSA for compatibility).
+ *          data:      Arbitrary data pointer that is passed through.
+ *          attempt:   how many iterations we have tried to find a nonce.
+ *                     This will almost always be 0, but different attempt values
+ *                     are required to result in a different nonce.
+ *
+ * Except for test cases, this function should compute some cryptographic hash of
+ * the message, the algorithm, the key and the attempt.
+ */
+typedef int (*secp256k1_nonce_function)(
+    unsigned char *nonce32,
+    const unsigned char *msg32,
+    const unsigned char *key32,
+    const unsigned char *algo16,
+    void *data,
+    unsigned int attempt
+);
+
+# if !defined(SECP256K1_GNUC_PREREQ)
+#  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) \
+ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
+#  else
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) 0
+#  endif
+# endif
+
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(2,7)
+#   define SECP256K1_INLINE __inline__
+#  elif (defined(_MSC_VER))
+#   define SECP256K1_INLINE __inline
+#  else
+#   define SECP256K1_INLINE
+#  endif
+# else
+#  define SECP256K1_INLINE inline
+# endif
+
+#ifndef SECP256K1_API
+# if defined(_WIN32)
+#  ifdef SECP256K1_BUILD
+#   define SECP256K1_API __declspec(dllexport)
+#  else
+#   define SECP256K1_API
+#  endif
+# elif defined(__GNUC__) && defined(SECP256K1_BUILD)
+#  define SECP256K1_API __attribute__ ((visibility ("default")))
+# else
+#  define SECP256K1_API
+# endif
+#endif
+
+/**Warning attributes
+  * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
+  * some paranoid null checks. */
+# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
+# else
+#  define SECP256K1_WARN_UNUSED_RESULT
+# endif
+# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_ARG_NONNULL(_x)  __attribute__ ((__nonnull__(_x)))
+# else
+#  define SECP256K1_ARG_NONNULL(_x)
+# endif
+
+/** All flags' lower 8 bits indicate what they're for. Do not use directly. */
+#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1)
+#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0)
+#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1)
+/** The higher bits contain the actual data. Do not use directly. */
+#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8)
+#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9)
+#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8)
+
+/** Flags to pass to secp256k1_context_create. */
+#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY)
+#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN)
+#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
+
+/** Flag to pass to secp256k1_ec_pubkey_serialize and secp256k1_ec_privkey_export. */
+#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION)
+#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION)
+
+/** Prefix byte used to tag various encoded curvepoints for specific purposes */
+#define SECP256K1_TAG_PUBKEY_EVEN 0x02
+#define SECP256K1_TAG_PUBKEY_ODD 0x03
+#define SECP256K1_TAG_PUBKEY_UNCOMPRESSED 0x04
+#define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06
+#define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07
+
+/** A simple secp256k1 context object with no precomputed tables. These are useful for
+ *  type serialization/parsing functions which require a context object to maintain
+ *  API consistency, but currently do not require expensive precomputations or dynamic
+ *  allocations.
+ */
+SECP256K1_API extern const secp256k1_context *secp256k1_context_no_precomp;
+
+/** Create a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  In:      flags: which parts of the context to initialize.
+ *
+ *  See also secp256k1_context_randomize.
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_create(
+    unsigned int flags
+) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Copies a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  Args:    ctx: an existing context to copy (cannot be NULL)
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_clone(
+    const secp256k1_context* ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Destroy a secp256k1 context object.
+ *
+ *  The context pointer may not be used afterwards.
+ *  Args:   ctx: an existing context to destroy (cannot be NULL)
+ */
+SECP256K1_API void secp256k1_context_destroy(
+    secp256k1_context* ctx
+);
+
+/** Set a callback function to be called when an illegal argument is passed to
+ *  an API call. It will only trigger for violations that are mentioned
+ *  explicitly in the header.
+ *
+ *  The philosophy is that these shouldn't be dealt with through a
+ *  specific return value, as calling code should not have branches to deal with
+ *  the case that this code itself is broken.
+ *
+ *  On the other hand, during debug stage, one would want to be informed about
+ *  such mistakes, and the default (crashing) may be inadvisable.
+ *  When this callback is triggered, the API function called is guaranteed not
+ *  to cause a crash, though its return value and output arguments are
+ *  undefined.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an illegal argument is
+ *              passed to the API, taking a message and an opaque pointer
+ *              (NULL restores a default handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_illegal_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Set a callback function to be called when an internal consistency check
+ *  fails. The default is crashing.
+ *
+ *  This can only trigger in case of a hardware failure, miscompilation,
+ *  memory corruption, serious bug in the library, or other error would can
+ *  otherwise result in undefined behaviour. It will not trigger due to mere
+ *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
+ *  for that). After this callback returns, anything may happen, including
+ *  crashing.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an internal error occurs,
+ *              taking a message and an opaque pointer (NULL restores a default
+ *              handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_error_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Create a secp256k1 scratch space object.
+ *
+ *  Returns: a newly created scratch space.
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   max_size: maximum amount of memory to allocate
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT secp256k1_scratch_space* secp256k1_scratch_space_create(
+    const secp256k1_context* ctx,
+    size_t max_size
+) SECP256K1_ARG_NONNULL(1);
+
+/** Destroy a secp256k1 scratch space.
+ *
+ *  The pointer may not be used afterwards.
+ *  Args:   scratch: space to destroy
+ */
+SECP256K1_API void secp256k1_scratch_space_destroy(
+    secp256k1_scratch_space* scratch
+);
+
+/** Parse a variable-length public key into the pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *  Args: ctx:      a secp256k1 context object.
+ *  Out:  pubkey:   pointer to a pubkey object. If 1 is returned, it is set to a
+ *                  parsed version of input. If not, its value is undefined.
+ *  In:   input:    pointer to a serialized public key
+ *        inputlen: length of the array pointed to by input
+ *
+ *  This function supports parsing compressed (33 bytes, header byte 0x02 or
+ *  0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header
+ *  byte 0x06 or 0x07) format public keys.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey* pubkey,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a pubkey object into a serialized byte sequence.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx:        a secp256k1 context object.
+ *  Out:    output:     a pointer to a 65-byte (if compressed==0) or 33-byte (if
+ *                      compressed==1) byte array to place the serialized key
+ *                      in.
+ *  In/Out: outputlen:  a pointer to an integer which is initially set to the
+ *                      size of output, and is overwritten with the written
+ *                      size.
+ *  In:     pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                      initialized public key.
+ *          flags:      SECP256K1_EC_COMPRESSED if serialization should be in
+ *                      compressed format, otherwise SECP256K1_EC_UNCOMPRESSED.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_pubkey* pubkey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Parse an ECDSA signature in compact (64 bytes) format.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input64:  a pointer to the 64-byte array to parse
+ *
+ *  The signature must consist of a 32-byte big endian R value, followed by a
+ *  32-byte big endian S value. If R or S fall outside of [0..order-1], the
+ *  encoding is invalid. R and S with value 0 are allowed in the encoding.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or R or
+ *  S are zero, the resulting sig value is guaranteed to fail validation for any
+ *  message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a DER ECDSA signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in DER format.
+ *
+ *  Returns: 1 if enough space was available to serialize, 0 otherwise
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output:    a pointer to an array to store the DER serialization
+ *  In/Out: outputlen: a pointer to a length integer. Initially, this integer
+ *                     should be set to the length of output. After the call
+ *                     it will be set to the length of the serialization (even
+ *                     if 0 was returned).
+ *  In:     sig:       a pointer to an initialized signature object
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_der(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Serialize an ECDSA signature in compact (64 byte) format.
+ *
+ *  Returns: 1
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output64:  a pointer to a 64-byte array to store the compact serialization
+ *  In:     sig:       a pointer to an initialized signature object
+ *
+ *  See secp256k1_ecdsa_signature_parse_compact for details about the encoding.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Verify an ECDSA signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig:       the signature being verified (cannot be NULL)
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           pubkey:    pointer to an initialized public key to verify with (cannot be NULL)
+ *
+ * To avoid accepting malleable signatures, only ECDSA signatures in lower-S
+ * form are accepted.
+ *
+ * If you need to accept ECDSA signatures from sources that do not obey this
+ * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to
+ * validation, but be aware that doing so results in malleable signatures.
+ *
+ * For details, see the comments for that function.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Convert a signature to a normalized lower-S form.
+ *
+ *  Returns: 1 if sigin was not normalized, 0 if it already was.
+ *  Args: ctx:    a secp256k1 context object
+ *  Out:  sigout: a pointer to a signature to fill with the normalized form,
+ *                or copy if the input was already normalized. (can be NULL if
+ *                you're only interested in whether the input was already
+ *                normalized).
+ *  In:   sigin:  a pointer to a signature to check/normalize (cannot be NULL,
+ *                can be identical to sigout)
+ *
+ *  With ECDSA a third-party can forge a second distinct signature of the same
+ *  message, given a single initial signature, but without knowing the key. This
+ *  is done by negating the S value modulo the order of the curve, 'flipping'
+ *  the sign of the random point R which is not included in the signature.
+ *
+ *  Forgery of the same message isn't universally problematic, but in systems
+ *  where message malleability or uniqueness of signatures is important this can
+ *  cause issues. This forgery can be blocked by all verifiers forcing signers
+ *  to use a normalized form.
+ *
+ *  The lower-S form reduces the size of signatures slightly on average when
+ *  variable length encodings (such as DER) are used and is cheap to verify,
+ *  making it a good choice. Security of always using lower-S is assured because
+ *  anyone can trivially modify a signature after the fact to enforce this
+ *  property anyway.
+ *
+ *  The lower S value is always between 0x1 and
+ *  0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
+ *  inclusive.
+ *
+ *  No other forms of ECDSA malleability are known and none seem likely, but
+ *  there is no formal proof that ECDSA, even with this additional restriction,
+ *  is free of other malleability. Commonly used serialization schemes will also
+ *  accept various non-unique encodings, so care should be taken when this
+ *  property is required for an application.
+ *
+ *  The secp256k1_ecdsa_sign function will by default create signatures in the
+ *  lower-S form, and secp256k1_ecdsa_verify will not accept others. In case
+ *  signatures come from a system that cannot enforce this property,
+ *  secp256k1_ecdsa_signature_normalize must be called before verification.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_normalize(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sigout,
+    const secp256k1_ecdsa_signature *sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
+
+/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
+ * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
+ * extra entropy.
+ */
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979;
+
+/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_default;
+
+/** Create an ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *
+ * The created signature is always in lower-S form. See
+ * secp256k1_ecdsa_signature_normalize for more details.
+ */
+SECP256K1_API int secp256k1_ecdsa_sign(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify an ECDSA secret key.
+ *
+ *  Returns: 1: secret key is valid
+ *           0: secret key is invalid
+ *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
+    const secp256k1_context* ctx,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Compute the public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key stores
+ *           0: secret was invalid, try again
+ *  Args:   ctx:        pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:    pubkey:     pointer to the created public key (cannot be NULL)
+ *  In:     seckey:     pointer to a 32-byte private key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Negates a private key in place.
+ *
+ *  Returns: 1 always
+ *  Args:   ctx:        pointer to a context object
+ *  In/Out: seckey:     pointer to the 32-byte private key to be negated (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate(
+    const secp256k1_context* ctx,
+    unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Negates a public key in place.
+ *
+ *  Returns: 1 always
+ *  Args:   ctx:        pointer to a context object
+ *  In/Out: pubkey:     pointer to the public key to be negated (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Tweak a private key by adding tweak to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting private key
+ *          would be invalid (only when the tweak is the complement of the
+ *          private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object (cannot be NULL).
+ * In/Out:  seckey: pointer to a 32-byte private key.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by adding tweak times the generator to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting public key
+ *          would be invalid (only when the tweak is the complement of the
+ *          corresponding private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                  (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key object.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a private key by multiplying it by a tweak.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:   ctx:    pointer to a context object (cannot be NULL).
+ * In/Out: seckey: pointer to a 32-byte private key.
+ * In:     tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by multiplying it by a tweak value.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                 (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key obkect.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Updates the context randomization to protect against side-channel leakage.
+ *  Returns: 1: randomization successfully updated or nothing to randomize
+ *           0: error
+ *  Args:    ctx:       pointer to a context object (cannot be NULL)
+ *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
+ *
+ * While secp256k1 code is written to be constant-time no matter what secret
+ * values are, it's possible that a future compiler may output code which isn't,
+ * and also that the CPU may not emit the same radio frequencies or draw the same
+ * amount power for all values.
+ *
+ * This function provides a seed which is combined into the blinding value: that
+ * blinding value is added before each multiplication (and removed afterwards) so
+ * that it does not affect function results, but shields against attacks which
+ * rely on any input-dependent behaviour.
+ *
+ * This function has currently an effect only on contexts initialized for signing
+ * because randomization is currently used only for signing. However, this is not
+ * guaranteed and may change in the future. It is safe to call this function on
+ * contexts not initialized for signing; then it will have no effect and return 1.
+ *
+ * You should call this after secp256k1_context_create or
+ * secp256k1_context_clone, and may call this repeatedly afterwards.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
+    secp256k1_context* ctx,
+    const unsigned char *seed32
+) SECP256K1_ARG_NONNULL(1);
+
+/** Add a number of public keys together.
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *  Args:   ctx:        pointer to a context object
+ *  Out:    out:        pointer to a public key object for placing the resulting public key
+ *                      (cannot be NULL)
+ *  In:     ins:        pointer to array of pointers to public keys (cannot be NULL)
+ *          n:          the number of public keys to add together (must be at least 1)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *out,
+    const secp256k1_pubkey * const * ins,
+    size_t n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_H */

