


/**********************************************************************




* 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/mitlicense.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, cb);




}




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 (nb)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 cacheline 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/chesrump20130822.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_t 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
