/** * Doubles a point represented in affine coordinates on an ordinary prime * elliptic curve. * * @param[out] r - the result. * @param[out] s - the resulting slope. * @param[in] p - the point to double. */ static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) { fp2_t t0, t1, t2; fp2_null(t0); fp2_null(t1); fp2_null(t2); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); /* t0 = 1/(2 * y1). */ fp2_dbl(t0, p->y); fp2_inv(t0, t0); /* t1 = 3 * x1^2 + a. */ fp2_sqr(t1, p->x); fp2_copy(t2, t1); fp2_dbl(t1, t1); fp2_add(t1, t1, t2); ep2_curve_get_a(t2); fp2_add(t1, t1, t2); /* t1 = (3 * x1^2 + a)/(2 * y1). */ fp2_mul(t1, t1, t0); if (s != NULL) { fp2_copy(s, t1); } /* t2 = t1^2. */ fp2_sqr(t2, t1); /* x3 = t1^2 - 2 * x1. */ fp2_dbl(t0, p->x); fp2_sub(t0, t2, t0); /* y3 = t1 * (x1 - x3) - y1. */ fp2_sub(t2, p->x, t0); fp2_mul(t1, t1, t2); fp2_sub(r->y, t1, p->y); fp2_copy(r->x, t0); fp2_copy(r->z, p->z); r->norm = 1; } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); fp2_free(t2); } }
void fp6_inv(fp6_t c, fp6_t a) { fp2_t v0; fp2_t v1; fp2_t v2; fp2_t t0; fp2_null(v0); fp2_null(v1); fp2_null(v2); fp2_null(t0); TRY { fp2_new(v0); fp2_new(v1); fp2_new(v2); fp2_new(t0); /* v0 = a_0^2 - E * a_1 * a_2. */ fp2_sqr(t0, a[0]); fp2_mul(v0, a[1], a[2]); fp2_mul_nor(v2, v0); fp2_sub(v0, t0, v2); /* v1 = E * a_2^2 - a_0 * a_1. */ fp2_sqr(t0, a[2]); fp2_mul_nor(v2, t0); fp2_mul(v1, a[0], a[1]); fp2_sub(v1, v2, v1); /* v2 = a_1^2 - a_0 * a_2. */ fp2_sqr(t0, a[1]); fp2_mul(v2, a[0], a[2]); fp2_sub(v2, t0, v2); fp2_mul(t0, a[1], v2); fp2_mul_nor(c[1], t0); fp2_mul(c[0], a[0], v0); fp2_mul(t0, a[2], v1); fp2_mul_nor(c[2], t0); fp2_add(t0, c[0], c[1]); fp2_add(t0, t0, c[2]); fp2_inv(t0, t0); fp2_mul(c[0], v0, t0); fp2_mul(c[1], v1, t0); fp2_mul(c[2], v2, t0); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(v0); fp2_free(v1); fp2_free(v2); fp2_free(t0); } }
void ep2_rhs(fp2_t rhs, ep2_t p) { fp2_t t0; fp2_t t1; fp2_null(t0); fp2_null(t1); TRY { fp2_new(t0); fp2_new(t1); /* t0 = x1^2. */ fp2_sqr(t0, p->x); /* t1 = x1^3. */ fp2_mul(t1, t0, p->x); ep2_curve_get_a(t0); fp2_mul(t0, p->x, t0); fp2_add(t1, t1, t0); ep2_curve_get_b(t0); fp2_add(t1, t1, t0); fp2_copy(rhs, t1); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); } }
/** * Doubles a point represented in affine coordinates on an ordinary prime * elliptic curve. * * @param[out] r - the result. * @param[in] p - the point to double. */ static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) { fp2_t t0, t1, t2, t3; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_sqr(t0, p->x); fp2_add(t2, t0, t0); fp2_add(t0, t2, t0); fp2_sqr(t3, p->y); fp2_mul(t1, t3, p->x); fp2_add(t1, t1, t1); fp2_add(t1, t1, t1); fp2_sqr(r->x, t0); fp2_add(t2, t1, t1); fp2_sub(r->x, r->x, t2); fp2_mul(r->z, p->z, p->y); fp2_add(r->z, r->z, r->z); fp2_add(t3, t3, t3); fp2_sqr(t3, t3); fp2_add(t3, t3, t3); fp2_sub(t1, t1, r->x); fp2_mul(r->y, t0, t1); fp2_sub(r->y, r->y, t3); r->norm = 0; } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); fp2_free(t2); fp2_free(t3); } }
