* context. */
typedef int32_t fe[10];
+static const int64_t kBottom25Bits = 0x1ffffffLL;
+static const int64_t kBottom26Bits = 0x3ffffffLL;
+static const int64_t kTop39Bits = 0xfffffffffe000000LL;
+static const int64_t kTop38Bits = 0xfffffffffc000000LL;
+
static uint64_t load_3(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
int64_t carry8;
int64_t carry9;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
- int32_t carry0;
- int32_t carry1;
- int32_t carry2;
- int32_t carry3;
- int32_t carry4;
- int32_t carry5;
- int32_t carry6;
- int32_t carry7;
- int32_t carry8;
- int32_t carry9;
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
q = (h0 + q) >> 26;
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
- carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
- carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
- carry9 = h9 >> 25; h9 -= carry9 << 25;
+ h1 += h0 >> 26; h0 &= kBottom26Bits;
+ h2 += h1 >> 25; h1 &= kBottom25Bits;
+ h3 += h2 >> 26; h2 &= kBottom26Bits;
+ h4 += h3 >> 25; h3 &= kBottom25Bits;
+ h5 += h4 >> 26; h4 &= kBottom26Bits;
+ h6 += h5 >> 25; h5 &= kBottom25Bits;
+ h7 += h6 >> 26; h6 &= kBottom26Bits;
+ h8 += h7 >> 25; h7 &= kBottom25Bits;
+ h9 += h8 >> 26; h8 &= kBottom26Bits;
+ h9 &= kBottom25Bits;
/* h10 = carry9 */
/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
- s[3] = (h0 >> 24) | (h1 << 2);
+ s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
s[4] = h1 >> 6;
s[5] = h1 >> 14;
- s[6] = (h1 >> 22) | (h2 << 3);
+ s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
s[7] = h2 >> 5;
s[8] = h2 >> 13;
- s[9] = (h2 >> 21) | (h3 << 5);
+ s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
s[10] = h3 >> 3;
s[11] = h3 >> 11;
- s[12] = (h3 >> 19) | (h4 << 6);
+ s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
- s[19] = (h5 >> 24) | (h6 << 1);
+ s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
s[20] = h6 >> 7;
s[21] = h6 >> 15;
- s[22] = (h6 >> 23) | (h7 << 3);
+ s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
s[23] = h7 >> 5;
s[24] = h7 >> 13;
- s[25] = (h7 >> 21) | (h8 << 4);
+ s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
s[26] = h8 >> 4;
s[27] = h8 >> 12;
- s[28] = (h8 >> 20) | (h9 << 6);
+ s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
* |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
int64_t carry8;
int64_t carry9;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
fe_mul(out, t1, t0);
}
-#if 0 /* Ed25519 code: not used yet */
-
/* h = -f
*
* Preconditions:
}
}
-/* return 0 if f == 0
- * return 1 if f != 0
- *
- * Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnonzero(const fe f) {
- uint8_t s[32];
- static const uint8_t zero[32] = {0};
-
- fe_tobytes(s, f);
- return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
-}
-
-/* return 1 if f is in {1,3,5,...,q-2}
- * return 0 if f is in {0,2,4,...,q-1}
- *
- * Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnegative(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
- return s[0] & 1;
-}
-
/* h = 2 * f * f
* Can overlap h with f.
*
h8 += h8;
h9 += h9;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[9] = h9;
}
-static void fe_pow22523(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- int i;
-
- fe_sq(t0, z);
- for (i = 1; i < 1; ++i) {
- fe_sq(t0, t0);
- }
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t0, t0);
- for (i = 1; i < 1; ++i) {
- fe_sq(t0, t0);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 20; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 100; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t0, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t0, t0);
- }
- fe_mul(out, t0, z);
-}
-
/* ge means group element.