src/secp256k1_tests/include/secp256k1_recovery.h

@@ -0,0 +1,110 @@
+#ifndef SECP256K1_RECOVERY_H
+#define SECP256K1_RECOVERY_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Opaque data structured that holds a parsed ECDSA signature,
+ *  supporting pubkey recovery.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 65 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ *
+ *  Furthermore, it is guaranteed that identical signatures (including their
+ *  recoverability) will have identical representation, so they can be
+ *  memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[65];
+} secp256k1_ecdsa_recoverable_signature;
+
+/** Parse a compact ECDSA signature (64 bytes + recovery id).
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise
+ *  Args: ctx:     a secp256k1 context object
+ *  Out:  sig:     a pointer to a signature object
+ *  In:   input64: a pointer to a 64-byte compact signature
+ *        recid:   the recovery id (0, 1, 2 or 3)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature* sig,
+    const unsigned char *input64,
+    int recid
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Convert a recoverable signature into a normal signature.
+ *
+ *  Returns: 1
+ *  Out: sig:    a pointer to a normal signature (cannot be NULL).
+ *  In:  sigin:  a pointer to a recoverable signature (cannot be NULL).
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const secp256k1_ecdsa_recoverable_signature* sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
+ *
+ *  Returns: 1
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  output64: a pointer to a 64-byte array of the compact signature (cannot be NULL)
+ *        recid:    a pointer to an integer to hold the recovery id (can be NULL).
+ *  In:   sig:      a pointer to an initialized signature object (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    int *recid,
+    const secp256k1_ecdsa_recoverable_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Create a recoverable ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an ECDSA public key from a signature.
+ *
+ *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to the recovered public key (cannot be NULL)
+ *  In:      sig:        pointer to initialized signature that supports pubkey recovery (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_RECOVERY_H */

