void fp2_rdcn_low(fp2_t c, dv2_t a) { #if FP_RDC == MONTY fp_rdcn_low(c[0], a[0]); fp_rdcn_low(c[1], a[1]); #else fp_rdc(c[0], a[0]); fp_rdc(c[1], a[1]); #endif }
void fp_invn_low(dig_t *c, const dig_t *a) { mp_size_t cn; align dig_t s[FP_DIGS], t[2 * FP_DIGS], u[FP_DIGS + 1]; #if FP_RDC == MONTY dv_zero(t + FP_DIGS, FP_DIGS); dv_copy(t, a, FP_DIGS); fp_rdcn_low(u, t); #else fp_copy(u, a); #endif dv_copy(s, fp_prime_get(), FP_DIGS); mpn_gcdext(t, c, &cn, u, FP_DIGS, s, FP_DIGS); if (cn < 0) { dv_zero(c - cn, FP_DIGS + cn); mpn_sub_n(c, fp_prime_get(), c, FP_DIGS); } else { dv_zero(c + cn, FP_DIGS - cn); } #if FP_RDC == MONTY dv_zero(t, FP_DIGS); dv_copy(t + FP_DIGS, c, FP_DIGS); mpn_tdiv_qr(u, c, 0, t, 2 * FP_DIGS, fp_prime_get(), FP_DIGS); #endif }
void fp_rdc_monty_comba(fp_t c, dv_t a) { fp_rdcn_low(c, a); }
void pp_dbl_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q) { fp_t t0, t1, t2, t3, t4, t5; dv_t u0, u1; fp_null(t0); fp_null(t1); fp_null(t2); fp_null(t3); fp_null(t4); fp_null(t5); dv_null(u0); dv_null(u1); TRY { fp_new(t0); fp_new(t1); fp_new(t2); fp_new(t3); fp_new(t4); fp_new(t5); dv_new(u0); dv_new(u1); /* For these curves, we always can choose a = -3. */ /* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */ /* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */ /* t0 = delta = z1^2. */ fp_sqr(t0, p->z); /* t1 = gamma = y1^2. */ fp_sqr(t1, p->y); /* t2 = beta = x1 * y1^2. */ fp_mul(t2, p->x, t1); /* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */ fp_sub(t3, p->x, t0); fp_add(t4, p->x, t0); fp_mul(t4, t3, t4); fp_dbl(t3, t4); fp_add(t3, t3, t4); /* t2 = 4 * beta. */ fp_dbl(t2, t2); fp_dbl(t2, t2); /* z3 = (y1 + z1)^2 - gamma - delta. */ fp_add(r->z, p->y, p->z); fp_sqr(r->z, r->z); fp_sub(r->z, r->z, t1); fp_sub(r->z, r->z, t0); /* l0 = 2 * gamma - alpha * (delta * xq + x1). */ fp_dbl(t1, t1); fp_mul(t5, t0, q->x); fp_add(t5, t5, p->x); fp_mul(t5, t5, t3); fp_sub(l[0], t1, t5); /* x3 = alpha^2 - 8 * beta. */ fp_dbl(t5, t2); fp_sqr(r->x, t3); fp_sub(r->x, r->x, t5); /* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */ fp_sqrn_low(u0, t1); fp_addc_low(u0, u0, u0); fp_subm_low(r->y, t2, r->x); fp_muln_low(u1, r->y, t3); fp_subc_low(u1, u1, u0); fp_rdcn_low(r->y, u1); /* l1 = - z3 * delta * yq. */ fp_mul(l[1], r->z, t0); fp_mul(l[1], l[1], q->y); r->norm = 0; } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp_free(t0); fp_free(t1); fp_free(t2); fp_free(t3); fp_free(t4); fp_free(t5); dv_free(u0); dv_free(u1); } }