* Here the group is the set of pairs (x,y) of field elements (see fe.h)
fe T2d;
} ge_cached;
-static void ge_tobytes(uint8_t *s, const ge_p2 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116};
-
-static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482};
-
-static int ge_frombytes_negate_vartime(ge_p3 *h, const uint8_t *s) {
- fe u;
- fe v;
- fe v3;
- fe vxx;
- fe check;
-
- fe_frombytes(h->Y, s);
- fe_1(h->Z);
- fe_sq(u, h->Y);
- fe_mul(v, u, d);
- fe_sub(u, u, h->Z); /* u = y^2-1 */
- fe_add(v, v, h->Z); /* v = dy^2+1 */
-
- fe_sq(v3, v);
- fe_mul(v3, v3, v); /* v3 = v^3 */
- fe_sq(h->X, v3);
- fe_mul(h->X, h->X, v);
- fe_mul(h->X, h->X, u); /* x = uv^7 */
-
- fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
- fe_mul(h->X, h->X, v3);
- fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
-
- fe_sq(vxx, h->X);
- fe_mul(vxx, vxx, v);
- fe_sub(check, vxx, u); /* vx^2-u */
- if (fe_isnonzero(check)) {
- fe_add(check, vxx, u); /* vx^2+u */
- if (fe_isnonzero(check)) {
- return -1;
- }
- fe_mul(h->X, h->X, sqrtm1);
- }
-
- if (fe_isnegative(h->X) == (s[31] >> 7)) {
- fe_neg(h->X, h->X);
- }
-
- fe_mul(h->T, h->X, h->Y);
- return 0;
-}
-
-static void ge_p2_0(ge_p2 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
-}
-
static void ge_p3_0(ge_p3 *h) {
fe_0(h->X);
fe_1(h->Y);
fe_copy(r->Z, p->Z);
}
-static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199};
-
-/* r = p */
-static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
- fe_add(r->YplusX, p->Y, p->X);
- fe_sub(r->YminusX, p->Y, p->X);
- fe_copy(r->Z, p->Z);
- fe_mul(r->T2d, p->T, d2);
-}
-
/* r = p */
static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
fe_mul(r->X, p->X, p->T);
fe_sub(r->T, t0, r->T);
}
-/* r = p - q */
-static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yminusx);
- fe_mul(r->Y, r->Y, q->yplusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
-/* r = p + q */
-static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YplusX);
- fe_mul(r->Y, r->Y, q->YminusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
-}
-
-/* r = p - q */
-static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YminusX);
- fe_mul(r->Y, r->Y, q->YplusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
static uint8_t equal(signed char b, signed char c) {
uint8_t ub = b;
uint8_t uc = c;
return y;
}
-static void cmov(ge_precomp *t, ge_precomp *u, uint8_t b) {
+static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
fe_cmov(t->yplusx, u->yplusx, b);
fe_cmov(t->yminusx, u->yminusx, b);
fe_cmov(t->xy2d, u->xy2d, b);
}
-#if defined(OPENSSL_SMALL)
-
-/* This block of code replaces the standard base-point table with a much smaller
- * one. The standard table is 30,720 bytes while this one is just 960.
- *
- * This table contains 15 pairs of group elements, (x, y), where each field
- * element is serialised with |fe_tobytes|. If |i| is the index of the group
- * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
- * is the most significant bit). The value of the group element is then:
- * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */
-static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
- 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
- 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
- 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
- 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
- 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
- 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
- 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
- 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
- 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
- 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
- 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
- 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
- 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
- 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
- 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
- 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
- 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
- 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
- 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
- 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
- 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
- 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
- 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
- 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
- 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
- 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
- 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
- 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
- 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
- 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
- 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
- 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
- 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
- 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
- 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
- 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
- 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
- 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
- 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
- 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
- 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
- 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
- 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
- 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
- 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
- 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
- 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
- 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
- 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