/** * Compute the Miller loop for pairings of type G_1 x G_2 over the bits of a * given parameter. * * @param[out] r - the result. * @param[out] t - the resulting point. * @param[in] p - the first pairing argument in affine coordinates. * @param[in] q - the second pairing argument in affine coordinates. * @param[in] a - the loop parameter. */ static void pp_mil_lit_k2(fp2_t r, ep_t *t, ep_t *p, ep_t *q, int m, bn_t a) { fp2_t l, _l; ep_t _q[m]; int i, j; fp2_null(_l); ep_null(_q); TRY { fp2_new(_l); for (j = 0; j < m; j++) { ep_null(_q[j]); ep_new(_q[j]); ep_copy(t[j], p[j]); ep_neg(_q[j], q[j]); } for (i = bn_bits(a) - 2; i >= 0; i--) { fp2_sqr(r, r); for (j = 0; j < m; j++) { pp_dbl_k2(l, t[j], t[j], _q[j]); fp_copy(_l[0], l[1]); fp_copy(_l[1], l[0]); fp2_mul(r, r, _l); if (bn_get_bit(a, i)) { pp_add_k2(l, t[j], p[j], q[j]); fp_copy(_l[0], l[1]); fp_copy(_l[1], l[0]); fp2_mul(r, r, _l); } } } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(_l); fp2_free(m); ep_free(_q); } }
int ep2_is_valid(ep2_t p) { ep2_t t; int r = 0; ep2_null(t); TRY { ep2_new(t); ep2_norm(t, p); ep2_rhs(t->x, t); fp2_sqr(t->y, t->y); r = (fp2_cmp(t->x, t->y) == CMP_EQ) || ep2_is_infty(p); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { ep2_free(t); } return r; }
/** * Doubles a point represented in affine coordinates on an ordinary prime * elliptic curve. * * @param[out] r - the result. * @param[out] s - the resulting slope. * @param[in] p - the point to double. */ static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) { fp2_t t0, t1, t2; fp2_null(t0); fp2_null(t1); fp2_null(t2); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); /* t0 = 1/(2 * y1). */ fp2_dbl(t0, p->y); fp2_inv(t0, t0); /* t1 = 3 * x1^2 + a. */ fp2_sqr(t1, p->x); fp2_copy(t2, t1); fp2_dbl(t1, t1); fp2_add(t1, t1, t2); if (ep2_curve_is_twist()) { switch (ep_curve_opt_a()) { case OPT_ZERO: break; case OPT_ONE: fp_set_dig(t2[0], 1); fp2_mul_art(t2, t2); fp2_mul_art(t2, t2); fp2_add(t1, t1, t2); break; case OPT_DIGIT: fp_set_dig(t2[0], ep_curve_get_a()[0]); fp2_mul_art(t2, t2); fp2_mul_art(t2, t2); fp2_add(t1, t1, t2); break; default: fp_copy(t2[0], ep_curve_get_a()); fp_zero(t2[1]); fp2_mul_art(t2, t2); fp2_mul_art(t2, t2); fp2_add(t1, t1, t2); break; } } /* t1 = (3 * x1^2 + a)/(2 * y1). */ fp2_mul(t1, t1, t0); if (s != NULL) { fp2_copy(s, t1); } /* t2 = t1^2. */ fp2_sqr(t2, t1); /* x3 = t1^2 - 2 * x1. */ fp2_dbl(t0, p->x); fp2_sub(t0, t2, t0); /* y3 = t1 * (x1 - x3) - y1. */ fp2_sub(t2, p->x, t0); fp2_mul(t1, t1, t2); fp2_sub(r->y, t1, p->y); fp2_copy(r->x, t0); fp2_copy(r->z, p->z); r->norm = 1; } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); fp2_free(t2); } }
