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Diffstat (limited to 'src/secp256k1/src/scalar_impl.h')
| -rw-r--r-- | src/secp256k1/src/scalar_impl.h | 152 |
1 files changed, 152 insertions, 0 deletions
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h index ddc5061c76..7fc159df77 100644 --- a/src/secp256k1/src/scalar_impl.h +++ b/src/secp256k1/src/scalar_impl.h @@ -9,6 +9,7 @@ #include <string.h> +#include "group.h" #include "scalar.h" #if defined HAVE_CONFIG_H @@ -23,12 +24,132 @@ #error "Please select scalar implementation" #endif +typedef struct { +#ifndef USE_NUM_NONE + secp256k1_num_t order; +#endif +#ifdef USE_ENDOMORPHISM + secp256k1_scalar_t minus_lambda, minus_b1, minus_b2, g1, g2; +#endif +} secp256k1_scalar_consts_t; + +static const secp256k1_scalar_consts_t *secp256k1_scalar_consts = NULL; + +static void secp256k1_scalar_start(void) { + if (secp256k1_scalar_consts != NULL) + return; + + /* Allocate. */ + secp256k1_scalar_consts_t *ret = (secp256k1_scalar_consts_t*)malloc(sizeof(secp256k1_scalar_consts_t)); + +#ifndef USE_NUM_NONE + static const unsigned char secp256k1_scalar_consts_order[] = { + 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 + }; + secp256k1_num_set_bin(&ret->order, secp256k1_scalar_consts_order, sizeof(secp256k1_scalar_consts_order)); +#endif +#ifdef USE_ENDOMORPHISM + /** + * Lambda is a scalar which has the property for secp256k1 that point multiplication by + * it is efficiently computable (see secp256k1_gej_mul_lambda). */ + static const unsigned char secp256k1_scalar_consts_lambda[32] = { + 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'). + */ + static const unsigned char secp256k1_scalar_consts_minus_b1[32] = { + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28, + 0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3 + }; + static const unsigned char secp256k1_scalar_consts_b2[32] = { + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd, + 0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15 + }; + static const unsigned char secp256k1_scalar_consts_g1[32] = { + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x30,0x86, + 0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c, + 0x90,0xe4,0x92,0x84,0xeb,0x15,0x3d,0xab + }; + static const unsigned char secp256k1_scalar_consts_g2[32] = { + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0xe4,0x43, + 0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54, + 0x7f,0xa9,0x0a,0xbf,0xe4,0xc4,0x22,0x12 + }; + + secp256k1_scalar_set_b32(&ret->minus_lambda, secp256k1_scalar_consts_lambda, NULL); + secp256k1_scalar_negate(&ret->minus_lambda, &ret->minus_lambda); + secp256k1_scalar_set_b32(&ret->minus_b1, secp256k1_scalar_consts_minus_b1, NULL); + secp256k1_scalar_set_b32(&ret->minus_b2, secp256k1_scalar_consts_b2, NULL); + secp256k1_scalar_negate(&ret->minus_b2, &ret->minus_b2); + secp256k1_scalar_set_b32(&ret->g1, secp256k1_scalar_consts_g1, NULL); + secp256k1_scalar_set_b32(&ret->g2, secp256k1_scalar_consts_g2, NULL); +#endif + + /* Set the global pointer. */ + secp256k1_scalar_consts = ret; +} + +static void secp256k1_scalar_stop(void) { + if (secp256k1_scalar_consts == NULL) + return; + + secp256k1_scalar_consts_t *c = (secp256k1_scalar_consts_t*)secp256k1_scalar_consts; + secp256k1_scalar_consts = NULL; + free(c); +} + +#ifndef USE_NUM_NONE static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) { unsigned char c[32]; secp256k1_scalar_get_b32(c, a); secp256k1_num_set_bin(r, c, 32); } +static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) { + *r = secp256k1_scalar_consts->order; +} +#endif static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) { /* First compute x ^ (2^N - 1) for some values of N. */ @@ -181,4 +302,35 @@ static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scal secp256k1_scalar_mul(r, t, &x6); /* 111111 */ } +static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) { +#if defined(USE_SCALAR_INV_BUILTIN) + secp256k1_scalar_inverse(r, x); +#elif defined(USE_SCALAR_INV_NUM) + unsigned char b[32]; + secp256k1_scalar_get_b32(b, x); + secp256k1_num_t n; + secp256k1_num_set_bin(&n, b, 32); + secp256k1_num_mod_inverse(&n, &n, &secp256k1_scalar_consts->order); + secp256k1_num_get_bin(b, 32, &n); + secp256k1_scalar_set_b32(r, b, NULL); +#else +#error "Please select scalar inverse implementation" +#endif +} + +#ifdef USE_ENDOMORPHISM +static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) { + VERIFY_CHECK(r1 != a); + VERIFY_CHECK(r2 != a); + secp256k1_scalar_t c1, c2; + secp256k1_scalar_mul_shift_var(&c1, a, &secp256k1_scalar_consts->g1, 272); + secp256k1_scalar_mul_shift_var(&c2, a, &secp256k1_scalar_consts->g2, 272); + secp256k1_scalar_mul(&c1, &c1, &secp256k1_scalar_consts->minus_b1); + secp256k1_scalar_mul(&c2, &c2, &secp256k1_scalar_consts->minus_b2); + secp256k1_scalar_add(r2, &c1, &c2); + secp256k1_scalar_mul(r1, r2, &secp256k1_scalar_consts->minus_lambda); + secp256k1_scalar_add(r1, r1, a); +} +#endif + #endif |