void fp3_sqrn_low(dv3_t c, fp3_t a) { align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS]; align dig_t t3[2 * FP_DIGS], t4[2 * FP_DIGS], t5[2 * FP_DIGS]; /* t0 = a_0^2. */ fp_sqrn_low(t0, a[0]); /* t1 = 2 * a_1 * a_2. */ #ifdef FP_SPACE fp_dbln_low(t2, a[1]); #else fp_dblm_low(t2, a[1]); #endif fp_muln_low(t1, t2, a[2]); /* t2 = a_2^2. */ fp_sqrn_low(t2, a[2]); /* t3 = (a_0 + a_2 + a_1)^2, t4 = (a_0 + a_2 - a_1)^2. */ #ifdef FP_SPACE fp_addn_low(t3, a[0], a[2]); fp_addn_low(t4, t3, a[1]); #else fp_addm_low(t3, a[0], a[2]); fp_addm_low(t4, t3, a[1]); #endif fp_subm_low(t5, t3, a[1]); fp_sqrn_low(t3, t4); fp_sqrn_low(t4, t5); /* t4 = (t4 + t3)/2. */ fp_addd_low(t4, t4, t3); fp_hlvd_low(t4, t4); /* t3 = t3 - t4 - t1. */ fp_addc_low(t5, t1, t4); fp_subc_low(t3, t3, t5); /* c_2 = t4 - t0 - t2. */ fp_addc_low(t5, t0, t2); fp_subc_low(c[2], t4, t5); /* c_0 = t0 + t1 * B. */ fp_subc_low(c[0], t0, t1); for (int i = -1; i > fp_prime_get_cnr(); i--) { fp_subc_low(c[0], c[0], t1); } /* c_1 = t3 + t2 * B. */ fp_subc_low(c[1], t3, t2); for (int i = -1; i > fp_prime_get_cnr(); i--) { fp_subc_low(c[1], c[1], t2); } }
void fp2_sqrn_low(dv2_t c, fp2_t a) { align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS]; /* t0 = (a0 + a1). */ #ifdef FP_SPACE /* if we have room for carries, we can avoid reductions here. */ fp_addn_low(t0, a[0], a[1]); #else fp_addm_low(t0, a[0], a[1]); #endif /* t1 = (a0 - a1). */ fp_subm_low(t1, a[0], a[1]); #ifdef FP_QNRES #ifdef FP_SPACE fp_dbln_low(t2, a[0]); #else fp_dblm_low(t2, a[0]); #endif /* c1 = 2 * a0 * a1. */ fp_muln_low(c[1], t2, a[1]); /* c_0 = a_0^2 + a_1^2 * u^2. */ fp_muln_low(c[0], t0, t1); #else /* !FP_QNRES */ /* t1 = u^2 * (a1 * b1). */ for (int i = -1; i > fp_prime_get_qnr(); i--) { fp_subm_low(t1, t1, a[1]); } if (fp_prime_get_qnr() == -1) { /* t2 = 2 * a0. */ fp_dbl(t2, a[0]); /* c1 = 2 * a0 * a1. */ fp_muln_low(c[1], t2, a[1]); /* c0 = a0^2 + b_0^2 * u^2. */ fp_muln_low(c[0], t0, t1); } else { /* c1 = a0 * a1. */ fp_muln_low(c[1], a[0], a[1]); /* c0 = a0^2 + b_0^2 * u^2. */ fp_muln_low(c[0], t0, t1); #ifdef FP_SPACE for (int i = -1; i > fp_prime_get_qnr(); i--) { fp_addd_low(c[0], c[0], c[1]); } /* c1 = 2 * a0 * a1. */ fp_addd_low(c[1], c[1], c[1]); #else for (int i = -1; i > fp_prime_get_qnr(); i--) { fp_addc_low(c[0], c[0], c[1]); } /* c1 = 2 * a0 * a1. */ fp_addc_low(c[1], c[1], c[1]); #endif } #endif /* c = c0 + c1 * u. */ }
void fp2_subm_low(fp2_t c, fp2_t a, fp2_t b) { fp_subm_low(c[0], a[0], b[0]); fp_subm_low(c[1], a[1], b[1]); }
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); } }
void fp3_subm_low(fp3_t c, fp3_t a, fp3_t b) { fp_subm_low(c[0], a[0], b[0]); fp_subm_low(c[1], a[1], b[1]); fp_subm_low(c[2], a[2], b[2]); }