/** * Doubles a point represented in affine coordinates on an ordinary prime * elliptic curve. * * @param[out] r - the result. * @param[in] p - the point to double. */ static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) { fp2_t t0, t1, t2, t3, t4, t5; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); TRY { if (ep_curve_opt_a() == OPT_ZERO) { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_sqr(t0, p->x); fp2_add(t2, t0, t0); fp2_add(t0, t2, t0); fp2_sqr(t3, p->y); fp2_mul(t1, t3, p->x); fp2_add(t1, t1, t1); fp2_add(t1, t1, t1); fp2_sqr(r->x, t0); fp2_add(t2, t1, t1); fp2_sub(r->x, r->x, t2); fp2_mul(r->z, p->z, p->y); fp2_add(r->z, r->z, r->z); fp2_add(t3, t3, t3); fp2_sqr(t3, t3); fp2_add(t3, t3, t3); fp2_sub(t1, t1, r->x); fp2_mul(r->y, t0, t1); fp2_sub(r->y, r->y, t3); } else { /* dbl-2007-bl formulas: 1M + 8S + 1*a + 10add + 1*8 + 2*2 + 1*3 */ /* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl */ /* t0 = x1^2, t1 = y1^2, t2 = y1^4. */ fp2_sqr(t0, p->x); fp2_sqr(t1, p->y); fp2_sqr(t2, t1); if (!p->norm) { /* t3 = z1^2. */ fp2_sqr(t3, p->z); if (ep_curve_get_a() == OPT_ZERO) { /* z3 = 2 * y1 * z1. */ fp2_mul(r->z, p->y, p->z); fp2_dbl(r->z, r->z); } else { /* z3 = (y1 + z1)^2 - y1^2 - z1^2. */ fp2_add(r->z, p->y, p->z); fp2_sqr(r->z, r->z); fp2_sub(r->z, r->z, t1); fp2_sub(r->z, r->z, t3); } } else { /* z3 = 2 * y1. */ fp2_dbl(r->z, p->y); } /* t4 = S = 2*((x1 + y1^2)^2 - x1^2 - y1^4). */ fp2_add(t4, p->x, t1); fp2_sqr(t4, t4); fp2_sub(t4, t4, t0); fp2_sub(t4, t4, t2); fp2_dbl(t4, t4); /* t5 = M = 3 * x1^2 + a * z1^4. */ fp2_dbl(t5, t0); fp2_add(t5, t5, t0); ep2_curve_get_a(t0); if (!p->norm) { fp2_sqr(t3, t3); fp2_mul(t1, t0, t3); fp2_add(t5, t5, t1); } else { fp2_add(t5, t5, t0); } /* x3 = T = M^2 - 2 * S. */ fp2_sqr(r->x, t5); fp2_dbl(t1, t4); fp2_sub(r->x, r->x, t1); /* y3 = M * (S - T) - 8 * y1^4. */ fp2_dbl(t2, t2); fp2_dbl(t2, t2); fp2_dbl(t2, t2); fp2_sub(t4, t4, r->x); fp2_mul(t5, t5, t4); fp2_sub(r->y, t5, t2); } r->norm = 0; 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); } }
/** * Adds two points represented in affine coordinates on an ordinary prime * elliptic curve. * * @param r - the result. * @param s - the resulting slope. * @param p - the first point to add. * @param q - the second point to add. */ static void ep2_add_basic_imp(ep2_t r, fp2_t s, ep2_t p, ep2_t q) { fp2_t t0, t1, t2; fp2_null(t0); fp2_null(t1); fp2_null(t2); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); /* t0 = x2 - x1. */ fp2_sub(t0, q->x, p->x); /* t1 = y2 - y1. */ fp2_sub(t1, q->y, p->y); /* If t0 is zero. */ if (fp2_is_zero(t0)) { if (fp2_is_zero(t1)) { /* If t1 is zero, q = p, should have doubled. */ ep2_dbl_basic(r, p); } else { /* If t1 is not zero and t0 is zero, q = -p and r = infty. */ ep2_set_infty(r); } } else { /* t2 = 1/(x2 - x1). */ fp2_inv(t2, t0); /* t2 = lambda = (y2 - y1)/(x2 - x1). */ fp2_mul(t2, t1, t2); /* x3 = lambda^2 - x2 - x1. */ fp2_sqr(t1, t2); fp2_sub(t0, t1, p->x); fp2_sub(t0, t0, q->x); /* y3 = lambda * (x1 - x3) - y1. */ fp2_sub(t1, p->x, t0); fp2_mul(t1, t2, t1); fp2_sub(r->y, t1, p->y); fp2_copy(r->x, t0); fp2_copy(r->z, p->z); if (s != NULL) { fp2_copy(s, t2); } r->norm = 1; } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp2_free(t0); fp2_free(t1); fp2_free(t2); } }
/** * Adds two points represented in projective coordinates on an ordinary prime * elliptic curve. * * @param r - the result. * @param p - the first point to add. * @param q - the second point to add. */ static void ep2_add_projc_imp(ep2_t r, ep2_t p, ep2_t q) { #if defined(EP_MIXED) && defined(STRIP) ep2_add_projc_mix(r, p, q); #else /* General addition. */ fp2_t t0, t1, t2, t3, t4, t5, t6; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); fp2_null(t6); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_new(t6); if (q->norm) { ep2_add_projc_mix(r, p, q); } else { /* t0 = z1^2. */ fp2_sqr(t0, p->z); /* t1 = z2^2. */ fp2_sqr(t1, q->z); /* t2 = U1 = x1 * z2^2. */ fp2_mul(t2, p->x, t1); /* t3 = U2 = x2 * z1^2. */ fp2_mul(t3, q->x, t0); /* t6 = z1^2 + z2^2. */ fp2_add(t6, t0, t1); /* t0 = S2 = y2 * z1^3. */ fp2_mul(t0, t0, p->z); fp2_mul(t0, t0, q->y); /* t1 = S1 = y1 * z2^3. */ fp2_mul(t1, t1, q->z); fp2_mul(t1, t1, p->y); /* t3 = H = U2 - U1. */ fp2_sub(t3, t3, t2); /* t0 = R = 2 * (S2 - S1). */ fp2_sub(t0, t0, t1); fp2_dbl(t0, t0); /* If E is zero. */ if (fp2_is_zero(t3)) { if (fp2_is_zero(t0)) { /* If I is zero, p = q, should have doubled. */ ep2_dbl_projc(r, p); } else { /* If I is not zero, q = -p, r = infinity. */ ep2_set_infty(r); } } else { /* t4 = I = (2*H)^2. */ fp2_dbl(t4, t3); fp2_sqr(t4, t4); /* t5 = J = H * I. */ fp2_mul(t5, t3, t4); /* t4 = V = U1 * I. */ fp2_mul(t4, t2, t4); /* x3 = R^2 - J - 2 * V. */ fp2_sqr(r->x, t0); fp2_sub(r->x, r->x, t5); fp2_dbl(t2, t4); fp2_sub(r->x, r->x, t2); /* y3 = R * (V - x3) - 2 * S1 * J. */ fp2_sub(t4, t4, r->x); fp2_mul(t4, t4, t0); fp2_mul(t1, t1, t5); fp2_dbl(t1, t1); fp2_sub(r->y, t4, t1); /* z3 = ((z1 + z2)^2 - z1^2 - z2^2) * H. */ fp2_add(r->z, p->z, q->z); fp2_sqr(r->z, r->z); fp2_sub(r->z, r->z, t6); fp2_mul(r->z, r->z, t3); } } 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); } #endif }
