#include "ec.hpp" namespace llarp { namespace sodium { static inline uint64_t load_3(const byte_t *in) { uint64_t result; result = (uint64_t)in[0]; result |= ((uint64_t)in[1]) << 8; result |= ((uint64_t)in[2]) << 16; return result; } static inline uint64_t load_4(const byte_t *in) { uint64_t result; result = (uint64_t)in[0]; result |= ((uint64_t)in[1]) << 8; result |= ((uint64_t)in[2]) << 16; result |= ((uint64_t)in[3]) << 24; return result; } /* From ge_msub.c */ /* r = p - q */ static void ge25519_msub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->yminusx); fe25519_mul(r->Y, r->Y, q->yplusx); fe25519_mul(r->T, q->xy2d, p->T); fe25519_add(t0, p->Z, p->Z); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_sub(r->Z, t0, r->T); fe25519_add(r->T, t0, r->T); } typedef ge25519_cached ge25519_dsmp[8]; static const ge25519_precomp ge_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}}}; /* From ge_p2_0.c */ static void ge25519_p2_0(ge25519_p2 *h) { fe25519_0(h->X); fe25519_1(h->Y); fe25519_1(h->Z); } static void ge25519_madd(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->yplusx); fe25519_mul(r->Y, r->Y, q->yminusx); fe25519_mul(r->T, q->xy2d, p->T); fe25519_add(t0, p->Z, p->Z); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_add(r->Z, t0, r->T); fe25519_sub(r->T, t0, r->T); } /* From ge_p2_dbl.c */ /* r = 2 * p */ static void ge25519_p2_dbl(ge25519_p1p1 *r, const ge25519_p2 *p) { fe25519 t0; fe25519_sq(r->X, p->X); fe25519_sq(r->Z, p->Y); fe25519_sq2(r->T, p->Z); fe25519_add(r->Y, p->X, p->Y); fe25519_sq(t0, r->Y); fe25519_add(r->Y, r->Z, r->X); fe25519_sub(r->Z, r->Z, r->X); fe25519_sub(r->X, t0, r->Y); fe25519_sub(r->T, r->T, r->Z); } /* From ge_p3_to_p2.c */ /* r = p */ static void ge25519_p3_to_p2(ge25519_p2 *r, const ge25519_p3 *p) { fe25519_copy(r->X, p->X); fe25519_copy(r->Y, p->Y); fe25519_copy(r->Z, p->Z); } /* From ge_p3_dbl.c */ /* r = 2 * p */ static void ge25519_p3_dbl(ge25519_p1p1 *r, const ge25519_p3 *p) { ge25519_p2 q; ge25519_p3_to_p2(&q, p); ge25519_p2_dbl(r, &q); } /* From ge_double_scalarmult.c, modified */ static void slide(signed char *r, const byte_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 void ge25519_dsm_precomp(ge25519_dsmp &r, const ge25519_p3 *s) { ge25519_p1p1 t; ge25519_p3 s2, u; ge25519_p3_to_cached(&r[0], s); ge25519_p3_dbl(&t, s); ge25519_p1p1_to_p3(&s2, &t); ge25519_add(&t, &s2, &r[0]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[1], &u); ge25519_add(&t, &s2, &r[1]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[2], &u); ge25519_add(&t, &s2, &r[2]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[3], &u); ge25519_add(&t, &s2, &r[3]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[4], &u); ge25519_add(&t, &s2, &r[4]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[5], &u); ge25519_add(&t, &s2, &r[5]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[6], &u); ge25519_add(&t, &s2, &r[6]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&r[7], &u); } void sc25519_reduce32(byte_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 = (load_4(s + 28) >> 7); int64_t s12 = 0; 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; 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; 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] = (c-ab) mod l where l = 2^252 + 27742317777372353535851937790883648493. */ void sc25519_mulsub(byte_t *s, const byte_t *a, const byte_t *b, const byte_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; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; 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; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; 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; 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 sc25519_sub(byte_t *s, const byte_t *a, const byte_t *b) { 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 s0 = a0 - b0; int64_t s1 = a1 - b1; int64_t s2 = a2 - b2; int64_t s3 = a3 - b3; int64_t s4 = a4 - b4; int64_t s5 = a5 - b5; int64_t s6 = a6 - b6; int64_t s7 = a7 - b7; int64_t s8 = a8 - b8; int64_t s9 = a9 - b9; int64_t s10 = a10 - b10; int64_t s11 = a11 - b11; int64_t s12 = 0; 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; 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; 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; } static int64_t signum(int64_t a) { return a > 0 ? 