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ge25519.c
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ge25519.c
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#include "fe25519.h"
#include "cleanup.h"
#include "ge25519.h"
/* D = -121665/121666 */
static fe D = {0x135978a3, 0x75eb4dca, 0x4141d8ab, 0x00700a4d,
0x7779e898, 0x8cc74079, 0x2b6ffe73, 0x52036cee};
/* D2 = 2 * -121665/121666 */
static fe D2 = {0x26b2f159, 0xebd69b94, 0x8283b156, 0x00e0149a,
0xeef3d130, 0x198e80f2, 0x56dffce7, 0x2406d9dc};
static fe sqrtm1 = {
0x4a0ea0b0, 0xc4ee1b27, 0xad2fe478, 0x2f431806,
0x3dfbd7a7, 0x2b4d0099, 0x4fc1df0b, 0x2b832480,
};
static void neutral(ge25519 p) {
fe_0(p[0]);
fe_1(p[1]);
fe_1(p[2]);
fe_0(p[3]);
}
/*
p = q
*/
static void copy(ge25519 p, ge25519 q) {
fe_copy(p[0], q[0]);
fe_copy(p[1], q[1]);
fe_copy(p[2], q[2]);
fe_copy(p[3], q[3]);
}
/*
if (b) p = q;
*/
static void cmov(ge25519 p, ge25519 q, crypto_uint32 b) {
fe_cmov(p[0], q[0], b);
fe_cmov(p[1], q[1], b);
fe_cmov(p[2], q[2], b);
fe_cmov(p[3], q[3], b);
}
void ge25519_add(ge25519 o, ge25519 p, ge25519 q) {
fe a, b, c, d, t, e, f, g, h;
fe25519_sub(a, p[1], p[0]);
fe25519_sub(t, q[1], q[0]);
fe25519_mul(a, a, t);
fe25519_add(b, p[0], p[1]);
fe25519_add(t, q[0], q[1]);
fe25519_mul(b, b, t);
fe25519_mul(c, p[3], q[3]);
fe25519_mul(c, c, D2);
fe25519_mul(d, p[2], q[2]);
fe25519_add(d, d, d);
fe25519_sub(e, b, a);
fe25519_sub(f, d, c);
fe25519_add(g, d, c);
fe25519_add(h, b, a);
fe25519_mul(o[0], e, f);
fe25519_mul(o[1], h, g);
fe25519_mul(o[2], g, f);
fe25519_mul(o[3], e, h);
cleanup(a);
cleanup(b);
cleanup(c);
cleanup(d);
cleanup(t);
cleanup(e);
cleanup(f);
cleanup(g);
cleanup(h);
}
/* https://hyperelliptic.org/EFD/g1p/auto-code/twisted/extended/doubling/dbl-2008-hwcd.op3
*/
static void dbl(ge25519 o, ge25519 p) {
fe a, b, c, d, e, f, g, h;
fe25519_sq(a, p[0]); /* A = X1^2 */
fe25519_sq(b, p[1]); /* B = Y1^2 */
fe25519_sq(c, p[2]); /* t0 = Z1^2 */
fe25519_add(c, c, c); /* C = 2*t0 */
fe25519_neg(d, a); /* D = a*A */
fe25519_add(e, p[0], p[1]); /* t1 = X1+Y1 */
fe25519_sq(e, e); /* t2 = t1^2 */
fe25519_sub(e, e, a); /* t3 = t2-A */
fe25519_sub(e, e, b); /* E = t3-B */
fe25519_add(g, d, b); /* G = D+B */
fe25519_sub(f, g, c); /* F = G-C */
fe25519_sub(h, d, b); /* H = D-B */
fe25519_mul(o[0], e, f); /* X3 = E*F */
fe25519_mul(o[1], g, h); /* Y3 = G*H */
fe25519_mul(o[2], f, g); /* Z3 = F*G */
fe25519_mul(o[3], e, h); /* T3 = E*H */
cleanup(a);
cleanup(b);
cleanup(c);
cleanup(d);
cleanup(e);