/** * Adds a point represented in affine coordinates to a point represented in * projective coordinates. * * @param r - the result. * @param s - the slope. * @param p - the affine point. * @param q - the projective point. */ static void ep2_add_projc_mix(ep2_t r, ep2_t p, ep2_t q) { fp2_t t0, t1, t2, t3, t4, t5, t6; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); fp2_null(t6); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_new(t6); if (!p->norm) { /* t0 = z1^2. */ fp2_sqr(t0, p->z); /* t3 = U2 = x2 * z1^2. */ fp2_mul(t3, q->x, t0); /* t1 = S2 = y2 * z1^3. */ fp2_mul(t1, t0, p->z); fp2_mul(t1, t1, q->y); /* t3 = H = U2 - x1. */ fp2_sub(t3, t3, p->x); /* t1 = R = 2 * (S2 - y1). */ fp2_sub(t1, t1, p->y); } else { /* H = x2 - x1. */ fp2_sub(t3, q->x, p->x); /* t1 = R = 2 * (y2 - y1). */ fp2_sub(t1, q->y, p->y); } /* t2 = HH = H^2. */ fp2_sqr(t2, t3); /* If E is zero. */ if (fp2_is_zero(t3)) { if (fp2_is_zero(t1)) { /* If I is zero, p = q, should have doubled. */ ep2_dbl_projc(r, p); } else { /* If I is not zero, q = -p, r = infinity. */ ep2_set_infty(r); } } else { /* t5 = J = H * HH. */ fp2_mul(t5, t3, t2); /* t4 = V = x1 * HH. */ fp2_mul(t4, p->x, t2); /* x3 = R^2 - J - 2 * V. */ fp2_sqr(r->x, t1); fp2_sub(r->x, r->x, t5); fp2_dbl(t6, t4); fp2_sub(r->x, r->x, t6); /* y3 = R * (V - x3) - Y1 * J. */ fp2_sub(t4, t4, r->x); fp2_mul(t4, t4, t1); fp2_mul(t1, p->y, t5); fp2_sub(r->y, t4, t1); if (!p->norm) { /* z3 = z1 * H. */ fp2_mul(r->z, p->z, t3); } else { /* z3 = H. */ fp2_copy(r->z, t3); } } 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); } }
/** * Computes the constantes required for evaluating Frobenius maps. */ static void fp2_calc() { bn_t e; fp2_t t0; fp2_t t1; ctx_t *ctx = core_get(); bn_null(e); fp2_null(t0); fp2_null(t1); TRY { bn_new(e); fp2_new(t0); fp2_new(t1); fp2_zero(t0); fp_set_dig(t0[0], 1); fp2_mul_nor(t0, t0); e->used = FP_DIGS; dv_copy(e->dp, fp_prime_get(), FP_DIGS); bn_sub_dig(e, e, 1); bn_div_dig(e, e, 6); fp2_exp(t0, t0, e); #if ALLOC == AUTO fp2_copy(ctx->fp2_p[0], t0); fp2_sqr(ctx->fp2_p[1], ctx->fp2_p[0]); fp2_mul(ctx->fp2_p[2], ctx->fp2_p[1], ctx->fp2_p[0]); fp2_sqr(ctx->fp2_p[3], ctx->fp2_p[1]); fp2_mul(ctx->fp2_p[4], ctx->fp2_p[3], ctx->fp2_p[0]); #else fp_copy(ctx->fp2_p[0][0], t0[0]); fp_copy(ctx->fp2_p[0][1], t0[1]); fp2_sqr(t1, t0); fp_copy(ctx->fp2_p[1][0], t1[0]); fp_copy(ctx->fp2_p[1][1], t1[1]); fp2_mul(t1, t1, t0); fp_copy(ctx->fp2_p[2][0], t1[0]); fp_copy(ctx->fp2_p[2][1], t1[1]); fp2_sqr(t1, t0); fp2_sqr(t1, t1); fp_copy(ctx->fp2_p[3][0], t1[0]); fp_copy(ctx->fp2_p[3][1], t1[1]); fp2_mul(t1, t1, t0); fp_copy(ctx->fp2_p[4][0], t1[0]); fp_copy(ctx->fp2_p[4][1], t1[1]); #endif fp2_frb(t1, t0, 1); fp2_mul(t0, t1, t0); fp_copy(ctx->fp2_p2[0], t0[0]); fp_sqr(ctx->fp2_p2[1], ctx->fp2_p2[0]); fp_mul(ctx->fp2_p2[2], ctx->fp2_p2[1], ctx->fp2_p2[0]); fp_sqr(ctx->fp2_p2[3], ctx->fp2_p2[1]); for (int i = 0; i < 5; i++) { fp_mul(ctx->fp2_p3[i][0], ctx->fp2_p2[i % 3], ctx->fp2_p[i][0]); fp_mul(ctx->fp2_p3[i][1], ctx->fp2_p2[i % 3], ctx->fp2_p[i][1]); } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { bn_free(e); fp2_free(t0); fp2_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); } }