- 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
- 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
- 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
- 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
- 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
- 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
- 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
- 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
- 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
- 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
- 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
- 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
- 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
- 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
- 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
- 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
- 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
- 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
- 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
- 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
- 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
- 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
- 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
- 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
- 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
- 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
- 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
- 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
-};
-
-static void ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
- /* k25519SmallPrecomp is first expanded into matching |ge_precomp|
- * elements. */
- ge_precomp multiples[15];
-
- unsigned i;
- for (i = 0; i < 15; i++) {
- const uint8_t *bytes = &k25519SmallPrecomp[i*(2 * 32)];
- fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
-
- ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
- }
-
- /* See the comment above |k25519SmallPrecomp| about the structure of the
- * precomputed elements. This loop does 64 additions and 64 doublings to
- * calculate the result. */
- ge_p3_0(h);
-
- for (i = 63; i < 64; i--) {
- unsigned j;
- signed char index = 0;
-
- for (j = 0; j < 4; j++) {
- const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
- index |= (bit << j);
- }
-
- ge_precomp e;
- ge_precomp_0(&e);
-
- for (j = 1; j < 16; j++) {
- cmov(&e, &multiples[j-1], equal(index, j));
- }
-
- ge_cached cached;
- ge_p1p1 r;
- ge_p3_to_cached(&cached, h);
- ge_add(&r, h, &cached);
- ge_p1p1_to_p3(h, &r);
-
- ge_madd(&r, h, &e);
- ge_p1p1_to_p3(h, &r);
- }
-}
-
-#else
-
/* k25519Precomp[i][j] = (j+1)*256^i*B */
-static ge_precomp k25519Precomp[32][8] = {
+static const ge_precomp k25519Precomp[32][8] = {
{
{
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
static void table_select(ge_precomp *t, int pos, signed char b) {
ge_precomp minust;
uint8_t bnegative = negative(b);
- uint8_t babs = b - (((-bnegative) & b) << 1);
+ uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
ge_precomp_0(t);
cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
}
}
-#endif
-
-static void slide(signed char *r, const uint8_t *a) {
- int i;
- int b;
- int k;
-
- for (i = 0; i < 256; ++i) {
- r[i] = 1 & (a[i >> 3] >> (i & 7));
- }
-
- for (i = 0; i < 256; ++i) {
- if (r[i]) {
- for (b = 1; b <= 6 && i + b < 256; ++b) {
- if (r[i + b]) {
- if (r[i] + (r[i + b] << b) <= 15) {
- r[i] += r[i + b] << b;
- r[i + b] = 0;
- } else if (r[i] - (r[i + b] << b) >= -15) {
- r[i] -= r[i + b] << b;
- for (k = i + b; k < 256; ++k) {
- if (!r[k]) {
- r[k] = 1;
- break;
- }
- r[k] = 0;
- }
- } else {
- break;
- }
- }
- }
- }
- }
-}
-
-static ge_precomp Bi[8] = {
- {
- {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
- -11754271, -6079156, 2047605},
- {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378},
- {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
- 11864899, -24514362, -4438546},
- },
- {
- {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
- -14772189, 28944400, -1550024},
- {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
- -11775962, 7689662, 11199574},
- {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
- 10017326, -17749093, -9920357},
- },
- {
- {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
- 14515107, -15438304, 10819380},
- {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306},
- {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
- 13850243, -23678021, -15815942},
- },
- {
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
- 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
- 1370708, 29794553, -1409300},
- },
- {
- {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
- -1361450, -13062696, 13821877},
- {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
- -7212327, 18853322, -14220951},
- {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
- -10431137, 2207753, -3209784},
- },
- {
- {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
- -663000, -31111463, -16132436},
- {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
- 15725684, 171356, 6466918},
- {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
- -14088058, -30714912, 16193877},
- },
- {
- {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
- 4729455, -18074513, 9256800},
- {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
- 9761698, -19827198, 630305},
- {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
- -15960994, -2449256, -14291300},
- },
- {
- {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
- 15033784, 25105118, -7894876},
- {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
- 1573892, -2625887, 2198790, -15804619},
- {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
- -16236442, -32461234, -12290683},
- },
-};
-
-/* r = a * A + b * B
- * where a = a[0]+256*a[1]+...+256^31 a[31].
- * and b = b[0]+256*b[1]+...+256^31 b[31].
