void ep_rhs(fp_t rhs, const ep_t p) { fp_t t0; fp_t t1; fp_null(t0); fp_null(t1); TRY { fp_new(t0); fp_new(t1); /* t0 = x1^2. */ fp_sqr(t0, p->x); /* t1 = x1^3. */ fp_mul(t1, t0, p->x); /* t1 = x1^3 + a * x1 + b. */ switch (ep_curve_opt_a()) { case OPT_ZERO: break; case OPT_ONE: fp_add(t1, t1, p->x); break; #if FP_RDC != MONTY case OPT_DIGIT: fp_mul_dig(t0, p->x, ep_curve_get_a()[0]); fp_add(t1, t1, t0); break; #endif default: fp_mul(t0, p->x, ep_curve_get_a()); fp_add(t1, t1, t0); break; } switch (ep_curve_opt_b()) { case OPT_ZERO: break; case OPT_ONE: fp_add_dig(t1, t1, 1); break; #if FP_RDC != MONTY case OPT_DIGIT: fp_add_dig(t1, t1, ep_curve_get_b()[0]); break; #endif default: fp_add(t1, t1, ep_curve_get_b()); break; } fp_copy(rhs, t1); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp_free(t0); fp_free(t1); } }
void pp_dbl_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p) { fp2_t t0, t1, t2, t3, t4, t5, t6; dv2_t u0, u1; int one = 1, zero = 0; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); fp2_null(t6); dv2_null(u0); dv2_null(u1); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_new(t6); dv2_new(u0); dv2_new(u1); if (ep2_curve_is_twist() == EP_MTYPE) { one ^= 1; zero ^= 1; } if (ep_curve_opt_b() == RLC_TWO) { /* C = z1^2. */ fp2_sqr(t0, q->z); /* B = y1^2. */ fp2_sqr(t1, q->y); /* t5 = B + C. */ fp2_add(t5, t0, t1); /* t3 = E = 3b'C = 3C * (1 - i). */ fp2_dbl(t3, t0); fp2_add(t0, t0, t3); fp_add(t2[0], t0[0], t0[1]); fp_sub(t2[1], t0[1], t0[0]); /* t0 = x1^2. */ fp2_sqr(t0, q->x); /* t4 = A = (x1 * y1)/2. */ fp2_mul(t4, q->x, q->y); fp_hlv(t4[0], t4[0]); fp_hlv(t4[1], t4[1]); /* t3 = F = 3E. */ fp2_dbl(t3, t2); fp2_add(t3, t3, t2); /* x3 = A * (B - F). */ fp2_sub(r->x, t1, t3); fp2_mul(r->x, r->x, t4); /* G = (B + F)/2. */ fp2_add(t3, t1, t3); fp_hlv(t3[0], t3[0]); fp_hlv(t3[1], t3[1]); /* y3 = G^2 - 3E^2. */ fp2_sqrn_low(u0, t2); fp2_addd_low(u1, u0, u0); fp2_addd_low(u1, u1, u0); fp2_sqrn_low(u0, t3); fp2_subc_low(u0, u0, u1); /* H = (Y + Z)^2 - B - C. */ fp2_add(t3, q->y, q->z); fp2_sqr(t3, t3); fp2_sub(t3, t3, t5); fp2_rdcn_low(r->y, u0); /* z3 = B * H. */ fp2_mul(r->z, t1, t3); /* l11 = E - B. */ fp2_sub(l[1][1], t2, t1); /* l10 = (3 * xp) * t0. */ fp_mul(l[one][zero][0], p->x, t0[0]); fp_mul(l[one][zero][1], p->x, t0[1]); /* l01 = F * (-yp). */ fp_mul(l[zero][zero][0], t3[0], p->y); fp_mul(l[zero][zero][1], t3[1], p->y); } else { /* A = x1^2. */ fp2_sqr(t0, q->x); /* B = y1^2. */ fp2_sqr(t1, q->y); /* C = z1^2. */ fp2_sqr(t2, q->z); /* D = 3bC, for general b. */ fp2_dbl(t3, t2); fp2_add(t3, t3, t2); ep2_curve_get_b(t4); fp2_mul(t3, t3, t4); /* E = (x1 + y1)^2 - A - B. */ fp2_add(t4, q->x, q->y); fp2_sqr(t4, t4); fp2_sub(t4, t4, t0); fp2_sub(t4, t4, t1); /* F = (y1 + z1)^2 - B - C. */ fp2_add(t5, q->y, q->z); fp2_sqr(t5, t5); fp2_sub(t5, t5, t1); fp2_sub(t5, t5, t2); /* G = 3D. */ fp2_dbl(t6, t3); fp2_add(t6, t6, t3); /* x3 = E * (B - G). */ fp2_sub(r->x, t1, t6); fp2_mul(r->x, r->x, t4); /* y3 = (B + G)^2 -12D^2. */ fp2_add(t6, t6, t1); fp2_sqr(t6, t6); fp2_sqr(t2, t3); fp2_dbl(r->y, t2); fp2_dbl(t2, r->y); fp2_dbl(r->y, t2); fp2_add(r->y, r->y, t2); fp2_sub(r->y, t6, r->y); /* z3 = 4B * F. */ fp2_dbl(r->z, t1); fp2_dbl(r->z, r->z); fp2_mul(r->z, r->z, t5); /* l00 = D - B. */ fp2_sub(l[one][one], t3, t1); /* l10 = (3 * xp) * A. */ fp_mul(l[one][zero][0], p->x, t0[0]); fp_mul(l[one][zero][1], p->x, t0[1]); /* l01 = F * (-yp). */ fp_mul(l[zero][zero][0], t5[0], p->y); fp_mul(l[zero][zero][1], t5[1], p->y); } r->norm = 0; } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); fp2_free(t2); fp2_free(t3); fp2_free(t4); fp2_free(t5); fp2_free(t6); dv2_free(u0); dv2_free(u1); } }