void ge_montx_to_p2(ge_p2* p, const fe u, const unsigned char ed_sign_bit)
{
fe x, y, A, v, v2, iv, nx;
fe_frombytes(A, A_bytes);
/* given u, recover edwards y */
/* given u, recover v */
/* given u and v, recover edwards x */
fe_montx_to_edy(y, u); /* y = (u - 1) / (u + 1) */
fe_mont_rhs(v2, u); /* v^2 = u(u^2 + Au + 1) */
fe_sqrt(v, v2); /* v = sqrt(v^2) */
fe_mul(x, u, A); /* x = u * sqrt(-(A+2)) */
fe_invert(iv, v); /* 1/v */
fe_mul(x, x, iv); /* x = (u/v) * sqrt(-(A+2)) */
fe_neg(nx, x); /* negate x to match sign bit */
fe_cmov(x, nx, fe_isnegative(x) ^ ed_sign_bit);
fe_copy(p->X, x);
fe_copy(p->Y, y);
fe_1(p->Z);
/* POSTCONDITION: check that p->X and p->Y satisfy the Ed curve equation */
/* -x^2 + y^2 = 1 + dx^2y^2 */
#ifndef NDEBUG
{
fe one, d, x2, y2, x2y2, dx2y2;
unsigned char dbytes[32] = {
0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75,
0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00,
0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c,
0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52
};
fe_frombytes(d, dbytes);
fe_1(one);
fe_sq(x2, p->X); /* x^2 */
fe_sq(y2, p->Y); /* y^2 */
fe_mul(dx2y2, x2, y2); /* x^2y^2 */
fe_mul(dx2y2, dx2y2, d); /* dx^2y^2 */
fe_add(dx2y2, dx2y2, one); /* dx^2y^2 + 1 */
fe_neg(x2y2, x2); /* -x^2 */
fe_add(x2y2, x2y2, y2); /* -x^2 + y^2 */
assert(fe_isequal(x2y2, dx2y2));
}
#endif
}
void fe_sqrt(fe out, const fe a)
{
fe exp, b, b2, bi, i;
#ifndef NDEBUG
fe legendre, zero, one;
#endif
fe_frombytes(i, i_bytes);
fe_pow22523(exp, a); /* b = a^(q-5)/8 */
/* PRECONDITION: legendre symbol == 1 (square) or 0 (a == zero) */
#ifndef NDEBUG
fe_sq(legendre, exp); /* in^((q-5)/4) */
fe_sq(legendre, legendre); /* in^((q-5)/2) */
fe_mul(legendre, legendre, a); /* in^((q-3)/2) */
fe_mul(legendre, legendre, a); /* in^((q-1)/2) */
fe_0(zero);
fe_1(one);
assert(fe_isequal(legendre, zero) || fe_isequal(legendre, one));
#endif
fe_mul(b, a, exp); /* b = a * a^(q-5)/8 */
fe_sq(b2, b); /* b^2 = a * a^(q-1)/4 */
/* note b^4 == a^2, so b^2 == a or -a
* if b^2 != a, multiply it by sqrt(-1) */
fe_mul(bi, b, i);
fe_cmov(b, bi, 1 ^ fe_isequal(b2, a));
fe_copy(out, b);
/* PRECONDITION: out^2 == a */
#ifndef NDEBUG
fe_sq(b2, out);
assert(fe_isequal(a, b2));
#endif
}
int elligator_fast_test(int silent)
{
unsigned char elligator_correct_output[32] =
{
0x5f, 0x35, 0x20, 0x00, 0x1c, 0x6c, 0x99, 0x36,
0xa3, 0x12, 0x06, 0xaf, 0xe7, 0xc7, 0xac, 0x22,
0x4e, 0x88, 0x61, 0x61, 0x9b, 0xf9, 0x88, 0x72,
0x44, 0x49, 0x15, 0x89, 0x9d, 0x95, 0xf4, 0x6e
};
unsigned char hashtopoint_correct_output1[32] =
{
0xce, 0x89, 0x9f, 0xb2, 0x8f, 0xf7, 0x20, 0x91,
0x5e, 0x14, 0xf5, 0xb7, 0x99, 0x08, 0xab, 0x17,
0xaa, 0x2e, 0xe2, 0x45, 0xb4, 0xfc, 0x2b, 0xf6,
0x06, 0x36, 0x29, 0x40, 0xed, 0x7d, 0xe7, 0xed
};
unsigned char hashtopoint_correct_output2[32] =
{
0xa0, 0x35, 0xbb, 0xa9, 0x4d, 0x30, 0x55, 0x33,
0x0d, 0xce, 0xc2, 0x7f, 0x83, 0xde, 0x79, 0xd0,
0x89, 0x67, 0x72, 0x4c, 0x07, 0x8d, 0x68, 0x9d,
0x61, 0x52, 0x1d, 0xf9, 0x2c, 0x5c, 0xba, 0x77
};
unsigned char calculatev_correct_output[32] =
{
0x1b, 0x77, 0xb5, 0xa0, 0x44, 0x84, 0x7e, 0xb9,
0x23, 0xd7, 0x93, 0x18, 0xce, 0xc2, 0xc5, 0xe2,
0x84, 0xd5, 0x79, 0x6f, 0x65, 0x63, 0x1b, 0x60,
0x9b, 0xf1, 0xf8, 0xce, 0x88, 0x0b, 0x50, 0x9c,
};
int count;
fe in, out;
unsigned char bytes[32];
fe_0(in);
fe_0(out);
for (count = 0; count < 32; count++) {
bytes[count] = count;
}
fe_frombytes(in, bytes);
elligator(out, in);
fe_tobytes(bytes, out);
TEST("Elligator vector", memcmp(bytes, elligator_correct_output, 32) == 0);
/* Elligator(0) == 0 test */
fe_0(in);
elligator(out, in);
TEST("Elligator(0) == 0", memcmp(in, out, 32) == 0);
/* ge_montx_to_p3(0) -> order2 point test */
fe one, negone, zero;
fe_1(one);
fe_0(zero);
fe_sub(negone, zero, one);
ge_p3 p3;
ge_montx_to_p3(&p3, zero, 0);
TEST("ge_montx_to_p3(0) == order 2 point",
fe_isequal(p3.X, zero) &&
fe_isequal(p3.Y, negone) &&
fe_isequal(p3.Z, one) &&
fe_isequal(p3.T, zero));
/* Hash to point vector test */
unsigned char htp[32];
for (count=0; count < 32; count++) {
htp[count] = count;
}
hash_to_point(&p3, htp, 32);
ge_p3_tobytes(htp, &p3);
TEST("hash_to_point #1", memcmp(htp, hashtopoint_correct_output1, 32) == 0);
for (count=0; count < 32; count++) {
htp[count] = count+1;
}
hash_to_point(&p3, htp, 32);
ge_p3_tobytes(htp, &p3);
TEST("hash_to_point #2", memcmp(htp, hashtopoint_correct_output2, 32) == 0);
/* calculate_U vector test */
ge_p3 Bv;
unsigned char V[32];
unsigned char Vbuf[200];
unsigned char a[32];
unsigned char A[32];
unsigned char Vmsg[3];
Vmsg[0] = 0;
Vmsg[1] = 1;
Vmsg[2] = 2;
for (count=0; count < 32; count++) {
a[count] = 8 + count;
A[count] = 9 + count;
}
sc_clamp(a);
calculate_Bv_and_V(&Bv, V, Vbuf, a, A, Vmsg, 3);
TEST("calculate_Bv_and_V vector", memcmp(V, calculatev_correct_output, 32) == 0);
return 0;
}
