ed25519/src/ge_double_scalarmult.c

#include "ge.h"

static void slide(signed char *r, const unsigned char *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 unsigned char *a, const ge_p3 *A, const unsigned char *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);
    }
}