468 lines
10 KiB
C
468 lines
10 KiB
C
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#include "ge.h"
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#include "precomp_data.h"
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/*
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r = p + q
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*/
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void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
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fe t0;
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fe_add(r->X, p->Y, p->X);
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fe_sub(r->Y, p->Y, p->X);
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fe_mul(r->Z, r->X, q->YplusX);
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fe_mul(r->Y, r->Y, q->YminusX);
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fe_mul(r->T, q->T2d, p->T);
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fe_mul(r->X, p->Z, q->Z);
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fe_add(t0, r->X, r->X);
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fe_sub(r->X, r->Z, r->Y);
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fe_add(r->Y, r->Z, r->Y);
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fe_add(r->Z, t0, r->T);
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fe_sub(r->T, t0, r->T);
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}
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static void slide(signed char *r, const unsigned char *a) {
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int i;
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int b;
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int k;
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for (i = 0; i < 256; ++i) {
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r[i] = 1 & (a[i >> 3] >> (i & 7));
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}
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for (i = 0; i < 256; ++i)
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if (r[i]) {
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for (b = 1; b <= 6 && i + b < 256; ++b) {
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if (r[i + b]) {
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if (r[i] + (r[i + b] << b) <= 15) {
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r[i] += r[i + b] << b;
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r[i + b] = 0;
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} else if (r[i] - (r[i + b] << b) >= -15) {
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r[i] -= r[i + b] << b;
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for (k = i + b; k < 256; ++k) {
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if (!r[k]) {
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r[k] = 1;
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break;
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}
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r[k] = 0;
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}
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} else {
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break;
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}
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}
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}
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}
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}
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/*
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r = a * A + b * B
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where a = a[0]+256*a[1]+...+256^31 a[31].
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and b = b[0]+256*b[1]+...+256^31 b[31].
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B is the Ed25519 base point (x,4/5) with x positive.
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*/
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void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
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signed char aslide[256];
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signed char bslide[256];
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ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
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ge_p1p1 t;
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ge_p3 u;
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ge_p3 A2;
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int i;
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slide(aslide, a);
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slide(bslide, b);
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ge_p3_to_cached(&Ai[0], A);
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ge_p3_dbl(&t, A);
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ge_p1p1_to_p3(&A2, &t);
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ge_add(&t, &A2, &Ai[0]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[1], &u);
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ge_add(&t, &A2, &Ai[1]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[2], &u);
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ge_add(&t, &A2, &Ai[2]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[3], &u);
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ge_add(&t, &A2, &Ai[3]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[4], &u);
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ge_add(&t, &A2, &Ai[4]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[5], &u);
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ge_add(&t, &A2, &Ai[5]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[6], &u);
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ge_add(&t, &A2, &Ai[6]);
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ge_p1p1_to_p3(&u, &t);
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ge_p3_to_cached(&Ai[7], &u);
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ge_p2_0(r);
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for (i = 255; i >= 0; --i) {
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if (aslide[i] || bslide[i]) {
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break;
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}
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}
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for (; i >= 0; --i) {
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ge_p2_dbl(&t, r);
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if (aslide[i] > 0) {
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ge_p1p1_to_p3(&u, &t);
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ge_add(&t, &u, &Ai[aslide[i] / 2]);
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} else if (aslide[i] < 0) {
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ge_p1p1_to_p3(&u, &t);
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ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
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}
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if (bslide[i] > 0) {
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ge_p1p1_to_p3(&u, &t);
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ge_madd(&t, &u, &Bi[bslide[i] / 2]);
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} else if (bslide[i] < 0) {
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ge_p1p1_to_p3(&u, &t);
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ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
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}
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ge_p1p1_to_p2(r, &t);
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}
