src/ecmult_gen_impl.h

   1 /**********************************************************************
   2  * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
   3  * Distributed under the MIT software license, see the accompanying   *
   4  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   5  **********************************************************************/
   6
   7 #ifndef SECP256K1_ECMULT_GEN_IMPL_H
   8 #define SECP256K1_ECMULT_GEN_IMPL_H
   9
  10 #include "scalar.h"
  11 #include "group.h"
  12 #include "ecmult_gen.h"
  13 #include "hash_impl.h"
  14 #ifdef USE_ECMULT_STATIC_PRECOMPUTATION
  15 #include "ecmult_static_context.h"
  16 #endif
  17 static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
  18     ctx->prec = NULL;
  19 }
  20
  21 static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
  22 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
  23     secp256k1_ge prec[1024];
  24     secp256k1_gej gj;
  25     secp256k1_gej nums_gej;
  26     int i, j;
  27 #endif
  28
  29     if (ctx->prec != NULL) {
  30         return;
  31     }
  32 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
  33     ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
  34
  35     /* get the generator */
  36     secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
  37
  38     /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
  39     {
  40         static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
  41         secp256k1_fe nums_x;
  42         secp256k1_ge nums_ge;
  43         int r;
  44         r = secp256k1_fe_set_b32(&nums_x, nums_b32);
  45         (void)r;
  46         VERIFY_CHECK(r);
  47         r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
  48         (void)r;
  49         VERIFY_CHECK(r);
  50         secp256k1_gej_set_ge(&nums_gej, &nums_ge);
  51         /* Add G to make the bits in x uniformly distributed. */
  52         secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
  53     }
  54
  55     /* compute prec. */
  56     {
  57         secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
  58         secp256k1_gej gbase;
  59         secp256k1_gej numsbase;
  60         gbase = gj; /* 16^j * G */
  61         numsbase = nums_gej; /* 2^j * nums. */
  62         for (j = 0; j < 64; j++) {
  63             /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
  64             precj[j*16] = numsbase;
  65             for (i = 1; i < 16; i++) {
  66                 secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
  67             }
  68             /* Multiply gbase by 16. */
  69             for (i = 0; i < 4; i++) {
  70                 secp256k1_gej_double_var(&gbase, &gbase, NULL);
  71             }
  72             /* Multiply numbase by 2. */
  73             secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
  74             if (j == 62) {
  75                 /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
  76                 secp256k1_gej_neg(&numsbase, &numsbase);
  77                 secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
  78             }
  79         }
  80         secp256k1_ge_set_all_gej_var(prec, precj, 1024, cb);
  81     }
  82     for (j = 0; j < 64; j++) {
  83         for (i = 0; i < 16; i++) {
  84             secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
  85         }
  86     }
  87 #else
  88     (void)cb;
  89     ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
  90 #endif
  91     secp256k1_ecmult_gen_blind(ctx, NULL);
  92 }
  93
  94 static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
  95     return ctx->prec != NULL;
  96 }
  97
  98 static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
  99                                                const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
 100     if (src->prec == NULL) {
 101         dst->prec = NULL;
 102     } else {
 103 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
 104         dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
 105         memcpy(dst->prec, src->prec, sizeof(*dst->prec));
 106 #else
 107         (void)cb;
 108         dst->prec = src->prec;
 109 #endif
 110         dst->initial = src->initial;
 111         dst->blind = src->blind;
 112     }
 113 }
 114
 115 static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
 116 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
 117     free(ctx->prec);
 118 #endif
 119     secp256k1_scalar_clear(&ctx->blind);
 120     secp256k1_gej_clear(&ctx->initial);
 121     ctx->prec = NULL;
 122 }
 123
 124 static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
 125     secp256k1_ge add;
 126     secp256k1_ge_storage adds;
 127     secp256k1_scalar gnb;
 128     int bits;
 129     int i, j;
 130     memset(&adds, 0, sizeof(adds));
 131     *r = ctx->initial;
 132     /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
 133     secp256k1_scalar_add(&gnb, gn, &ctx->blind);
 134     add.infinity = 0;
 135     for (j = 0; j < 64; j++) {
 136         bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
 137         for (i = 0; i < 16; i++) {
 138             /** This uses a conditional move to avoid any secret data in array indexes.
 139              *   _Any_ use of secret indexes has been demonstrated to result in timing
 140              *   sidechannels, even when the cache-line access patterns are uniform.
 141              *  See also:
 142              *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
 143              *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
 144              *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
 145              *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
 146              *    (http://www.tau.ac.il/~tromer/papers/cache.pdf)
 147              */
 148             secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
 149         }
 150         secp256k1_ge_from_storage(&add, &adds);
 151         secp256k1_gej_add_ge(r, r, &add);
 152     }
 153     bits = 0;
 154     secp256k1_ge_clear(&add);
 155     secp256k1_scalar_clear(&gnb);
 156 }
 157
 158 /* Setup blinding values for secp256k1_ecmult_gen. */
 159 static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
 160     secp256k1_scalar b;
 161     secp256k1_gej gb;
 162     secp256k1_fe s;
 163     unsigned char nonce32[32];
 164     secp256k1_rfc6979_hmac_sha256_t rng;
 165     int retry;
 166     unsigned char keydata[64] = {0};
 167     if (seed32 == NULL) {
 168         /* When seed is NULL, reset the initial point and blinding value. */
 169         secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
 170         secp256k1_gej_neg(&ctx->initial, &ctx->initial);
 171         secp256k1_scalar_set_int(&ctx->blind, 1);
 172     }
 173     /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
 174     secp256k1_scalar_get_b32(nonce32, &ctx->blind);
 175     /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
 176      *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
 177      *   asking the caller for blinding values directly and expecting them to retry on failure.
 178      */
 179     memcpy(keydata, nonce32, 32);
 180     if (seed32 != NULL) {
 181         memcpy(keydata + 32, seed32, 32);
 182     }
 183     secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
 184     memset(keydata, 0, sizeof(keydata));
 185     /* Retry for out of range results to achieve uniformity. */
 186     do {
 187         secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
 188         retry = !secp256k1_fe_set_b32(&s, nonce32);
 189         retry |= secp256k1_fe_is_zero(&s);
 190     } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
 191     /* Randomize the projection to defend against multiplier sidechannels. */
 192     secp256k1_gej_rescale(&ctx->initial, &s);
 193     secp256k1_fe_clear(&s);
 194     do {
 195         secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
 196         secp256k1_scalar_set_b32(&b, nonce32, &retry);
 197         /* A blinding value of 0 works, but would undermine the projection hardening. */
 198         retry |= secp256k1_scalar_is_zero(&b);
 199     } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
 200     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 201     memset(nonce32, 0, 32);
 202     secp256k1_ecmult_gen(ctx, &gb, &b);
 203     secp256k1_scalar_negate(&b, &b);
 204     ctx->blind = b;
 205     ctx->initial = gb;
 206     secp256k1_scalar_clear(&b);
 207     secp256k1_gej_clear(&gb);
 208 }
 209
 210 #endif /* SECP256K1_ECMULT_GEN_IMPL_H */