src/secp256k1_tests/libsecp256k1-config.h

@@ -0,0 +1,147 @@
+/* src/libsecp256k1-config.h.  Generated from libsecp256k1-config.h.in by configure.  */
+/* src/libsecp256k1-config.h.in.  Generated from configure.ac by autoheader.  */
+
+#ifndef LIBSECP256K1_CONFIG_H
+
+#define LIBSECP256K1_CONFIG_H
+
+/* Define if building universal (internal helper macro) */
+/* #undef AC_APPLE_UNIVERSAL_BUILD */
+
+/* Define this symbol to compile out all VERIFY code */
+/* #undef COVERAGE */
+
+/* Define this symbol to enable the ECDH module */
+/* #undef ENABLE_MODULE_ECDH */
+
+/* Define this symbol to enable the ECDSA pubkey recovery module */
+/* #undef ENABLE_MODULE_RECOVERY */
+
+/* Define this symbol if OpenSSL EC functions are available */
+/* #undef ENABLE_OPENSSL_TESTS */
+
+/* Define to 1 if you have the <dlfcn.h> header file. */
+#define HAVE_DLFCN_H 1
+
+/* Define to 1 if you have the <inttypes.h> header file. */
+#define HAVE_INTTYPES_H 1
+
+/* Define this symbol if libcrypto is installed */
+#define HAVE_LIBCRYPTO 1
+
+/* Define this symbol if libgmp is installed */
+/* #undef HAVE_LIBGMP */
+
+/* Define to 1 if you have the <memory.h> header file. */
+#define HAVE_MEMORY_H 1
+
+/* Define to 1 if you have the <stdint.h> header file. */
+#define HAVE_STDINT_H 1
+
+/* Define to 1 if you have the <stdlib.h> header file. */
+#define HAVE_STDLIB_H 1
+
+/* Define to 1 if you have the <strings.h> header file. */
+#define HAVE_STRINGS_H 1
+
+/* Define to 1 if you have the <string.h> header file. */
+#define HAVE_STRING_H 1
+
+/* Define to 1 if you have the <sys/stat.h> header file. */
+#define HAVE_SYS_STAT_H 1
+
+/* Define to 1 if you have the <sys/types.h> header file. */
+#define HAVE_SYS_TYPES_H 1
+
+/* Define to 1 if you have the <unistd.h> header file. */
+#define HAVE_UNISTD_H 1
+
+/* Define to 1 if the system has the type `__int128'. */
+#define HAVE___INT128 1
+
+/* Define to the sub-directory where libtool stores uninstalled libraries. */
+#define LT_OBJDIR ".libs/"
+
+/* Name of package */
+#define PACKAGE "libsecp256k1"
+
+/* Define to the address where bug reports for this package should be sent. */
+#define PACKAGE_BUGREPORT ""
+
+/* Define to the full name of this package. */
+#define PACKAGE_NAME "libsecp256k1"
+
+/* Define to the full name and version of this package. */
+#define PACKAGE_STRING "libsecp256k1 0.1"
+
+/* Define to the one symbol short name of this package. */
+#define PACKAGE_TARNAME "libsecp256k1"
+
+/* Define to the home page for this package. */
+#define PACKAGE_URL ""
+
+/* Define to the version of this package. */
+#define PACKAGE_VERSION "0.1"
+
+/* Define to 1 if you have the ANSI C header files. */
+#define STDC_HEADERS 1
+
+/* Define this symbol to enable x86_64 assembly optimizations */
+/* #undef USE_ASM_X86_64 */
+
+/* Define this symbol to use a statically generated ecmult table */
+#define USE_ECMULT_STATIC_PRECOMPUTATION 1
+
+/* Define this symbol to use endomorphism optimization */
+/* #undef USE_ENDOMORPHISM */
+
+/* Define this symbol if an external (non-inline) assembly implementation is
+   used */
+/* #undef USE_EXTERNAL_ASM */
+
+/* Define this symbol to use the FIELD_10X26 implementation */
+/* #undef USE_FIELD_10X26 */
+
+/* Define this symbol to use the FIELD_5X52 implementation */
+#define USE_FIELD_5X52 1
+
+/* Define this symbol to use the native field inverse implementation */
+#define USE_FIELD_INV_BUILTIN 1
+
+/* Define this symbol to use the num-based field inverse implementation */
+/* #undef USE_FIELD_INV_NUM */
+
+/* Define this symbol to use the gmp implementation for num */
+/* #undef USE_NUM_GMP */
+
+/* Define this symbol to use no num implementation */
+#define USE_NUM_NONE 1
+
+/* Define this symbol to use the 4x64 scalar implementation */
+#define USE_SCALAR_4X64 1
+
+/* Define this symbol to use the 8x32 scalar implementation */
+/* #undef USE_SCALAR_8X32 */
+
+/* Define this symbol to use the native scalar inverse implementation */
+#define USE_SCALAR_INV_BUILTIN 1
+
+/* Define this symbol to use the num-based scalar inverse implementation */
+/* #undef USE_SCALAR_INV_NUM */
+
+/* Version number of package */
+#define VERSION "0.1"
+
+/* Define WORDS_BIGENDIAN to 1 if your processor stores words with the most
+   significant byte first (like Motorola and SPARC, unlike Intel). */
+#if defined AC_APPLE_UNIVERSAL_BUILD
+# if defined __BIG_ENDIAN__
+#  define WORDS_BIGENDIAN 1
+# endif
+#else
+# ifndef WORDS_BIGENDIAN
+/* #  undef WORDS_BIGENDIAN */
+# endif
+#endif
+
+#endif /*LIBSECP256K1_CONFIG_H*/

src/secp256k1_tests/num.h

@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_NUM_H
+#define SECP256K1_NUM_H
+
+#ifndef USE_NUM_NONE
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(USE_NUM_GMP)
+#include "num_gmp.h"
+#else
+#error "Please select num implementation"
+#endif
+
+/** Copy a number. */
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
+
+/** Convert a number's absolute value to a binary big-endian string.
+ *  There must be enough place. */
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a);
+
+/** Set a number to the value of a binary big-endian string. */
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen);
+
+/** Compute a modular inverse. The input must be less than the modulus. */
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
+
+/** Compute the jacobi symbol (a|b). b must be positive and odd. */
+static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Compare the absolute value of two numbers. */
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Test whether two number are equal (including sign). */
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Add two (signed) numbers. */
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Subtract two (signed) numbers. */
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Multiply two (signed) numbers. */
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
+    even if r was negative. */
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
+
+/** Right-shift the passed number by bits bits. */
+static void secp256k1_num_shift(secp256k1_num *r, int bits);
+
+/** Check whether a number is zero. */
+static int secp256k1_num_is_zero(const secp256k1_num *a);
+
+/** Check whether a number is one. */
+static int secp256k1_num_is_one(const secp256k1_num *a);
+
+/** Check whether a number is strictly negative. */
+static int secp256k1_num_is_neg(const secp256k1_num *a);
+
+/** Change a number's sign. */
+static void secp256k1_num_negate(secp256k1_num *r);
+
+#endif
+
+#endif /* SECP256K1_NUM_H */

src/secp256k1_tests/num_impl.h

@@ -0,0 +1,24 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_NUM_IMPL_H
+#define SECP256K1_NUM_IMPL_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "num.h"
+
+#if defined(USE_NUM_GMP)
+#include "num_gmp_impl.h"
+#elif defined(USE_NUM_NONE)
+/* Nothing. */
+#else
+#error "Please select num implementation"
+#endif
+
+#endif /* SECP256K1_NUM_IMPL_H */

src/secp256k1_tests/scalar.h

@@ -0,0 +1,106 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_H
+#define SECP256K1_SCALAR_H
+
+#include "num.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+/** Clear a scalar to prevent the leak of sensitive data. */
+static void secp256k1_scalar_clear(secp256k1_scalar *r);
+
+/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
+static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Access bits from a scalar. Not constant time. */
+static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Set a scalar from a big endian byte array. */
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
+
+/** Set a scalar to an unsigned integer. */
+static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
+
+/** Convert a scalar to a byte array. */
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
+
+/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
+
+/** Multiply two scalars (modulo the group order). */
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Shift a scalar right by some amount strictly between 0 and 16, returning
+ *  the low bits that were shifted off */
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
+
+/** Compute the square of a scalar (modulo the group order). */
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order). */
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the complement of a scalar (modulo the group order). */
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Check whether a scalar equals zero. */
+static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
+
+/** Check whether a scalar equals one. */
+static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
+
+/** Check whether a scalar, considered as an nonnegative integer, is even. */
+static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
+
+/** Check whether a scalar is higher than the group order divided by 2. */
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
+
+/** Conditionally negate a number, in constant time.
+ * Returns -1 if the number was negated, 1 otherwise */
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
+
+#ifndef USE_NUM_NONE
+/** Convert a scalar to a number. */
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
+
+/** Get the order of the group as a number. */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r);
+#endif
+
+/** Compare two scalars. */
+static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+#ifdef USE_ENDOMORPHISM
+/** Find r1 and r2 such that r1+r2*2^128 = a. */
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+#endif
+
+/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
+
+#endif /* SECP256K1_SCALAR_H */

src/secp256k1_tests/scalar_4x64.h

@@ -0,0 +1,19 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_H
+#define SECP256K1_SCALAR_REPR_H
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef struct {
+    uint64_t d[4];
+} secp256k1_scalar;
+
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
+
+#endif /* SECP256K1_SCALAR_REPR_H */