1 : a < 0 ? -1 : 0; } int sc25519_check(const byte_t *s) { int64_t s0 = load_4(s); int64_t s1 = load_4(s + 4); int64_t s2 = load_4(s + 8); int64_t s3 = load_4(s + 12); int64_t s4 = load_4(s + 16); int64_t s5 = load_4(s + 20); int64_t s6 = load_4(s + 24); int64_t s7 = load_4(s + 28); return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8; } static const fe25519 fe25519_d = {-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116}; /* d */ const fe25519 fe25519_sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482}; /* sqrt(-1) */ static int fe25519_isnonzero(const fe25519 &f) { unsigned char s[32]; fe25519_tobytes(s, f); return (((int)(s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; } static void fe25519_divpowm1(fe25519 &r, const fe25519 u, const fe25519 v) { fe25519 v3, uv7, t0, t1, t2; int i; fe25519_sq(v3, v); fe25519_mul(v3, v3, v); /* v3 = v^3 */ fe25519_sq(uv7, v3); fe25519_mul(uv7, uv7, v); fe25519_mul(uv7, uv7, u); /* uv7 = uv^7 */ /*fe_pow22523(uv7, uv7);*/ /* From fe_pow22523.c */ fe25519_sq(t0, uv7); fe25519_sq(t1, t0); fe25519_sq(t1, t1); fe25519_mul(t1, uv7, t1); fe25519_mul(t0, t0, t1); fe25519_sq(t0, t0); fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for(i = 0; i < 4; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for(i = 0; i < 9; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t1, t1, t0); fe25519_sq(t2, t1); for(i = 0; i < 19; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); for(i = 0; i < 10; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for(i = 0; i < 49; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t1, t1, t0); fe25519_sq(t2, t1); for(i = 0; i < 99; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); for(i = 0; i < 50; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t0, t0); fe25519_sq(t0, t0); fe25519_mul(t0, t0, uv7); /* End fe_pow22523.c */ /* t0 = (uv^7)^((q-5)/8) */ fe25519_mul(t0, t0, v3); fe25519_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */ } int ge25519_frombytes_vartime(ge25519_p3 *h, const byte_t *s) { fe25519 u; fe25519 v; fe25519 vxx; fe25519 check; /* From fe_frombytes.c */ int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = (load_3(s + 29) & 8388607) << 2; 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; /* Validate the number to be canonical */ if(h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 && h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 && h1 == 1073741760 && h0 >= 4294967277) { return -1; } 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; 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; h->Y[0] = h0; h->Y[1] = h1; h->Y[2] = h2; h->Y[3] = h3; h->Y[4] = h4; h->Y[5] = h5; h->Y[6] = h6; h->Y[7] = h7; h->Y[8] = h8; h->Y[9] = h9; /* End fe_frombytes.c */ fe25519_1(h->Z); fe25519_sq(u, h->Y); fe25519_mul(v, u, fe25519_d); fe25519_sub(u, u, h->Z); /* u = y^2-1 */ fe25519_add(v, v, h->Z); /* v = dy^2+1 */ fe25519_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */ fe25519_sq(vxx, h->X); fe25519_mul(vxx, vxx, v); fe25519_sub(check, vxx, u); /* vx^2-u */ if(fe25519_isnonzero(check)) { fe25519_add(check, vxx, u); /* vx^2+u */ if(fe25519_isnonzero(check)) { return -1; } fe25519_mul(h->X, h->X, fe25519_sqrtm1); } if(fe25519_isnegative(h->X) != (s[31] >> 7)) { /* If x = 0, the sign must be positive */ if(!fe25519_isnonzero(h->X)) { return -1; } fe25519_neg(h->X, h->X); } fe25519_mul(h->T, h->X, h->Y); return 0; } /* 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 ge25519_double_scalarmult_base_vartime(ge25519_p2 *r, const byte_t *a, const ge25519_p3 *A, const byte_t *b) { signed char aslide[256]; signed char bslide[256]; ge25519_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ ge25519_p1p1 t; ge25519_p3 u; int i; slide(aslide, a); slide(bslide, b); ge25519_dsm_precomp(Ai, A); ge25519_p2_0(r); for(i = 255; i >= 0; --i) { if(aslide[i] || bslide[i]) break; } for(; i >= 0; --i) { ge25519_p2_dbl(&t, r); if(aslide[i] > 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_add(&t, &u, &Ai[aslide[i] / 2]); } else if(aslide[i] < 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_sub(&t, &u, &Ai[(-aslide[i]) / 2]); } if(bslide[i] > 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_madd(&t, &u, &ge_Bi[bslide[i] / 2]); } else if(bslide[i] < 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_msub(&t, &u, &ge_Bi[(-bslide[i]) / 2]); } ge25519_p1p1_to_p2(r, &t); } } } // namespace sodium } // namespace llarp