- * B is the Ed25519 base point (x,4/5) with x positive. */
-void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
- const ge_p3 *A, const uint8_t *b) {
- signed char aslide[256];
- signed char bslide[256];
- ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
- ge_p1p1 t;
- ge_p3 u;
- ge_p3 A2;
- int i;
-
- slide(aslide, a);
- slide(bslide, b);
-
- ge_p3_to_cached(&Ai[0], A);
- ge_p3_dbl(&t, A);
- ge_p1p1_to_p3(&A2, &t);
- ge_add(&t, &A2, &Ai[0]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[1], &u);
- ge_add(&t, &A2, &Ai[1]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[2], &u);
- ge_add(&t, &A2, &Ai[2]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[3], &u);
- ge_add(&t, &A2, &Ai[3]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[4], &u);
- ge_add(&t, &A2, &Ai[4]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[5], &u);
- ge_add(&t, &A2, &Ai[5]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[6], &u);
- ge_add(&t, &A2, &Ai[6]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[7], &u);
-
- ge_p2_0(r);
-
- for (i = 255; i >= 0; --i) {
- if (aslide[i] || bslide[i]) {
- break;
- }
- }
-
- for (; i >= 0; --i) {
- ge_p2_dbl(&t, r);
-
- if (aslide[i] > 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_add(&t, &u, &Ai[aslide[i] / 2]);
- } else if (aslide[i] < 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
- }
-
- if (bslide[i] > 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_madd(&t, &u, &Bi[bslide[i] / 2]);
- } else if (bslide[i] < 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
- }
-
- ge_p1p1_to_p2(r, &t);
- }
-}
-
-/* The set of scalars is \Z/l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-
-/* Input:
- * s[0]+256*s[1]+...+256^63*s[63] = s
- *
- * Output:
- * s[0]+256*s[1]+...+256^31*s[31] = s mod l
- * where l = 2^252 + 27742317777372353535851937790883648493.
- * Overwrites s in place. */
-static void sc_reduce(uint8_t *s) {
- int64_t s0 = 2097151 & load_3(s);
- int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
- int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
- int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
- int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
- int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
- int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
- int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
- int64_t s8 = 2097151 & load_3(s + 21);
- int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
- int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
- int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
- int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
- int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
- int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
- int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
- int64_t s16 = 2097151 & load_3(s + 42);
- int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
- int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
- int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
- int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
- int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
- int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
- int64_t s23 = (load_4(s + 60) >> 3);
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-/* Input:
- * a[0]+256*a[1]+...+256^31*a[31] = a
- * b[0]+256*b[1]+...+256^31*b[31] = b
- * c[0]+256*c[1]+...+256^31*c[31] = c
- *
- * Output:
- * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
- const uint8_t *c) {
- int64_t a0 = 2097151 & load_3(a);
- int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
- int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
- int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
- int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
- int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
- int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
- int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
- int64_t a8 = 2097151 & load_3(a + 21);
- int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
- int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
- int64_t a11 = (load_4(a + 28) >> 7);
- int64_t b0 = 2097151 & load_3(b);
- int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
- int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
- int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
- int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
- int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
- int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
- int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
- int64_t b8 = 2097151 & load_3(b + 21);
- int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
- int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
- int64_t b11 = (load_4(b + 28) >> 7);
- int64_t c0 = 2097151 & load_3(c);
- int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
- int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
- int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
- int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
- int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
- int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
- int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
- int64_t c8 = 2097151 & load_3(c + 21);
- int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
- int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
- int64_t c11 = (load_4(c + 28) >> 7);
- int64_t s0;
- int64_t s1;
- int64_t s2;
- int64_t s3;
- int64_t s4;
- int64_t s5;
- int64_t s6;
- int64_t s7;
- int64_t s8;
- int64_t s9;
- int64_t s10;
- int64_t s11;
- int64_t s12;
- int64_t s13;
- int64_t s14;
- int64_t s15;
- int64_t s16;
- int64_t s17;
- int64_t s18;
- int64_t s19;
- int64_t s20;
- int64_t s21;
- int64_t s22;