void fp12_sqr_pck_basic(fp12_t c, fp12_t a) { fp2_t t0, t1, t2, t3, t4, t5, t6; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); fp2_null(t6); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_new(t6); fp2_sqr(t0, a[0][1]); fp2_sqr(t1, a[1][2]); fp2_add(t5, a[0][1], a[1][2]); fp2_sqr(t2, t5); fp2_add(t3, t0, t1); fp2_sub(t5, t2, t3); fp2_add(t6, a[1][0], a[0][2]); fp2_sqr(t3, t6); fp2_sqr(t2, a[1][0]); fp2_mul_nor(t6, t5); fp2_add(t5, t6, a[1][0]); fp2_dbl(t5, t5); fp2_add(c[1][0], t5, t6); fp2_mul_nor(t4, t1); fp2_add(t5, t0, t4); fp2_sub(t6, t5, a[0][2]); fp2_sqr(t1, a[0][2]); fp2_dbl(t6, t6); fp2_add(c[0][2], t6, t5); fp2_mul_nor(t4, t1); fp2_add(t5, t2, t4); fp2_sub(t6, t5, a[0][1]); fp2_dbl(t6, t6); fp2_add(c[0][1], t6, t5); fp2_add(t0, t2, t1); fp2_sub(t5, t3, t0); fp2_add(t6, t5, a[1][2]); fp2_dbl(t6, t6); fp2_add(c[1][2], t5, t6); } 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); } }
void fp12_sqr_cyc_basic(fp12_t c, fp12_t a) { fp2_t t0, t1, t2, t3, t4, t5, t6; fp2_null(t0); fp2_null(t1); fp2_null(t2); fp2_null(t3); fp2_null(t4); fp2_null(t5); fp2_null(t6); TRY { fp2_new(t0); fp2_new(t1); fp2_new(t2); fp2_new(t3); fp2_new(t4); fp2_new(t5); fp2_new(t6); /* Define z = sqrt(E) */ /* Now a is seen as (t0,t1) + (t2,t3) * w + (t4,t5) * w^2 */ /* (t0, t1) = (a00 + a11*z)^2. */ fp2_sqr(t2, a[0][0]); fp2_sqr(t3, a[1][1]); fp2_add(t1, a[0][0], a[1][1]); fp2_mul_nor(t0, t3); fp2_add(t0, t0, t2); fp2_sqr(t1, t1); fp2_sub(t1, t1, t2); fp2_sub(t1, t1, t3); fp2_sub(c[0][0], t0, a[0][0]); fp2_add(c[0][0], c[0][0], c[0][0]); fp2_add(c[0][0], t0, c[0][0]); fp2_add(c[1][1], t1, a[1][1]); fp2_add(c[1][1], c[1][1], c[1][1]); fp2_add(c[1][1], t1, c[1][1]); fp2_sqr(t0, a[0][1]); fp2_sqr(t1, a[1][2]); fp2_add(t5, a[0][1], a[1][2]); fp2_sqr(t2, t5); fp2_add(t3, t0, t1); fp2_sub(t5, t2, t3); fp2_add(t6, a[1][0], a[0][2]); fp2_sqr(t3, t6); fp2_sqr(t2, a[1][0]); fp2_mul_nor(t6, t5); fp2_add(t5, t6, a[1][0]); fp2_dbl(t5, t5); fp2_add(c[1][0], t5, t6); fp2_mul_nor(t4, t1); fp2_add(t5, t0, t4); fp2_sub(t6, t5, a[0][2]); fp2_sqr(t1, a[0][2]); fp2_dbl(t6, t6); fp2_add(c[0][2], t6, t5); fp2_mul_nor(t4, t1); fp2_add(t5, t2, t4); fp2_sub(t6, t5, a[0][1]); fp2_dbl(t6, t6); fp2_add(c[0][1], t6, t5); fp2_add(t0, t2, t1); fp2_sub(t5, t3, t0); fp2_add(t6, t5, a[1][2]); fp2_dbl(t6, t6); fp2_add(c[1][2], t5, t6); } 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); } }