src/secp256k1_tests/scalar_4x64_impl.h

@@ -0,0 +1,949 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_IMPL_H
+#define SECP256K1_SCALAR_REPR_IMPL_H
+
+/* Limbs of the secp256k1 order. */
+#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
+#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
+#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
+#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
+
+/* Limbs of 2^256 minus the secp256k1 order. */
+#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
+#define SECP256K1_N_C_1 (~SECP256K1_N_1)
+#define SECP256K1_N_C_2 (1)
+
+/* Limbs of half the secp256k1 order. */
+#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
+#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
+#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
+#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
+    r->d[0] = 0;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
+    r->d[0] = v;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
+    return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(offset + count <= 256);
+    if ((offset + count - 1) >> 6 == offset >> 6) {
+        return secp256k1_scalar_get_bits(a, offset, count);
+    } else {
+        VERIFY_CHECK((offset >> 6) + 1 < 4);
+        return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
+    no |= (a->d[2] < SECP256K1_N_2);
+    yes |= (a->d[2] > SECP256K1_N_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_1);
+    yes |= (a->d[1] > SECP256K1_N_1) & ~no;
+    yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
+    return yes;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
+    uint128_t t;
+    VERIFY_CHECK(overflow <= 1);
+    t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint64_t)r->d[3];
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+    return overflow;
+}
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    int overflow;
+    uint128_t t = (uint128_t)a->d[0] + b->d[0];
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[1] + b->d[1];
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[2] + b->d[2];
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[3] + b->d[3];
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    overflow = t + secp256k1_scalar_check_overflow(r);
+    VERIFY_CHECK(overflow == 0 || overflow == 1);
+    secp256k1_scalar_reduce(r, overflow);
+    return overflow;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    uint128_t t;
+    VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
+    t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+#ifdef VERIFY
+    VERIFY_CHECK((t >> 64) == 0);
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    int over;
+    r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
+    r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
+    r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56;
+    r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56;
+    over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
+    if (overflow) {
+        *overflow = over;
+    }
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
+    bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
+    bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
+    bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
+    uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
+    r->d[3] = t & nonzero;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[3] < SECP256K1_N_H_3);
+    yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
+    no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
+    yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
+    return yes;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint64_t mask = !flag - 1;
+    uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
+    uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
+
+/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd(a,b) { \
+    uint64_t tl, th; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c1 += th;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
+}
+
+/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
+#define muladd_fast(a,b) { \
+    uint64_t tl, th; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c1 += th;                 /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK(c1 >= th); \
+}
+
+/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd2(a,b) { \
+    uint64_t tl, th, th2, tl2; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;               /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    th2 = th + th;                  /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
+    c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
+    tl2 = tl + tl;                  /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
+    th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c0 += tl2;                      /* overflow is handled on the next line */ \
+    th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
+    c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
+    c1 += th2;                      /* overflow is handled on the next line */ \
+    c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
+}
+
+/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define sumadd(a) { \
+    unsigned int over; \
+    c0 += (a);                  /* overflow is handled on the next line */ \
+    over = (c0 < (a)) ? 1 : 0; \
+    c1 += over;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
+}
+
+/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
+#define sumadd_fast(a) { \
+    c0 += (a);                 /* overflow is handled on the next line */ \
+    c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */
+#define extract(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = c2; \
+    c2 = 0; \
+}
+
+/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */
+#define extract_fast(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = 0; \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
+#ifdef USE_ASM_X86_64
+    /* Reduce 512 bits into 385. */
+    uint64_t m0, m1, m2, m3, m4, m5, m6;
+    uint64_t p0, p1, p2, p3, p4;
+    uint64_t c;
+
+    __asm__ __volatile__(
+    /* Preload. */
+    "movq 32(%%rsi), %%r11\n"
+    "movq 40(%%rsi), %%r12\n"
+    "movq 48(%%rsi), %%r13\n"
+    "movq 56(%%rsi), %%r14\n"
+    /* Initialize r8,r9,r10 */
+    "movq 0(%%rsi), %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9) += n0 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* extract m0 */
+    "movq %%r8, %q0\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10) += l1 */
+    "addq 8(%%rsi), %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r9,r10,r8) += n1 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += n0 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m1 */
+    "movq %%r9, %q1\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += l2 */
+    "addq 16(%%rsi), %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n2 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n1 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n0 */
+    "addq %%r11, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract m2 */
+    "movq %%r10, %q2\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += l3 */
+    "addq 24(%%rsi), %%r8\n"
+    "adcq $0, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n3 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n2 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n1 */
+    "addq %%r12, %%r8\n"
+    "adcq $0, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* extract m3 */
+    "movq %%r8, %q3\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += n3 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += n2 */
+    "addq %%r13, %%r9\n"
+    "adcq $0, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m4 */
+    "movq %%r9, %q4\n"
+    /* (r10,r8) += n3 */
+    "addq %%r14, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m5 */
+    "movq %%r10, %q5\n"
+    /* extract m6 */
+    "movq %%r8, %q6\n"
+    : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
+    : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
+
+    /* Reduce 385 bits into 258. */
+    __asm__ __volatile__(
+    /* Preload */
+    "movq %q9, %%r11\n"
+    "movq %q10, %%r12\n"
+    "movq %q11, %%r13\n"
+    /* Initialize (r8,r9,r10) */
+    "movq %q5, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9) += m4 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* extract p0 */
+    "movq %%r8, %q0\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10) += m1 */
+    "addq %q6, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r9,r10,r8) += m5 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += m4 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract p1 */
+    "movq %%r9, %q1\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += m2 */
+    "addq %q7, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m6 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m5 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m4 */
+    "addq %%r11, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract p2 */
+    "movq %%r10, %q2\n"
+    /* (r8,r9) += m3 */
+    "addq %q8, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r8,r9) += m6 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* (r8,r9) += m5 */
+    "addq %%r12, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract p3 */
+    "movq %%r8, %q3\n"
+    /* (r9) += m6 */
+    "addq %%r13, %%r9\n"
+    /* extract p4 */
+    "movq %%r9, %q4\n"
+    : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
