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 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; }