* Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
* Copyright 2015-2016 Cryptography Research, Inc.
*
- * Licensed under the OpenSSL license (the "License"). You may not use
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
#define COFACTOR 4
-/* Comb config: number of combs, n, t, s. */
-#define COMBS_N 5
-#define COMBS_T 5
-#define COMBS_S 18
#define C448_WNAF_FIXED_TABLE_BITS 5
#define C448_WNAF_VAR_TABLE_BITS 3
-static const int EDWARDS_D = -39081;
+#define EDWARDS_D (-39081)
+
static const curve448_scalar_t precomputed_scalarmul_adjustment = {
{
{
- SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad),
- SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
+ SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL),
+ SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL)
}
}
};
-#define TWISTED_D ((EDWARDS_D)-1)
+#define TWISTED_D (EDWARDS_D - 1)
#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
-/* Projective Niels coordinates */
-typedef struct {
- gf a, b, c;
-} niels_s, niels_t[1];
-typedef struct {
- niels_t n;
- gf z;
-} VECTOR_ALIGNED pniels_t[1];
-
-/* Precomputed base */
-struct curve448_precomputed_s {
- niels_t table[COMBS_N << (COMBS_T - 1)];
-};
-
-extern const gf curve448_precomputed_base_as_fe[];
-const curve448_precomputed_s *curve448_precomputed_base =
- (const curve448_precomputed_s *)&curve448_precomputed_base_as_fe;
-
/* Inverse. */
static void gf_invert(gf y, const gf x, int assert_nonzero)
{
mask_t ret;
-
gf t1, t2;
+
gf_sqr(t1, x); /* o^2 */
ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
(void)ret;
for (k = 0; k < t; k++) {
unsigned int bit = (i - 1) + s * (k + j * t);
- if (bit < C448_SCALAR_BITS) {
+ if (bit < C448_SCALAR_BITS)
tab |=
(scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
- }
}
invert = (tab >> (t - 1)) - 1;
1 << (t - 1), tab);
cond_neg_niels(ni, invert);
- if ((i != s) || j != 0) {
+ if ((i != s) || j != 0)
add_niels_to_pt(out, ni, j == n - 1 && i != 1);
- } else {
+ else
niels_to_pt(out, ni);
- }
}
}
mask_t swap = 0;
mask_t nz;
- ignore_result(gf_deserialize(x1, base, 1, 0));
+ (void)gf_deserialize(x1, base, 1, 0);
gf_copy(x2, ONE);
gf_copy(z2, ZERO);
gf_copy(x3, x1);
gf_cond_swap(z2, z3, swap);
swap = k_t;
- gf_add_nr(t1, x2, z2); /* A = x2 + z2 *//* 2+e */
- gf_sub_nr(t2, x2, z2); /* B = x2 - z2 *//* 3+e */
- gf_sub_nr(z2, x3, z3); /* D = x3 - z3 *//* 3+e */
+ /*
+ * The "_nr" below skips coefficient reduction. In the following
+ * comments, "2+e" is saying that the coefficients are at most 2+epsilon
+ * times the reduction limit.
+ */
+ gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */
+ gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */
+ gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */
gf_mul(x2, t1, z2); /* DA */
- gf_add_nr(z2, z3, x3); /* C = x3 + z3 *//* 2+e */
+ gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */
gf_mul(x3, t2, z2); /* CB */
- gf_sub_nr(z3, x2, x3); /* DA-CB *//* 3+e */
+ gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */
gf_sqr(z2, z3); /* (DA-CB)^2 */
gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */
- gf_add_nr(z2, x2, x3); /* (DA+CB) *//* 2+e */
+ gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */
gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */
gf_sqr(z2, t1); /* AA = A^2 */
gf_sqr(t1, t2); /* BB = B^2 */
gf_mul(x2, z2, t1); /* x2 = AA*BB */
- gf_sub_nr(t2, z2, t1); /* E = AA-BB *//* 3+e */
+ gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */
gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
- gf_add_nr(t1, t1, z2); /* AA + a24*E *//* 2+e */
+ gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */
gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */
}
curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
/* Compensate for the encoding ratio */
- for (i = 1; i < X448_ENCODE_RATIO; i <<= 1) {
+ for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
curve448_scalar_halve(the_scalar, the_scalar);
- }
+
curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar);
curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
curve448_point_destroy(p);
int power, addend;
};
-#if defined(__GNUC__) || defined(__clang__)
+#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))
# define NUMTRAILINGZEROS __builtin_ctz
#else
# define NUMTRAILINGZEROS numtrailingzeros
if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {
/* Refill the 16 high bits of current */
current += (uint32_t)((scalar->limb[w / B_OVER_16]
- >> (16 * (w % B_OVER_16))) << 16);
+ >> (16 * (w % B_OVER_16))) << 16);
}
while (current & 0xFFFF) {
assert(position >= 0);
if (odd & (1 << (table_bits + 1)))
delta -= (1 << (table_bits + 1));
- current -= delta << pos;
+ current -= delta * (1 << pos);
control[position].power = pos + 16 * (w - 1);
control[position].addend = delta;
position--;
OPENSSL_cleanse(twop, sizeof(twop));
}
-extern const gf curve448_precomputed_wnaf_as_fe[];
-static const niels_t *curve448_wnaf_base =
- (const niels_t *)curve448_precomputed_wnaf_as_fe;
-
void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
const curve448_scalar_t scalar1,
const curve448_point_t base2,
if (i < 0) {
curve448_point_copy(combo, curve448_point_identity);
return;
- } else if (i > control_pre[0].power) {
+ }
+ if (i > control_pre[0].power) {
pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
contv++;
} else if (i == control_pre[0].power && i >= 0) {
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