+    : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
+
+    /* Reduce 258 bits into 256. */
+    __asm__ __volatile__(
+    /* Preload */
+    "movq %q5, %%r10\n"
+    /* (rax,rdx) = p4 * c0 */
+    "movq %7, %%rax\n"
+    "mulq %%r10\n"
+    /* (rax,rdx) += p0 */
+    "addq %q1, %%rax\n"
+    "adcq $0, %%rdx\n"
+    /* extract r0 */
+    "movq %%rax, 0(%q6)\n"
+    /* Move to (r8,r9) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    /* (r8,r9) += p1 */
+    "addq %q2, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r8,r9) += p4 * c1 */
+    "movq %8, %%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* Extract r1 */
+    "movq %%r8, 8(%q6)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r8) += p4 */
+    "addq %%r10, %%r9\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r8) += p2 */
+    "addq %q3, %%r9\n"
+    "adcq $0, %%r8\n"
+    /* Extract r2 */
+    "movq %%r9, 16(%q6)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r8,r9) += p3 */
+    "addq %q4, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract r3 */
+    "movq %%r8, 24(%q6)\n"
+    /* Extract c */
+    "movq %%r9, %q0\n"
+    : "=g"(c)
+    : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
+#else
+    uint128_t c;
+    uint64_t c0, c1, c2;
+    uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
+    uint64_t m0, m1, m2, m3, m4, m5;
+    uint32_t m6;
+    uint64_t p0, p1, p2, p3;
+    uint32_t p4;
+
+    /* Reduce 512 bits into 385. */
+    /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
+    c0 = l[0]; c1 = 0; c2 = 0;
+    muladd_fast(n0, SECP256K1_N_C_0);
+    extract_fast(m0);
+    sumadd_fast(l[1]);
+    muladd(n1, SECP256K1_N_C_0);
+    muladd(n0, SECP256K1_N_C_1);
+    extract(m1);
+    sumadd(l[2]);
+    muladd(n2, SECP256K1_N_C_0);
+    muladd(n1, SECP256K1_N_C_1);
+    sumadd(n0);
+    extract(m2);
+    sumadd(l[3]);
+    muladd(n3, SECP256K1_N_C_0);
+    muladd(n2, SECP256K1_N_C_1);
+    sumadd(n1);
+    extract(m3);
+    muladd(n3, SECP256K1_N_C_1);
+    sumadd(n2);
+    extract(m4);
+    sumadd_fast(n3);
+    extract_fast(m5);
+    VERIFY_CHECK(c0 <= 1);
+    m6 = c0;
+
+    /* Reduce 385 bits into 258. */
+    /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
+    c0 = m0; c1 = 0; c2 = 0;
+    muladd_fast(m4, SECP256K1_N_C_0);
+    extract_fast(p0);
+    sumadd_fast(m1);
+    muladd(m5, SECP256K1_N_C_0);
+    muladd(m4, SECP256K1_N_C_1);
+    extract(p1);
+    sumadd(m2);
+    muladd(m6, SECP256K1_N_C_0);
+    muladd(m5, SECP256K1_N_C_1);
+    sumadd(m4);
+    extract(p2);
+    sumadd_fast(m3);
+    muladd_fast(m6, SECP256K1_N_C_1);
+    sumadd_fast(m5);
+    extract_fast(p3);
+    p4 = c0 + m6;
+    VERIFY_CHECK(p4 <= 2);
+
+    /* Reduce 258 bits into 256. */
+    /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
+    c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
+    r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
+    r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p2 + (uint128_t)p4;
+    r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p3;
+    r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+#endif
+
+    /* Final reduction of r. */
+    secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
+}
+
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
+#ifdef USE_ASM_X86_64
+    const uint64_t *pb = b->d;
+    __asm__ __volatile__(
+    /* Preload */
+    "movq 0(%%rdi), %%r15\n"
+    "movq 8(%%rdi), %%rbx\n"
+    "movq 16(%%rdi), %%rcx\n"
+    "movq 0(%%rdx), %%r11\n"
+    "movq 8(%%rdx), %%r12\n"
+    "movq 16(%%rdx), %%r13\n"
+    "movq 24(%%rdx), %%r14\n"
+    /* (rax,rdx) = a0 * b0 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r11\n"
+    /* Extract l0 */
+    "movq %%rax, 0(%%rsi)\n"
+    /* (r8,r9,r10) = (rdx) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += a0 * b1 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a1 * b0 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l1 */
+    "movq %%r8, 8(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += a0 * b2 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a1 * b1 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a2 * b0 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l2 */
+    "movq %%r9, 16(%%rsi)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += a0 * b3 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Preload a3 */
+    "movq 24(%%rdi), %%r15\n"
+    /* (r10,r8,r9) += a1 * b2 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += a2 * b1 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += a3 * b0 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract l3 */
+    "movq %%r10, 24(%%rsi)\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += a1 * b3 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a2 * b2 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a3 * b1 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l4 */
+    "movq %%r8, 32(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += a2 * b3 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a3 * b2 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l5 */
+    "movq %%r9, 40(%%rsi)\n"
+    /* (r10,r8) += a3 * b3 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    /* Extract l6 */
+    "movq %%r10, 48(%%rsi)\n"
+    /* Extract l7 */
+    "movq %%r8, 56(%%rsi)\n"
+    : "+d"(pb)
+    : "S"(l), "D"(a->d)
+    : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
+#else
+    /* 160 bit accumulator. */
+    uint64_t c0 = 0, c1 = 0;
+    uint32_t c2 = 0;
+
+    /* l[0..7] = a[0..3] * b[0..3]. */
+    muladd_fast(a->d[0], b->d[0]);
+    extract_fast(l[0]);
+    muladd(a->d[0], b->d[1]);
+    muladd(a->d[1], b->d[0]);
+    extract(l[1]);
+    muladd(a->d[0], b->d[2]);
+    muladd(a->d[1], b->d[1]);
+    muladd(a->d[2], b->d[0]);
+    extract(l[2]);
+    muladd(a->d[0], b->d[3]);
+    muladd(a->d[1], b->d[2]);
+    muladd(a->d[2], b->d[1]);
+    muladd(a->d[3], b->d[0]);
+    extract(l[3]);
+    muladd(a->d[1], b->d[3]);
+    muladd(a->d[2], b->d[2]);
+    muladd(a->d[3], b->d[1]);
+    extract(l[4]);
+    muladd(a->d[2], b->d[3]);
+    muladd(a->d[3], b->d[2]);
+    extract(l[5]);
+    muladd_fast(a->d[3], b->d[3]);
+    extract_fast(l[6]);
+    VERIFY_CHECK(c1 == 0);
+    l[7] = c0;
+#endif
+}
+
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
+#ifdef USE_ASM_X86_64
+    __asm__ __volatile__(
+    /* Preload */
+    "movq 0(%%rdi), %%r11\n"
+    "movq 8(%%rdi), %%r12\n"
+    "movq 16(%%rdi), %%r13\n"
+    "movq 24(%%rdi), %%r14\n"
+    /* (rax,rdx) = a0 * a0 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r11\n"
+    /* Extract l0 */
+    "movq %%rax, 0(%%rsi)\n"
+    /* (r8,r9,r10) = (rdx,0) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += 2 * a0 * a1 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l1 */
+    "movq %%r8, 8(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += 2 * a0 * a2 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a1 * a1 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l2 */
+    "movq %%r9, 16(%%rsi)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += 2 * a0 * a3 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += 2 * a1 * a2 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract l3 */
+    "movq %%r10, 24(%%rsi)\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += 2 * a1 * a3 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a2 * a2 */
+    "movq %%r13, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l4 */
+    "movq %%r8, 32(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += 2 * a2 * a3 */
+    "movq %%r13, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l5 */
+    "movq %%r9, 40(%%rsi)\n"
+    /* (r10,r8) += a3 * a3 */
+    "movq %%r14, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    /* Extract l6 */
+    "movq %%r10, 48(%%rsi)\n"
+    /* Extract l7 */
+    "movq %%r8, 56(%%rsi)\n"
+    :
+    : "S"(l), "D"(a->d)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory");
+#else
+    /* 160 bit accumulator. */
+    uint64_t c0 = 0, c1 = 0;
+    uint32_t c2 = 0;
+
+    /* l[0..7] = a[0..3] * b[0..3]. */
+    muladd_fast(a->d[0], a->d[0]);
+    extract_fast(l[0]);
+    muladd2(a->d[0], a->d[1]);
+    extract(l[1]);
+    muladd2(a->d[0], a->d[2]);
+    muladd(a->d[1], a->d[1]);
+    extract(l[2]);
+    muladd2(a->d[0], a->d[3]);
+    muladd2(a->d[1], a->d[2]);
+    extract(l[3]);
+    muladd2(a->d[1], a->d[3]);
+    muladd(a->d[2], a->d[2]);
+    extract(l[4]);
+    muladd2(a->d[2], a->d[3]);
+    extract(l[5]);
+    muladd_fast(a->d[3], a->d[3]);
+    extract_fast(l[6]);
+    VERIFY_CHECK(c1 == 0);
+    l[7] = c0;
+#endif
+}
+
+#undef sumadd
+#undef sumadd_fast
+#undef muladd
+#undef muladd_fast
+#undef muladd2
+#undef extract
+#undef extract_fast
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    uint64_t l[8];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
+    r->d[3] = (r->d[3] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint64_t l[8];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    r1->d[0] = a->d[0];
+    r1->d[1] = a->d[1];
+    r1->d[2] = 0;
+    r1->d[3] = 0;
+    r2->d[0] = a->d[2];
+    r2->d[1] = a->d[3];
+    r2->d[2] = 0;
+    r2->d[3] = 0;
+}
+#endif
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
+    uint64_t l[8];
+    unsigned int shiftlimbs;
+    unsigned int shiftlow;
+    unsigned int shifthigh;
+    VERIFY_CHECK(shift >= 256);
+    secp256k1_scalar_mul_512(l, a, b);
+    shiftlimbs = shift >> 6;
+    shiftlow = shift & 0x3F;
+    shifthigh = 64 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
+}
+
+#endif /* SECP256K1_SCALAR_REPR_IMPL_H */