- int64_t s23;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
- int64_t carry17;
- int64_t carry18;
- int64_t carry19;
- int64_t carry20;
- int64_t carry21;
- int64_t carry22;
-
- s0 = c0 + a0 * b0;
- s1 = c1 + a0 * b1 + a1 * b0;
- s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
- s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
- s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
- s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
- s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
- s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
- a6 * b1 + a7 * b0;
- s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
- a6 * b2 + a7 * b1 + a8 * b0;
- s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
- a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
- s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
- a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
- s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
- a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
- s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
- a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
- s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
- a9 * b4 + a10 * b3 + a11 * b2;
- s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
- a10 * b4 + a11 * b3;
- s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
- a11 * b4;
- s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
- s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
- s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
- s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
- s20 = a9 * b11 + a10 * b10 + a11 * b9;
- s21 = a10 * b11 + a11 * b10;
- s22 = a11 * b11;
- s23 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
- carry18 = (s18 + (1 << 20)) >> 21;
- s19 += carry18;
- s18 -= carry18 << 21;
- carry20 = (s20 + (1 << 20)) >> 21;
- s21 += carry20;
- s20 -= carry20 << 21;
- carry22 = (s22 + (1 << 20)) >> 21;
- s23 += carry22;
- s22 -= carry22 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
- carry17 = (s17 + (1 << 20)) >> 21;
- s18 += carry17;
- s17 -= carry17 << 21;
- carry19 = (s19 + (1 << 20)) >> 21;
- s20 += carry19;
- s19 -= carry19 << 21;
- carry21 = (s21 + (1 << 20)) >> 21;
- s22 += carry21;
- s21 -= carry21 << 21;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
- uint8_t seed[32];
- RAND_bytes(seed, 32);
-
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(seed, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- ge_p3 A;
- ge_scalarmult_base(&A, az);
- ge_p3_tobytes(out_public_key, &A);
-
- memcpy(out_private_key, seed, 32);
- memmove(out_private_key + 32, out_public_key, 32);
-}
-
-int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
- const uint8_t private_key[64]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(private_key, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, az + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t nonce[SHA512_DIGEST_LENGTH];
- SHA512_Final(nonce, &hash_ctx);
-
- sc_reduce(nonce);
- ge_p3 R;
- ge_scalarmult_base(&R, nonce);
- ge_p3_tobytes(out_sig, &R);
-
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, out_sig, 32);
- SHA512_Update(&hash_ctx, private_key + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t hram[SHA512_DIGEST_LENGTH];
- SHA512_Final(hram, &hash_ctx);
-
- sc_reduce(hram);
- sc_muladd(out_sig + 32, hram, az, nonce);
-
- return 1;
-}
-
-int ED25519_verify(const uint8_t *message, size_t message_len,
- const uint8_t signature[64], const uint8_t public_key[32]) {
- ge_p3 A;
- if ((signature[63] & 224) != 0 ||
- ge_frombytes_negate_vartime(&A, public_key) != 0) {
- return 0;
- }
-
- uint8_t pkcopy[32];
- memcpy(pkcopy, public_key, 32);
- uint8_t rcopy[32];
- memcpy(rcopy, signature, 32);
- uint8_t scopy[32];
- memcpy(scopy, signature + 32, 32);
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, signature, 32);
- SHA512_Update(&hash_ctx, public_key, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t h[SHA512_DIGEST_LENGTH];
- SHA512_Final(h, &hash_ctx);
-
- sc_reduce(h);
-
- ge_p2 R;
- ge_double_scalarmult_vartime(&R, h, &A, scopy);
-
- uint8_t rcheck[32];
- ge_tobytes(rcheck, &R);
-
- return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
-}
-
-#endif /* Ed25519 */
-
-
-#if defined(BORINGSSL_X25519_X86_64)
-
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
- x25519_x86_64(out, scalar, point);
-}
-
-#else
-
/* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
int64_t carry8;
int64_t carry9;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
const uint8_t point[32]) {
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- x25519_NEON(out, scalar, point);
- return;
- }
-#endif
-
x25519_scalar_mult_generic(out, scalar, point);
}
-#endif /* BORINGSSL_X25519_X86_64 */
-
-#if 0
-void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
- RAND_bytes(out_private_key, 32);
- X25519_public_from_private(out_public_value, out_private_key);
-}
-
-#endif
-
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
const uint8_t peer_public_value[32]) {
static const uint8_t kZeros[32] = {0};
return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}
-#if 0
-
-#if defined(BORINGSSL_X25519_X86_64)
-
-/* When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
- * the Montgomery ladder because it's faster. Otherwise it's done using the
- * Ed25519 tables. */
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
-}
-
-#else
-
void X25519_public_from_private(uint8_t out_public_value[32],
const uint8_t private_key[32]) {
uint8_t e[32];
ge_p3 A;
fe zplusy, zminusy, zminusy_inv;
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
- return;
- }
-#endif
-
memcpy(e, private_key, 32);
e[0] &= 248;
e[31] &= 127;
fe_mul(zplusy, zplusy, zminusy_inv);
fe_tobytes(out_public_value, zplusy);
}
-
-#endif /* BORINGSSL_X25519_X86_64 */
-
-#endif