-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)
projects / openssl.git / blobdiff