src/secp256k1_tests/scalar_impl.h

@@ -0,0 +1,333 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_IMPL_H
+#define SECP256K1_SCALAR_IMPL_H
+
+#include "group.h"
+#include "scalar.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low_impl.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64_impl.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32_impl.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+#ifndef USE_NUM_NONE
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
+    unsigned char c[32];
+    secp256k1_scalar_get_b32(c, a);
+    secp256k1_num_set_bin(r, c, 32);
+}
+
+/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    static const unsigned char order[32] = {
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
+    };
+#else
+    static const unsigned char order[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+    };
+#endif
+    secp256k1_num_set_bin(r, order, 32);
+}
+#endif
+
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    int i;
+    *r = 0;
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
+        if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
+            *r = i;
+    /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
+     * have a composite group order; fix it in exhaustive_tests.c). */
+    VERIFY_CHECK(*r != 0);
+}
+#else
+    secp256k1_scalar *t;
+    int i;
+    /* First compute xN as x ^ (2^N - 1) for some values of N,
+     * and uM as x ^ M for some values of M. */
+    secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126;
+    secp256k1_scalar u2, u5, u9, u11, u13;
+
+    secp256k1_scalar_sqr(&u2, x);
+    secp256k1_scalar_mul(&x2, &u2,  x);
+    secp256k1_scalar_mul(&u5, &u2, &x2);
+    secp256k1_scalar_mul(&x3, &u5,  &u2);
+    secp256k1_scalar_mul(&u9, &x3, &u2);
+    secp256k1_scalar_mul(&u11, &u9, &u2);
+    secp256k1_scalar_mul(&u13, &u11, &u2);
+
+    secp256k1_scalar_sqr(&x6, &u13);
+    secp256k1_scalar_sqr(&x6, &x6);
+    secp256k1_scalar_mul(&x6, &x6, &u11);
+
+    secp256k1_scalar_sqr(&x8, &x6);
+    secp256k1_scalar_sqr(&x8, &x8);
+    secp256k1_scalar_mul(&x8, &x8,  &x2);
+
+    secp256k1_scalar_sqr(&x14, &x8);
+    for (i = 0; i < 5; i++) {
+        secp256k1_scalar_sqr(&x14, &x14);
+    }
+    secp256k1_scalar_mul(&x14, &x14, &x6);
+
+    secp256k1_scalar_sqr(&x28, &x14);
+    for (i = 0; i < 13; i++) {
+        secp256k1_scalar_sqr(&x28, &x28);
+    }
+    secp256k1_scalar_mul(&x28, &x28, &x14);
+
+    secp256k1_scalar_sqr(&x56, &x28);
+    for (i = 0; i < 27; i++) {
+        secp256k1_scalar_sqr(&x56, &x56);
+    }
+    secp256k1_scalar_mul(&x56, &x56, &x28);
+
+    secp256k1_scalar_sqr(&x112, &x56);
+    for (i = 0; i < 55; i++) {
+        secp256k1_scalar_sqr(&x112, &x112);
+    }
+    secp256k1_scalar_mul(&x112, &x112, &x56);
+
+    secp256k1_scalar_sqr(&x126, &x112);
+    for (i = 0; i < 13; i++) {
+        secp256k1_scalar_sqr(&x126, &x126);
+    }
+    secp256k1_scalar_mul(&x126, &x126, &x14);
+
+    /* Then accumulate the final result (t starts at x126). */
+    t = &x126;
+    for (i = 0; i < 3; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 5; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+    for (i = 0; i < 4; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 5; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 6; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 3; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 5; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+    for (i = 0; i < 6; i++) { /* 000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 10; i++) { /* 0000000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 9; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
+    for (i = 0; i < 5; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+    for (i = 0; i < 6; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+    for (i = 0; i < 4; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 5; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 6; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 10; i++) { /* 000000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 4; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+    for (i = 0; i < 6; i++) { /* 00000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 8; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(r, t, &x6); /* 111111 */
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(a->d[0] & 1);
+}
+#endif
+
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(USE_SCALAR_INV_BUILTIN)
+    secp256k1_scalar_inverse(r, x);
+#elif defined(USE_SCALAR_INV_NUM)
+    unsigned char b[32];
+    secp256k1_num n, m;
+    secp256k1_scalar t = *x;
+    secp256k1_scalar_get_b32(b, &t);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_scalar_order_get_num(&m);
+    secp256k1_num_mod_inverse(&n, &n, &m);
+    secp256k1_num_get_bin(b, 32, &n);
+    secp256k1_scalar_set_b32(r, b, NULL);
+    /* Verify that the inverse was computed correctly, without GMP code. */
+    secp256k1_scalar_mul(&t, &t, r);
+    CHECK(secp256k1_scalar_is_one(&t));
+#else
+#error "Please select scalar inverse implementation"
+#endif
+}
+
+#ifdef USE_ENDOMORPHISM
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/**
+ * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the
+ * full case we don't bother making k1 and k2 be small, we just want them to be
+ * nontrivial to get full test coverage for the exhaustive tests. We therefore
+ * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda.
+ */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER;
+}
+#else
+/**
+ * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
+ * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
+ *            0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
+ *
+ * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
+ * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
+ * and k2 have a small size.
+ * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
+ *
+ * - a1 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ * - b1 =     -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
+ * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
+ * - b2 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ *
+ * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
+ * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
+ * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
+ *
+ * g1, g2 are precomputed constants used to replace division with a rounded multiplication
+ * when decomposing the scalar for an endomorphism-based point multiplication.
+ *
+ * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
+ * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
+ *
+ * The derivation is described in the paper "Efficient Software Implementation of Public-Key
+ * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
+ * Section 4.3 (here we use a somewhat higher-precision estimate):
+ * d = a1*b2 - b1*a2
+ * g1 = round((2^272)*b2/d)
+ * g2 = round((2^272)*b1/d)
+ *
+ * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
+ * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
+ *
+ * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
+ */
+
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    secp256k1_scalar c1, c2;
+    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
+        0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
+        0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
+    );
+    static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
+        0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
+    );
+    static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+        0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
+    );
+    static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
+        0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
+    );
+    static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
+        0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
+    );
+    VERIFY_CHECK(r1 != a);
+    VERIFY_CHECK(r2 != a);
+    /* these _var calls are constant time since the shift amount is constant */
+    secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
+    secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
+    secp256k1_scalar_mul(&c1, &c1, &minus_b1);
+    secp256k1_scalar_mul(&c2, &c2, &minus_b2);
+    secp256k1_scalar_add(r2, &c1, &c2);
+    secp256k1_scalar_mul(r1, r2, &minus_lambda);
+    secp256k1_scalar_add(r1, r1, a);
+}
+#endif
+#endif
+
+#endif /* SECP256K1_SCALAR_IMPL_H */

src/secp256k1_tests/scalar_low.h

@@ -0,0 +1,15 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_H
+#define SECP256K1_SCALAR_REPR_H
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef uint32_t secp256k1_scalar;
+
+#endif /* SECP256K1_SCALAR_REPR_H */

src/secp256k1_tests/scalar_low_impl.h

@@ -0,0 +1,114 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_IMPL_H
+#define SECP256K1_SCALAR_REPR_IMPL_H
+
+#include "scalar.h"
+
+#include <string.h>
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(*a & 1);
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; }
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; }
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    if (offset < 32)
+        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
+    else
+        return 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    return secp256k1_scalar_get_bits(a, offset, count);
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; }
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER;
+    return *r < *b;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    if (flag && bit < 32)
+        *r += (1 << bit);
+#ifdef VERIFY
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
+    int i;
+    *r = 0;
+    for (i = 0; i < 32; i++) {
+       *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+    }
+    /* just deny overflow, it basically always happens */
+    if (overflow) *overflow = 0;
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    memset(bin, 0, 32);
+    bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return *a == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    if (*a == 0) {
+        *r = 0;
+    } else {
+        *r = EXHAUSTIVE_TEST_ORDER - *a;
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return *a == 1;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    return *a > EXHAUSTIVE_TEST_ORDER / 2;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    if (flag) secp256k1_scalar_negate(r, r);
+    return flag ? -1 : 1;
+}
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = *r & ((1 << n) - 1);
+    *r >>= n;
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r1 = *a;
+    *r2 = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return *a == *b;
+}
+
+#endif /* SECP256K1_SCALAR_REPR_IMPL_H */

src/secp256k1_tests/scratch.h

@@ -0,0 +1,39 @@
+/**********************************************************************
+ * Copyright (c) 2017 Andrew Poelstra	                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCRATCH_
+#define _SECP256K1_SCRATCH_
+
+#define SECP256K1_SCRATCH_MAX_FRAMES	5
+
+/* The typedef is used internally; the struct name is used in the public API
+ * (where it is exposed as a different typedef) */
+typedef struct secp256k1_scratch_space_struct {
+    void *data[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t offset[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame_size[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame;
+    size_t max_size;
+    const secp256k1_callback* error_callback;
+} secp256k1_scratch;
+
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size);
+
+static void secp256k1_scratch_destroy(secp256k1_scratch* scratch);
+
+/** Attempts to allocate a new stack frame with `n` available bytes. Returns 1 on success, 0 on failure */
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects);
+
+/** Deallocates a stack frame */
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch);
+
+/** Returns the maximum allocation the scratch space will allow */
+static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t n_objects);
+
+/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */
+static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t n);
+
+#endif

