scalar.c

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/* Copyright (c) 2018, Google Inc.
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
 
#include <openssl/ec.h>
#include <openssl/err.h>
#include <openssl/mem.h>
 
#include "internal.h"
#include "../bn/internal.h"
#include "../../internal.h"
 
 
int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
                        const BIGNUM *in) {
  if (!bn_copy_words(out->words, group->order.width, in) ||
      !bn_less_than_words(out->words, group->order.d, group->order.width)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_SCALAR);
    return 0;
  }
  return 1;
}
 
int ec_scalar_equal_vartime(const EC_GROUP *group, const EC_SCALAR *a,
                            const EC_SCALAR *b) {
  return OPENSSL_memcmp(a->words, b->words,
                        group->order.width * sizeof(BN_ULONG)) == 0;
}
 
int ec_scalar_is_zero(const EC_GROUP *group, const EC_SCALAR *a) {
  BN_ULONG mask = 0;
  for (int i = 0; i < group->order.width; i++) {
    mask |= a->words[i];
  }
  return mask == 0;
}
 
int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out,
                             const uint8_t additional_data[32]) {
  return bn_rand_range_words(out->words, 1, group->order.d, group->order.width,
                             additional_data);
}
 
void ec_scalar_to_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len,
                        const EC_SCALAR *in) {
  size_t len = BN_num_bytes(&group->order);
  for (size_t i = 0; i < len; i++) {
    out[len - i - 1] = in->bytes[i];
  }
  *out_len = len;
}
 
int ec_scalar_from_bytes(const EC_GROUP *group, EC_SCALAR *out,
                         const uint8_t *in, size_t len) {
  if (len != BN_num_bytes(&group->order)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_SCALAR);
    return 0;
  }
 
  OPENSSL_memset(out, 0, sizeof(EC_SCALAR));
 
  for (size_t i = 0; i < len; i++) {
    out->bytes[i] = in[len - i - 1];
  }
 
  if (!bn_less_than_words(out->words, group->order.d, group->order.width)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_SCALAR);
    return 0;
  }
 
  return 1;
}
 
void ec_scalar_reduce(const EC_GROUP *group, EC_SCALAR *out,
                      const BN_ULONG *words, size_t num) {
  // Convert "from" Montgomery form so the value is reduced modulo the order.
  bn_from_montgomery_small(out->words, group->order.width, words, num,
                           group->order_mont);
  // Convert "to" Montgomery form to remove the R^-1 factor added.
  ec_scalar_to_montgomery(group, out, out);
}
 
void ec_scalar_add(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a,
                   const EC_SCALAR *b) {
  const BIGNUM *order = &group->order;
  BN_ULONG tmp[EC_MAX_WORDS];
  bn_mod_add_words(r->words, a->words, b->words, order->d, tmp, order->width);
  OPENSSL_cleanse(tmp, sizeof(tmp));
}
 
void ec_scalar_sub(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a,
                   const EC_SCALAR *b) {
  const BIGNUM *order = &group->order;
  BN_ULONG tmp[EC_MAX_WORDS];
  bn_mod_sub_words(r->words, a->words, b->words, order->d, tmp, order->width);
  OPENSSL_cleanse(tmp, sizeof(tmp));
}
 
void ec_scalar_neg(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a) {
  EC_SCALAR zero;
  OPENSSL_memset(&zero, 0, sizeof(EC_SCALAR));
  ec_scalar_sub(group, r, &zero, a);
}
 
void ec_scalar_select(const EC_GROUP *group, EC_SCALAR *out, BN_ULONG mask,
                      const EC_SCALAR *a, const EC_SCALAR *b) {
  const BIGNUM *order = &group->order;
  bn_select_words(out->words, mask, a->words, b->words, order->width);
}
 
void ec_scalar_to_montgomery(const EC_GROUP *group, EC_SCALAR *r,
                             const EC_SCALAR *a) {
  const BIGNUM *order = &group->order;
  bn_to_montgomery_small(r->words, a->words, order->width, group->order_mont);
}
 
void ec_scalar_from_montgomery(const EC_GROUP *group, EC_SCALAR *r,
                               const EC_SCALAR *a) {
  const BIGNUM *order = &group->order;
  bn_from_montgomery_small(r->words, order->width, a->words, order->width,
                           group->order_mont);
}
 
void ec_scalar_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r,
                              const EC_SCALAR *a, const EC_SCALAR *b) {
  const BIGNUM *order = &group->order;
  bn_mod_mul_montgomery_small(r->words, a->words, b->words, order->width,
                              group->order_mont);
}
 
void ec_simple_scalar_inv0_montgomery(const EC_GROUP *group, EC_SCALAR *r,
                                      const EC_SCALAR *a) {
  const BIGNUM *order = &group->order;
  bn_mod_inverse0_prime_mont_small(r->words, a->words, order->width,
                                   group->order_mont);
}
 
int ec_simple_scalar_to_montgomery_inv_vartime(const EC_GROUP *group,
                                               EC_SCALAR *r,
                                               const EC_SCALAR *a) {
  if (ec_scalar_is_zero(group, a)) {
    return 0;
  }
 
  // This implementation (in fact) runs in constant time,
  // even though for this interface it is not mandatory.
 
  // r = a^-1 in the Montgomery domain. This is
  // |ec_scalar_to_montgomery| followed by |ec_scalar_inv0_montgomery|, but
  // |ec_scalar_inv0_montgomery| followed by |ec_scalar_from_montgomery| is
  // equivalent and slightly more efficient.
  ec_scalar_inv0_montgomery(group, r, a);
  ec_scalar_from_montgomery(group, r, r);
  return 1;
}
 
void ec_scalar_inv0_montgomery(const EC_GROUP *group, EC_SCALAR *r,
                               const EC_SCALAR *a) {
  group->meth->scalar_inv0_montgomery(group, r, a);
}
 
int ec_scalar_to_montgomery_inv_vartime(const EC_GROUP *group, EC_SCALAR *r,
                                        const EC_SCALAR *a) {
  return group->meth->scalar_to_montgomery_inv_vartime(group, r, a);
}