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}
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static const fe d = {
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-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
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};
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static const fe sqrtm1 = {
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-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
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};
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int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) {
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fe u;
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fe v;
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fe v3;
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fe vxx;
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fe check;
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fe_frombytes(h->Y, s);
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fe_1(h->Z);
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fe_sq(u, h->Y);
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fe_mul(v, u, d);
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fe_sub(u, u, h->Z); /* u = y^2-1 */
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fe_add(v, v, h->Z); /* v = dy^2+1 */
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fe_sq(v3, v);
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fe_mul(v3, v3, v); /* v3 = v^3 */
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fe_sq(h->X, v3);
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fe_mul(h->X, h->X, v);
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fe_mul(h->X, h->X, u); /* x = uv^7 */
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fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
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fe_mul(h->X, h->X, v3);
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fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
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fe_sq(vxx, h->X);
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fe_mul(vxx, vxx, v);
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fe_sub(check, vxx, u); /* vx^2-u */
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if (fe_isnonzero(check)) {
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fe_add(check, vxx, u); /* vx^2+u */
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if (fe_isnonzero(check)) {
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return -1;
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}
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fe_mul(h->X, h->X, sqrtm1);
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}
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if (fe_isnegative(h->X) == (s[31] >> 7)) {
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fe_neg(h->X, h->X);
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}
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fe_mul(h->T, h->X, h->Y);
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return 0;
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}
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/*
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r = p + q
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*/
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void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
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fe t0;
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fe_add(r->X, p->Y, p->X);
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fe_sub(r->Y, p->Y, p->X);
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fe_mul(r->Z, r->X, q->yplusx);
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fe_mul(r->Y, r->Y, q->yminusx);
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fe_mul(r->T, q->xy2d, p->T);
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fe_add(t0, p->Z, p->Z);
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fe_sub(r->X, r->Z, r->Y);
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fe_add(r->Y, r->Z, r->Y);
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fe_add(r->Z, t0, r->T);
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fe_sub(r->T, t0, r->T);
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}
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/*
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r = p - q
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*/
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void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
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fe t0;
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fe_add(r->X, p->Y, p->X);
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fe_sub(r->Y, p->Y, p->X);
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fe_mul(r->Z, r->X, q->yminusx);
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fe_mul(r->Y, r->Y, q->yplusx);
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fe_mul(r->T, q->xy2d, p->T);
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fe_add(t0, p->Z, p->Z);
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fe_sub(r->X, r->Z, r->Y);
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fe_add(r->Y, r->Z, r->Y);
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fe_sub(r->Z, t0, r->T);
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fe_add(r->T, t0, r->T);
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}
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/*
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r = p
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*/
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void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
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fe_mul(r->X, p->X, p->T);
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fe_mul(r->Y, p->Y, p->Z);
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fe_mul(r->Z, p->Z, p->T);
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}
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/*
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r = p
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*/
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void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
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fe_mul(r->X, p->X, p->T);
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fe_mul(r->Y, p->Y, p->Z);
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fe_mul(r->Z, p->Z, p->T);
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fe_mul(r->T, p->X, p->Y);
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}
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void ge_p2_0(ge_p2 *h) {
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fe_0(h->X);
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fe_1(h->Y);
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fe_1(h->Z);
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}
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/*
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r = 2 * p
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*/
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void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
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fe t0;
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fe_sq(r->X, p->X);
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fe_sq(r->Z, p->Y);
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fe_sq2(r->T, p->Z);
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fe_add(r->Y, p->X, p->Y);