cleanup(f);
cleanup(g);
cleanup(h);
}
void ge25519_tobytes(unsigned char *s, ge25519 h) {
fe x, y, z;
fe25519_inv(z, h[2]);
fe25519_mul(x, h[0], z);
fe25519_mul(y, h[1], z);
fe25519_tobytes(s, y);
s[31] ^= fe25519_isnegative(x) << 7;
cleanup(x);
cleanup(y);
cleanup(z);
}
int ge25519_frombytes_negate_vartime(ge25519 h, const unsigned char *s) {
fe u, v, v3, vxx, check;
int ret = -1;
fe25519_frombytes(h[1], s);
fe_1(h[2]);
fe25519_sq(u, h[1]);
fe25519_mul(v, u, D);
fe25519_sub(u, u, h[2]); /* u = y^2-1 */
fe25519_add(v, v, h[2]); /* v = dy^2+1 */
fe25519_sq(v3, v);
fe25519_mul(v3, v3, v); /* v3 = v^3 */
fe25519_sq(h[0], v3);
fe25519_mul(h[0], h[0], v);
fe25519_mul(h[0], h[0], u); /* x = uv^7 */
fe25519_pow22523(h[0], h[0]); /* x = (uv^7)^((q-5)/8) */
fe25519_mul(h[0], h[0], v3);
fe25519_mul(h[0], h[0], u); /* x = uv^3(uv^7)^((q-5)/8) */
fe25519_sq(vxx, h[0]);
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)) { goto cleanup; }
fe25519_mul(h[0], h[0], sqrtm1);
}
if (fe25519_isnegative(h[0]) == (s[31] >> 7)) fe25519_neg(h[0], h[0]);
fe25519_mul(h[3], h[0], h[1]);
ret = 0;
cleanup:
cleanup(u);
cleanup(v);
cleanup(v3);
cleanup(vxx);
cleanup(check);
return ret;
}
/*
if (a == b) return 1;
else return 0;
*/
static unsigned char equal(unsigned char a, unsigned char b) {
unsigned char x = a ^ b;
crypto_uint32 y = x;
y -= 1;
y >>= 31;
return y;
}
/*
point multiplication using windowed method
*/
void ge25519_scalarmult(ge25519 o, ge25519 q, const unsigned char *a) {
long long i, j;
ge25519 t[16], p, sp = {0};
unsigned char e[64];
for (i = 0; i < 32; ++i) {
e[2 * i + 0] = (a[i] >> 0) & 0x0f;
e[2 * i + 1] = (a[i] >> 4) & 0x0f;
}
neutral(p);
/* precompute points */
copy(t[0], p);
copy(t[1], q);
for (i = 2; i < 16; ++i) {
if ((i & 1) == 0)
dbl(t[i], t[i / 2]);
else
ge25519_add(t[i], t[i - 1], q);
}
for (i = 63; i >= 0; --i) {
for (j = 0; j < 4; ++j) dbl(p, p);
for (j = 0; j < 16; ++j) cmov(sp, t[j], equal(e[i], j));
ge25519_add(p, p, sp);
}
copy(o, p);
cleanup(p);
cleanup(t);
cleanup(sp);
cleanup(e);
}
static ge25519 baseq = {
{0x8f25d51a, 0xc9562d60, 0x9525a7b2, 0x692cc760, 0xfdd6dc5c, 0xc0a4e231,
0xcd6e53fe, 0x216936d3},
{0x66666658, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666,
0x66666666, 0x66666666},
{0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000},
{0xa5b7dda3, 0x6dde8ab3, 0x775152f5, 0x20f09f80, 0x64abe37d, 0x66ea4e8e,
0xd78b7665, 0x67875f0f},
};
void ge25519_scalarmult_base(ge25519 p, const unsigned char *a) {
ge25519_scalarmult(p, baseq, a);
}