src/secp256k1_tests/scratch_impl.h

@@ -0,0 +1,86 @@
+/**********************************************************************
+ * Copyright (c) 2017 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCRATCH_IMPL_H_
+#define _SECP256K1_SCRATCH_IMPL_H_
+
+#include "scratch.h"
+
+/* Using 16 bytes alignment because common architectures never have alignment
+ * requirements above 8 for any of the types we care about. In addition we
+ * leave some room because currently we don't care about a few bytes.
+ * TODO: Determine this at configure time. */
+#define ALIGNMENT 16
+
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size) {
+    secp256k1_scratch* ret = (secp256k1_scratch*)checked_malloc(error_callback, sizeof(*ret));
+    if (ret != NULL) {
+        memset(ret, 0, sizeof(*ret));
+        ret->max_size = max_size;
+        ret->error_callback = error_callback;
+    }
+    return ret;
+}
+
+static void secp256k1_scratch_destroy(secp256k1_scratch* scratch) {
+    if (scratch != NULL) {
+        VERIFY_CHECK(scratch->frame == 0);
+        free(scratch);
+    }
+}
+
+static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t objects) {
+    size_t i = 0;
+    size_t allocated = 0;
+    for (i = 0; i < scratch->frame; i++) {
+        allocated += scratch->frame_size[i];
+    }
+    if (scratch->max_size - allocated <= objects * ALIGNMENT) {
+        return 0;
+    }
+    return scratch->max_size - allocated - objects * ALIGNMENT;
+}
+
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects) {
+    VERIFY_CHECK(scratch->frame < SECP256K1_SCRATCH_MAX_FRAMES);
+
+    if (n <= secp256k1_scratch_max_allocation(scratch, objects)) {
+        n += objects * ALIGNMENT;
+        scratch->data[scratch->frame] = checked_malloc(scratch->error_callback, n);
+        if (scratch->data[scratch->frame] == NULL) {
+            return 0;
+        }
+        scratch->frame_size[scratch->frame] = n;
+        scratch->offset[scratch->frame] = 0;
+        scratch->frame++;
+        return 1;
+    } else {
+        return 0;
+    }
+}
+
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch) {
+    VERIFY_CHECK(scratch->frame > 0);
+    scratch->frame -= 1;
+    free(scratch->data[scratch->frame]);
+}
+
+static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t size) {
+    void *ret;
+    size_t frame = scratch->frame - 1;
+    size = ((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT;
+
+    if (scratch->frame == 0 || size + scratch->offset[frame] > scratch->frame_size[frame]) {
+        return NULL;
+    }
+    ret = (void *) ((unsigned char *) scratch->data[frame] + scratch->offset[frame]);
+    memset(ret, 0, size);
+    scratch->offset[frame] += size;
+
+    return ret;
+}
+
+#endif

src/secp256k1_tests/secp256k1_c.h

@@ -0,0 +1,609 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include "include/secp256k1.h"
+
+#include "util.h"
+#include "num_impl.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_impl.h"
+#include "ecmult_const_impl.h"
+#include "ecmult_gen_impl.h"
+#include "ecdsa_impl.h"
+#include "eckey_impl.h"
+#include "hash_impl.h"
+#include "scratch_impl.h"
+
+#define ARG_CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        secp256k1_callback_call(&ctx->illegal_callback, #cond); \
+        return 0; \
+    } \
+} while(0)
+
+static void default_illegal_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_illegal_callback = {
+    default_illegal_callback_fn,
+    NULL
+};
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+
+struct secp256k1_context_struct {
+    secp256k1_ecmult_context ecmult_ctx;
+    secp256k1_ecmult_gen_context ecmult_gen_ctx;
+    secp256k1_callback illegal_callback;
+    secp256k1_callback error_callback;
+};
+
+static const secp256k1_context secp256k1_context_no_precomp_ = {
+    { 0 },
+    { 0 },
+    { default_illegal_callback_fn, 0 },
+    { default_error_callback_fn, 0 }
+};
+const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_no_precomp_;
+
+secp256k1_context* secp256k1_context_create(unsigned int flags) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = default_illegal_callback;
+    ret->error_callback = default_error_callback;
+
+    if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) {
+            secp256k1_callback_call(&ret->illegal_callback,
+                                    "Invalid flags");
+            free(ret);
+            return NULL;
+    }
+
+    secp256k1_ecmult_context_init(&ret->ecmult_ctx);
+    secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
+
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) {
+        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback);
+    }
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) {
+        secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback);
+    }
+
+    return ret;
+}
+
+secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = ctx->illegal_callback;
+    ret->error_callback = ctx->error_callback;
+    secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback);
+    secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback);
+    return ret;
+}
+
+void secp256k1_context_destroy(secp256k1_context* ctx) {
+    CHECK(ctx != secp256k1_context_no_precomp);
+    if (ctx != NULL) {
+        secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
+        secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
+
+        free(ctx);
+    }
+}
+
+void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    CHECK(ctx != secp256k1_context_no_precomp);
+    if (fun == NULL) {
+        fun = default_illegal_callback_fn;
+    }
+    ctx->illegal_callback.fn = fun;
+    ctx->illegal_callback.data = data;
+}
+
+void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    CHECK(ctx != secp256k1_context_no_precomp);
+    if (fun == NULL) {
+        fun = default_error_callback_fn;
+    }
+    ctx->error_callback.fn = fun;
+    ctx->error_callback.data = data;
+}
+
+secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) {
+    VERIFY_CHECK(ctx != NULL);
+    return secp256k1_scratch_create(&ctx->error_callback, max_size);
+}
+
+void secp256k1_scratch_space_destroy(secp256k1_scratch_space* scratch) {
+    secp256k1_scratch_destroy(scratch);
+}
+
+static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        /* When the secp256k1_ge_storage type is exactly 64 byte, use its
+         * representation inside secp256k1_pubkey, as conversion is very fast.
+         * Note that secp256k1_pubkey_save must use the same representation. */
+        secp256k1_ge_storage s;
+        memcpy(&s, &pubkey->data[0], sizeof(s));
+        secp256k1_ge_from_storage(ge, &s);
+    } else {
+        /* Otherwise, fall back to 32-byte big endian for X and Y. */
+        secp256k1_fe x, y;
+        secp256k1_fe_set_b32(&x, pubkey->data);
+        secp256k1_fe_set_b32(&y, pubkey->data + 32);
+        secp256k1_ge_set_xy(ge, &x, &y);
+    }
+    ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
+    return 1;
+}
+
+static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        secp256k1_ge_storage s;
+        secp256k1_ge_to_storage(&s, ge);
+        memcpy(&pubkey->data[0], &s, sizeof(s));
+    } else {
+        VERIFY_CHECK(!secp256k1_ge_is_infinity(ge));
+        secp256k1_fe_normalize_var(&ge->x);
+        secp256k1_fe_normalize_var(&ge->y);
+        secp256k1_fe_get_b32(pubkey->data, &ge->x);
+        secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
+    }
+}
+
+int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) {
+    secp256k1_ge Q;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(input != NULL);
+    if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
+        return 0;
+    }
+    secp256k1_pubkey_save(pubkey, &Q);
+    secp256k1_ge_clear(&Q);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) {
+    secp256k1_ge Q;
+    size_t len;
+    int ret = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33 : 65));
+    len = *outputlen;
+    *outputlen = 0;
+    ARG_CHECK(output != NULL);
+    memset(output, 0, len);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION);
+    if (secp256k1_pubkey_load(ctx, &Q, pubkey)) {
+        ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION);
+        if (ret) {
+            *outputlen = len;
+        }
+    }
+    return ret;
+}
+
+static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+}
+
+static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input != NULL);
+
+    if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+        return 1;
+    } else {
+        memset(sig, 0, sizeof(*sig));
+        return 0;
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) {
+    secp256k1_scalar r, s;
+    int ret = 1;
+    int overflow = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+    } else {
+        memset(sig, 0, sizeof(*sig));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s);
+}
+
+int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) {
+    secp256k1_scalar r, s;
+    int ret = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin);
+    ret = secp256k1_scalar_is_high(&s);
+    if (sigout != NULL) {
+        if (ret) {
+            secp256k1_scalar_negate(&s, &s);
+        }
+        secp256k1_ecdsa_signature_save(sigout, &r, &s);
+    }
+
+    return ret;
+}
+
+int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return (!secp256k1_scalar_is_high(&s) &&
+            secp256k1_pubkey_load(ctx, &q, pubkey) &&
+            secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
+}
+
+static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *offset, const void *data, unsigned int len) {
+    memcpy(buf + *offset, data, len);
+    *offset += len;
+}
+
+static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   unsigned char keydata[112];
+   unsigned int offset = 0;
+   secp256k1_rfc6979_hmac_sha256 rng;
+   unsigned int i;
+   /* We feed a byte array to the PRNG as input, consisting of:
+    * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
+    * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
+    * - optionally 16 extra bytes with the algorithm name.
+    * Because the arguments have distinct fixed lengths it is not possible for
+    *  different argument mixtures to emulate each other and result in the same
+    *  nonces.
+    */
+   buffer_append(keydata, &offset, key32, 32);
+   buffer_append(keydata, &offset, msg32, 32);
+   if (data != NULL) {
+       buffer_append(keydata, &offset, data, 32);
+   }
+   if (algo16 != NULL) {
+       buffer_append(keydata, &offset, algo16, 16);
+   }
+   secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, offset);
+   memset(keydata, 0, sizeof(keydata));
+   for (i = 0; i <= counter; i++) {
+       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+   }
+   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+   return 1;
+}
+
+const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
+const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
+
+int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            if (!overflow && !secp256k1_scalar_is_zero(&non)) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        memset(nonce32, 0, 32);
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_signature_save(signature, &r, &s);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) {
+    secp256k1_scalar sec;
+    int ret;
+    int overflow;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = !overflow && !secp256k1_scalar_is_zero(&sec);
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) {
+    secp256k1_gej pj;
+    secp256k1_ge p;
+    secp256k1_scalar sec;
+    int overflow;
+    int ret = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec));
+    if (ret) {
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec);
+        secp256k1_ge_set_gej(&p, &pj);
+        secp256k1_pubkey_save(pubkey, &p);
+    }
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) {
+    secp256k1_scalar sec;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    secp256k1_scalar_negate(&sec, &sec);
+    secp256k1_scalar_get_b32(seckey, &sec);
+
+    return 1;
+}
+
+int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *pubkey) {
+    int ret = 0;
+    secp256k1_ge p;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    ret = secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        secp256k1_ge_neg(&p, &p);
+        secp256k1_pubkey_save(pubkey, &p);
+    }
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar term;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+
+    ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term);
+    memset(seckey, 0, 32);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&term);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar term;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar factor;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor);
+    memset(seckey, 0, 32);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&factor);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar factor;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) {
+    VERIFY_CHECK(ctx != NULL);
+    if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) {
+        secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    }
+    return 1;
+}
+
+int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) {
+    size_t i;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+
+    ARG_CHECK(pubnonce != NULL);
+    memset(pubnonce, 0, sizeof(*pubnonce));
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(pubnonces != NULL);
+
+    secp256k1_gej_set_infinity(&Qj);
+
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
+        secp256k1_gej_add_ge(&Qj, &Qj, &Q);
+    }
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(&Q, &Qj);
+    secp256k1_pubkey_save(pubnonce, &Q);
+    return 1;
+}
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/main_impl.h"
+#endif