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fe_sq(t0, r->Y);
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fe_add(r->Y, r->Z, r->X);
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fe_sub(r->Z, r->Z, r->X);
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fe_sub(r->X, t0, r->Y);
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fe_sub(r->T, r->T, r->Z);
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}
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void ge_p3_0(ge_p3 *h) {
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fe_0(h->X);
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fe_1(h->Y);
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fe_1(h->Z);
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fe_0(h->T);
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}
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/*
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r = 2 * p
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*/
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void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
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ge_p2 q;
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ge_p3_to_p2(&q, p);
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ge_p2_dbl(r, &q);
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}
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/*
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r = p
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*/
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static const fe d2 = {
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-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
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};
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void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
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fe_add(r->YplusX, p->Y, p->X);
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fe_sub(r->YminusX, p->Y, p->X);
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fe_copy(r->Z, p->Z);
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fe_mul(r->T2d, p->T, d2);
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}
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/*
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r = p
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*/
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void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
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fe_copy(r->X, p->X);
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fe_copy(r->Y, p->Y);
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fe_copy(r->Z, p->Z);
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}
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void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
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fe recip;
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fe x;
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fe y;
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fe_invert(recip, h->Z);
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fe_mul(x, h->X, recip);
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fe_mul(y, h->Y, recip);
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fe_tobytes(s, y);
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s[31] ^= fe_isnegative(x) << 7;
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}
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static unsigned char equal(signed char b, signed char c) {
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unsigned char ub = b;
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unsigned char uc = c;
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unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
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uint64_t y = x; /* 0: yes; 1..255: no */
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y -= 1; /* large: yes; 0..254: no */
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y >>= 63; /* 1: yes; 0: no */
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return (unsigned char) y;
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}
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static unsigned char negative(signed char b) {
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uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
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x >>= 63; /* 1: yes; 0: no */
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return (unsigned char) x;
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}
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static void cmov(ge_precomp *t, ge_precomp *u, unsigned char b) {
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fe_cmov(t->yplusx, u->yplusx, b);
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fe_cmov(t->yminusx, u->yminusx, b);
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|
fe_cmov(t->xy2d, u->xy2d, b);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
static void select(ge_precomp *t, int pos, signed char b) {
|
||
|
|
ge_precomp minust;
|
||
|
|
unsigned char bnegative = negative(b);
|
||
|
|
unsigned char babs = b - (((-bnegative) & b) << 1);
|
||
|
|
fe_1(t->yplusx);
|
||
|
|
fe_1(t->yminusx);
|
||
|
|
fe_0(t->xy2d);
|
||
|
|
cmov(t, &base[pos][0], equal(babs, 1));
|
||
|
|
cmov(t, &base[pos][1], equal(babs, 2));
|
||
|
|
cmov(t, &base[pos][2], equal(babs, 3));
|
||
|
|
cmov(t, &base[pos][3], equal(babs, 4));
|
||
|
|
cmov(t, &base[pos][4], equal(babs, 5));
|
||
|
|
cmov(t, &base[pos][5], equal(babs, 6));
|
||
|
|
cmov(t, &base[pos][6], equal(babs, 7));
|
||
|
|
cmov(t, &base[pos][7], equal(babs, 8));
|
||
|
|
fe_copy(minust.yplusx, t->yminusx);
|
||
|
|
fe_copy(minust.yminusx, t->yplusx);
|
||
|
|
fe_neg(minust.xy2d, t->xy2d);
|
||
|
|
cmov(t, &minust, bnegative);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
h = a * B
|
||
|
|
where a = a[0]+256*a[1]+...+256^31 a[31]
|
||
|
|
B is the Ed25519 base point (x,4/5) with x positive.
|
||
|
|
|
||
|
|
Preconditions:
|
||
|
|
a[31] <= 127
|
||
|
|
*/
|
||
|
|
|
||
|
|
void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
|
||
|
|
signed char e[64];
|
||
|
|
signed char carry;
|
||
|
|
ge_p1p1 r;
|
||
|
|
ge_p2 s;
|
||
|
|
ge_precomp t;
|
||
|
|
int i;
|
||
|
|
|
||
|
|
for (i = 0; i < 32; ++i) {
|
||
|
|
e[2 * i + 0] = (a[i] >> 0) & 15;
|
||
|
|
e[2 * i + 1] = (a[i] >> 4) & 15;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* each e[i] is between 0 and 15 */
|
||
|
|
/* e[63] is between 0 and 7 */
|
||
|
|
carry = 0;
|
||
|
|
|
||
|
|
for (i = 0; i < 63; ++i) {
|
||
|
|
e[i] += carry;
|
||
|
|
carry = e[i] + 8;
|
||
|
|
carry >>= 4;
|
||
|
|
e[i] -= carry << 4;
|
||
|
|
}
|
||
|
|
|
||
|
|
e[63] += carry;
|
||
|
|
/* each e[i] is between -8 and 8 */
|
||
|
|
ge_p3_0(h);
|
||
|
|
|
||
|
|
for (i = 1; i < 64; i += 2) {
|
||
|
|
select(&t, i / 2, e[i]);
|
||
|
|
ge_madd(&r, h, &t);
|
||
|
|
ge_p1p1_to_p3(h, &r);
|
||
|
|
}
|
||
|
|
|
||
|
|
ge_p3_dbl(&r, h);
|
||
|
|
ge_p1p1_to_p2(&s, &r);
|
||
|
|
ge_p2_dbl(&r, &s);
|
||
|
|
ge_p1p1_to_p2(&s, &r);
|
||
|
|
ge_p2_dbl(&r, &s);
|
||
|
|
ge_p1p1_to_p2(&s, &r);
|
||
|
|
ge_p2_dbl(&r, &s);
|
||
|
|
ge_p1p1_to_p3(h, &r);
|
||
|
|
|
||
|
|
for (i = 0; i < 64; i += 2) {
|
||
|
|
select(&t, i / 2, e[i]);
|
||
|
|
ge_madd(&r, h, &t);
|
||
|
|
ge_p1p1_to_p3(h, &r);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
r = p - q
|
||
|
|
*/
|
||
|
|
|
||
|
|
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);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
void ge_tobytes(unsigned char *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;
|
||
|
|
}
|