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-rw-r--r--crypto/secp256k1/libsecp256k1/src/scalar_impl.h370
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diff --git a/crypto/secp256k1/libsecp256k1/src/scalar_impl.h b/crypto/secp256k1/libsecp256k1/src/scalar_impl.h
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--- a/crypto/secp256k1/libsecp256k1/src/scalar_impl.h
+++ /dev/null
@@ -1,370 +0,0 @@
-/**********************************************************************
- * 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 x ^ (2^N - 1) for some values of N. */
- secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
-
- secp256k1_scalar_sqr(&x2, x);
- secp256k1_scalar_mul(&x2, &x2, x);
-
- secp256k1_scalar_sqr(&x3, &x2);
- secp256k1_scalar_mul(&x3, &x3, x);
-
- secp256k1_scalar_sqr(&x4, &x3);
- secp256k1_scalar_mul(&x4, &x4, x);
-
- secp256k1_scalar_sqr(&x6, &x4);
- secp256k1_scalar_sqr(&x6, &x6);
- secp256k1_scalar_mul(&x6, &x6, &x2);
-
- secp256k1_scalar_sqr(&x7, &x6);
- secp256k1_scalar_mul(&x7, &x7, x);
-
- secp256k1_scalar_sqr(&x8, &x7);
- secp256k1_scalar_mul(&x8, &x8, x);
-
- secp256k1_scalar_sqr(&x15, &x8);
- for (i = 0; i < 6; i++) {
- secp256k1_scalar_sqr(&x15, &x15);
- }
- secp256k1_scalar_mul(&x15, &x15, &x7);
-
- secp256k1_scalar_sqr(&x30, &x15);
- for (i = 0; i < 14; i++) {
- secp256k1_scalar_sqr(&x30, &x30);
- }
- secp256k1_scalar_mul(&x30, &x30, &x15);
-
- secp256k1_scalar_sqr(&x60, &x30);
- for (i = 0; i < 29; i++) {
- secp256k1_scalar_sqr(&x60, &x60);
- }
- secp256k1_scalar_mul(&x60, &x60, &x30);
-
- secp256k1_scalar_sqr(&x120, &x60);
- for (i = 0; i < 59; i++) {
- secp256k1_scalar_sqr(&x120, &x120);
- }
- secp256k1_scalar_mul(&x120, &x120, &x60);
-
- secp256k1_scalar_sqr(&x127, &x120);
- for (i = 0; i < 6; i++) {
- secp256k1_scalar_sqr(&x127, &x127);
- }
- secp256k1_scalar_mul(&x127, &x127, &x7);
-
- /* Then accumulate the final result (t starts at x127). */
- t = &x127;
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 4; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x3); /* 111 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 4; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x3); /* 111 */
- for (i = 0; i < 3; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- 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 < 4; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 5; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x4); /* 1111 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 3; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 4; i++) { /* 000 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- 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 < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 3; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 3; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 5; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x4); /* 1111 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 5; i++) { /* 000 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- for (i = 0; i < 4; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- for (i = 0; i < 2; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- for (i = 0; i < 8; i++) { /* 000000 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- for (i = 0; i < 3; i++) { /* 0 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, &x2); /* 11 */
- for (i = 0; i < 3; i++) { /* 00 */
- secp256k1_scalar_sqr(t, t);
- }
- secp256k1_scalar_mul(t, t, x); /* 1 */
- 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
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