src/secp256k1_tests/testrand.h

@@ -0,0 +1,38 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_TESTRAND_H
+#define SECP256K1_TESTRAND_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+/* A non-cryptographic RNG used only for test infrastructure. */
+
+/** Seed the pseudorandom number generator for testing. */
+SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
+
+/** Generate a pseudorandom number in the range [0..2**32-1]. */
+static uint32_t secp256k1_rand32(void);
+
+/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or
+ *  more. */
+static uint32_t secp256k1_rand_bits(int bits);
+
+/** Generate a pseudorandom number in the range [0..range-1]. */
+static uint32_t secp256k1_rand_int(uint32_t range);
+
+/** Generate a pseudorandom 32-byte array. */
+static void secp256k1_rand256(unsigned char *b32);
+
+/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
+static void secp256k1_rand256_test(unsigned char *b32);
+
+/** Generate pseudorandom bytes with long sequences of zero and one bits. */
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len);
+
+#endif /* SECP256K1_TESTRAND_H */

src/secp256k1_tests/testrand_impl.h

@@ -0,0 +1,110 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_TESTRAND_IMPL_H
+#define SECP256K1_TESTRAND_IMPL_H
+
+#include <stdint.h>
+#include <string.h>
+
+#include "testrand.h"
+#include "hash.h"
+
+static secp256k1_rfc6979_hmac_sha256 secp256k1_test_rng;
+static uint32_t secp256k1_test_rng_precomputed[8];
+static int secp256k1_test_rng_precomputed_used = 8;
+static uint64_t secp256k1_test_rng_integer;
+static int secp256k1_test_rng_integer_bits_left = 0;
+
+SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
+    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
+}
+
+SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
+    if (secp256k1_test_rng_precomputed_used == 8) {
+        secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
+        secp256k1_test_rng_precomputed_used = 0;
+    }
+    return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
+}
+
+static uint32_t secp256k1_rand_bits(int bits) {
+    uint32_t ret;
+    if (secp256k1_test_rng_integer_bits_left < bits) {
+        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left);
+        secp256k1_test_rng_integer_bits_left += 32;
+    }
+    ret = secp256k1_test_rng_integer;
+    secp256k1_test_rng_integer >>= bits;
+    secp256k1_test_rng_integer_bits_left -= bits;
+    ret &= ((~((uint32_t)0)) >> (32 - bits));
+    return ret;
+}
+
+static uint32_t secp256k1_rand_int(uint32_t range) {
+    /* We want a uniform integer between 0 and range-1, inclusive.
+     * B is the smallest number such that range <= 2**B.
+     * two mechanisms implemented here:
+     * - generate B bits numbers until one below range is found, and return it
+     * - find the largest multiple M of range that is <= 2**(B+A), generate B+A
+     *   bits numbers until one below M is found, and return it modulo range
+     * The second mechanism consumes A more bits of entropy in every iteration,
+     * but may need fewer iterations due to M being closer to 2**(B+A) then
+     * range is to 2**B. The array below (indexed by B) contains a 0 when the
+     * first mechanism is to be used, and the number A otherwise.
+     */
+    static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0};
+    uint32_t trange, mult;
+    int bits = 0;
+    if (range <= 1) {
+        return 0;
+    }
+    trange = range - 1;
+    while (trange > 0) {
+        trange >>= 1;
+        bits++;
+    }
+    if (addbits[bits]) {
+        bits = bits + addbits[bits];
+        mult = ((~((uint32_t)0)) >> (32 - bits)) / range;
+        trange = range * mult;
+    } else {
+        trange = range;
+        mult = 1;
+    }
+    while(1) {
+        uint32_t x = secp256k1_rand_bits(bits);
+        if (x < trange) {
+            return (mult == 1) ? x : (x % range);
+        }
+    }
+}
+
+static void secp256k1_rand256(unsigned char *b32) {
+    secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
+}
+
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) {
+    size_t bits = 0;
+    memset(bytes, 0, len);
+    while (bits < len * 8) {
+        int now;
+        uint32_t val;
+        now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31;
+        val = secp256k1_rand_bits(1);
+        while (now > 0 && bits < len * 8) {
+            bytes[bits / 8] |= val << (bits % 8);
+            now--;
+            bits++;
+        }
+    }
+}
+
+static void secp256k1_rand256_test(unsigned char *b32) {
+    secp256k1_rand_bytes_test(b32, 32);
+}
+
+#endif /* SECP256K1_TESTRAND_IMPL_H */

src/secp256k1_tests/util.h

@@ -0,0 +1,121 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_UTIL_H
+#define SECP256K1_UTIL_H
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <stdio.h>
+
+typedef struct {
+    void (*fn)(const char *text, void* data);
+    const void* data;
+} secp256k1_callback;
+
+static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
+    cb->fn(text, (void*)cb->data);
+}
+
+#ifdef DETERMINISTIC
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s\n", msg); \
+    abort(); \
+} while(0);
+#else
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \
+    abort(); \
+} while(0)
+#endif
+
+#if SECP256K1_GNUC_PREREQ(3, 0)
+#define EXPECT(x,c) __builtin_expect((x),(c))
+#else
+#define EXPECT(x,c) (x)
+#endif
+
+#ifdef DETERMINISTIC
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed"); \
+    } \
+} while(0)
+#else
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed: " #cond); \
+    } \
+} while(0)
+#endif
+
+/* Like assert(), but when VERIFY is defined, and side-effect safe. */
+#if defined(COVERAGE)
+#define VERIFY_CHECK(check)
+#define VERIFY_SETUP(stmt)
+#elif defined(VERIFY)
+#define VERIFY_CHECK CHECK
+#define VERIFY_SETUP(stmt) do { stmt; } while(0)
+#else
+#define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
+#define VERIFY_SETUP(stmt)
+#endif
+
+static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
+    void *ret = malloc(size);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
+    return ret;
+}
+
+static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) {
+    void *ret = realloc(ptr, size);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
+    return ret;
+}
+
+/* Macro for restrict, when available and not in a VERIFY build. */
+#if defined(SECP256K1_BUILD) && defined(VERIFY)
+# define SECP256K1_RESTRICT
+#else
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(3,0)
+#   define SECP256K1_RESTRICT __restrict__
+#  elif (defined(_MSC_VER) && _MSC_VER >= 1400)
+#   define SECP256K1_RESTRICT __restrict
+#  else
+#   define SECP256K1_RESTRICT
+#  endif
+# else
+#  define SECP256K1_RESTRICT restrict
+# endif
+#endif
+
+#if defined(_WIN32)
+# define I64FORMAT "I64d"
+# define I64uFORMAT "I64u"
+#else
+# define I64FORMAT "lld"
+# define I64uFORMAT "llu"
+#endif
+
+#if defined(HAVE___INT128)
+# if defined(__GNUC__)
+#  define SECP256K1_GNUC_EXT __extension__
+# else
+#  define SECP256K1_GNUC_EXT
+# endif
+SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+#endif
+
+#endif /* SECP256K1_UTIL_H */