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Diffstat (limited to 'src/ecmult_gen_impl.h')
-rw-r--r-- | src/ecmult_gen_impl.h | 118 |
1 files changed, 118 insertions, 0 deletions
diff --git a/src/ecmult_gen_impl.h b/src/ecmult_gen_impl.h new file mode 100644 index 0000000000..07859ab04b --- /dev/null +++ b/src/ecmult_gen_impl.h @@ -0,0 +1,118 @@ +/********************************************************************** + * 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_IMPL_H_ +#define _SECP256K1_ECMULT_GEN_IMPL_H_ + +#include "scalar.h" +#include "group.h" +#include "ecmult_gen.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. + * To make memory access uniform, the bytes of prec(i, n_i) are sliced per value of n_i. */ + unsigned char prec[64][sizeof(secp256k1_ge_t)][16]; /* prec[j][k][i] = k'th byte of (16^j * i * G + U_i) */ +} secp256k1_ecmult_gen_consts_t; + +static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL; + +static void secp256k1_ecmult_gen_start(void) { + if (secp256k1_ecmult_gen_consts != NULL) + return; + + /* Allocate the precomputation table. */ + secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)malloc(sizeof(secp256k1_ecmult_gen_consts_t)); + + /* get the generator */ + const secp256k1_ge_t *g = &secp256k1_ge_consts->g; + secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g); + + /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */ + secp256k1_gej_t nums_gej; + { + static const unsigned char nums_b32[32] = "The scalar for this x is unknown"; + secp256k1_fe_t nums_x; + secp256k1_fe_set_b32(&nums_x, nums_b32); + secp256k1_ge_t nums_ge; + VERIFY_CHECK(secp256k1_ge_set_xo(&nums_ge, &nums_x, 0)); + 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, g); + } + + /* compute prec. */ + secp256k1_ge_t prec[1024]; + { + secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */ + secp256k1_gej_t gbase; gbase = gj; /* 16^j * G */ + secp256k1_gej_t numsbase; numsbase = nums_gej; /* 2^j * nums. */ + for (int j=0; j<64; j++) { + /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */ + precj[j*16] = numsbase; + for (int i=1; i<16; i++) { + secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase); + } + /* Multiply gbase by 16. */ + for (int i=0; i<4; i++) { + secp256k1_gej_double_var(&gbase, &gbase); + } + /* Multiply numbase by 2. */ + secp256k1_gej_double_var(&numsbase, &numsbase); + 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); + } + } + secp256k1_ge_set_all_gej_var(1024, prec, precj); + } + for (int j=0; j<64; j++) { + for (int i=0; i<16; i++) { + const unsigned char* raw = (const unsigned char*)(&prec[j*16 + i]); + for (size_t k=0; k<sizeof(secp256k1_ge_t); k++) + ret->prec[j][k][i] = raw[k]; + } + } + + /* Set the global pointer to the precomputation table. */ + secp256k1_ecmult_gen_consts = ret; +} + +static void secp256k1_ecmult_gen_stop(void) { + if (secp256k1_ecmult_gen_consts == NULL) + return; + + secp256k1_ecmult_gen_consts_t *c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts; + secp256k1_ecmult_gen_consts = NULL; + free(c); +} + +static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) { + const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts; + secp256k1_gej_set_infinity(r); + secp256k1_ge_t add; + int bits; + for (int j=0; j<64; j++) { + bits = secp256k1_scalar_get_bits(gn, j * 4, 4); + for (size_t k=0; k<sizeof(secp256k1_ge_t); k++) + ((unsigned char*)(&add))[k] = c->prec[j][k][bits]; + secp256k1_gej_add_ge(r, r, &add); + } + bits = 0; + secp256k1_ge_clear(&add); +} + +#endif |