/** * 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 ep2_neg_projc(ep2_t r, ep2_t p) { if (ep2_is_infty(p)) { ep2_set_infty(r); return; } if (r != p) { fp2_copy(r->x, p->x); fp2_copy(r->z, p->z); } fp2_neg(r->y, p->y); r->norm = p->norm; }
void ep2_curve_set(fp2_t a, fp2_t b, ep2_t g, bn_t r, bn_t h) { ctx_t *ctx = core_get(); ctx->ep2_is_twist = 0; fp2_copy(ctx->ep2_a, a); fp2_copy(ctx->ep2_b, b); ep2_norm(&(ctx->ep2_g), g); bn_copy(&(ctx->ep2_r), r); bn_copy(&(ctx->ep2_h), h); #if defined(EP_PRECO) ep2_mul_pre((ep2_t *)ep2_curve_get_tab(), &(ctx->ep2_g)); #endif }
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); } }
void fp2_pck(fp2_t c, fp2_t a) { int b = fp_get_bit(a[1], 0); if (fp2_test_uni(c)) { fp_copy(c[0], a[0]); fp_zero(c[1]); fp_set_bit(c[1], 0, b); } else { fp2_copy(c, a); } }
void fp2_inv_sim(fp2_t *c, fp2_t *a, int n) { int i; fp2_t u, t[n]; for (i = 0; i < n; i++) { fp2_null(t[i]); } fp2_null(u); TRY { for (i = 0; i < n; i++) { fp2_new(t[i]); } fp2_new(u); fp2_copy(c[0], a[0]); fp2_copy(t[0], a[0]); for (i = 1; i < n; i++) { fp2_copy(t[i], a[i]); fp2_mul(c[i], c[i - 1], t[i]); } fp2_inv(u, c[n - 1]); for (i = n - 1; i > 0; i--) { fp2_mul(c[i], c[i - 1], u); fp2_mul(u, u, t[i]); } fp2_copy(c[0], u); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { for (i = 0; i < n; i++) { fp2_free(t[i]); } fp2_free(u); } }
/** * 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); } }
void fp12_mul_dxs_lazyr(fp12_t c, fp12_t a, fp12_t b) { fp6_t t0; dv6_t u0, u1, u2; fp6_null(t0); dv6_null(u0); dv6_null(u1); dv6_null(u2); TRY { fp6_new(t0); dv6_new(u0); dv6_new(u1); dv6_new(u2); if (ep2_curve_is_twist() == EP_DTYPE) { #if EP_ADD == BASIC /* t0 = a_0 * b_0. */ fp_muln_low(u0[0][0], a[0][0][0], b[0][0][0]); fp_muln_low(u0[0][1], a[0][0][1], b[0][0][0]); fp_muln_low(u0[1][0], a[0][1][0], b[0][0][0]); fp_muln_low(u0[1][1], a[0][1][1], b[0][0][0]); fp_muln_low(u0[2][0], a[0][2][0], b[0][0][0]); fp_muln_low(u0[2][1], a[0][2][1], b[0][0][0]); /* t2 = b_0 + b_1. */ fp_add(t0[0][0], b[0][0][0], b[1][0][0]); fp_copy(t0[0][1], b[1][0][1]); fp2_copy(t0[1], b[1][1]); #elif EP_ADD == PROJC /* t0 = a_0 * b_0. */ #ifdef RLC_FP_ROOM fp2_mulc_low(u0[0], a[0][0], b[0][0]); fp2_mulc_low(u0[1], a[0][1], b[0][0]); fp2_mulc_low(u0[2], a[0][2], b[0][0]); #else fp2_muln_low(u0[0], a[0][0], b[0][0]); fp2_muln_low(u0[1], a[0][1], b[0][0]); fp2_muln_low(u0[2], a[0][2], b[0][0]); #endif /* t2 = b_0 + b_1. */ fp2_add(t0[0], b[0][0], b[1][0]); fp2_copy(t0[1], b[1][1]); #endif /* t1 = a_1 * b_1. */ fp6_mul_dxs_unr_lazyr(u1, a[1], b[1]); } else { /* t0 = a_0 * b_0. */ fp6_mul_dxs_unr_lazyr(u0, a[0], b[0]); #if EP_ADD == BASIC /* t0 = a_0 * b_0. */ fp_muln_low(u1[1][0], a[1][2][0], b[1][1][0]); fp_muln_low(u1[1][1], a[1][2][1], b[1][1][0]); fp2_nord_low(u1[0], u1[1]); fp_muln_low(u1[1][0], a[1][0][0], b[1][1][0]); fp_muln_low(u1[1][1], a[1][0][1], b[1][1][0]); fp_muln_low(u1[2][0], a[1][1][0], b[1][1][0]); fp_muln_low(u1[2][1], a[1][1][1], b[1][1][0]); /* t2 = b_0 + b_1. */ fp2_copy(t0[0], b[0][0]); fp_add(t0[1][0], b[0][1][0], b[1][1][0]); fp_copy(t0[1][1], b[0][1][1]); #elif EP_ADD == PROJC /* t1 = a_1 * b_1. */ fp2_muln_low(u1[1], a[1][2], b[1][1]); fp2_nord_low(u1[0], u1[1]); fp2_muln_low(u1[1], a[1][0], b[1][1]); fp2_muln_low(u1[2], a[1][1], b[1][1]); /* t2 = b_0 + b_1. */ fp2_copy(t0[0], b[0][0]); fp2_add(t0[1], b[0][1], b[1][1]); #endif } /* c_1 = a_0 + a_1. */ fp6_add(c[1], a[0], a[1]); /* c_1 = (a_0 + a_1) * (b_0 + b_1) */ fp6_mul_dxs_unr_lazyr(u2, c[1], t0); for (int i = 0; i < 3; i++) { fp2_subc_low(u2[i], u2[i], u0[i]); fp2_subc_low(u2[i], u2[i], u1[i]); } fp2_rdcn_low(c[1][0], u2[0]); fp2_rdcn_low(c[1][1], u2[1]); fp2_rdcn_low(c[1][2], u2[2]); fp2_nord_low(u2[0], u1[2]); fp2_addc_low(u0[0], u0[0], u2[0]); fp2_addc_low(u0[1], u0[1], u1[0]); fp2_addc_low(u0[2], u0[2], u1[1]); /* c_0 = a_0b_0 + v * a_1b_1. */ fp2_rdcn_low(c[0][0], u0[0]); fp2_rdcn_low(c[0][1], u0[1]); fp2_rdcn_low(c[0][2], u0[2]); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp6_free(t0); dv6_free(u0); dv6_free(u1); dv6_free(u2); } }
void fp12_mul_dxs_basic(fp12_t c, fp12_t a, fp12_t b) { fp6_t t0, t1, t2; fp6_null(t0); fp6_null(t1); fp6_null(t2); TRY { fp6_new(t0); fp6_new(t1); fp6_new(t2); if (ep2_curve_is_twist() == EP_DTYPE) { #if EP_ADD == BASIC /* t0 = a_0 * b_0 */ fp_mul(t0[0][0], a[0][0][0], b[0][0][0]); fp_mul(t0[0][1], a[0][0][1], b[0][0][0]); fp_mul(t0[1][0], a[0][1][0], b[0][0][0]); fp_mul(t0[1][1], a[0][1][1], b[0][0][0]); fp_mul(t0[2][0], a[0][2][0], b[0][0][0]); fp_mul(t0[2][1], a[0][2][1], b[0][0][0]); /* t2 = b_0 + b_1. */ fp_add(t2[0][0], b[0][0][0], b[1][0][0]); fp_copy(t2[0][1], b[1][0][1]); fp2_copy(t2[1], b[1][1]); #elif EP_ADD == PROJC /* t0 = a_0 * b_0 */ fp2_mul(t0[0], a[0][0], b[0][0]); fp2_mul(t0[1], a[0][1], b[0][0]); fp2_mul(t0[2], a[0][2], b[0][0]); /* t2 = b_0 + b_1. */ fp2_add(t2[0], b[0][0], b[1][0]); fp2_copy(t2[1], b[1][1]); #endif /* t1 = a_1 * b_1. */ fp6_mul_dxs(t1, a[1], b[1]); } else { /* t0 = a_0 * b_0. */ fp6_mul_dxs(t0, a[0], b[0]); #if EP_ADD == BASIC /* t1 = a_1 * b_1. */ fp_mul(t2[0][0], a[1][2][0], b[1][1][0]); fp_mul(t2[0][1], a[1][2][1], b[1][1][0]); fp2_mul_nor(t1[0], t2[0]); fp_mul(t1[1][0], a[1][0][0], b[1][1][0]); fp_mul(t1[1][1], a[1][0][1], b[1][1][0]); fp_mul(t1[2][0], a[1][1][0], b[1][1][0]); fp_mul(t1[2][1], a[1][1][1], b[1][1][0]); /* t2 = b_0 + b_1. */ fp2_copy(t2[0], b[0][0]); fp_add(t2[1][0], b[0][1][0], b[1][1][0]); fp_copy(t2[1][1], b[0][1][1]); #elif EP_ADD == PROJC /* t1 = a_1 * b_1. */ fp2_mul(t2[0], a[1][2], b[1][1]); fp2_mul_nor(t1[0], t2[0]); fp2_mul(t1[1], a[1][0], b[1][1]); fp2_mul(t1[2], a[1][1], b[1][1]); /* t2 = b_0 + b_1. */ fp2_copy(t2[0], b[0][0]); fp2_add(t2[1], b[0][1], b[1][1]); #endif } /* c_1 = a_0 + a_1. */ fp6_add(c[1], a[0], a[1]); /* c_1 = (a_0 + a_1) * (b_0 + b_1) - a_0 * b_0 - a_1 * b_1. */ fp6_mul_dxs(c[1], c[1], t2); fp6_sub(c[1], c[1], t0); fp6_sub(c[1], c[1], t1); /* c_0 = a_0 * b_0 + v * a_1 * b_1. */ fp6_mul_art(t1, t1); fp6_add(c[0], t0, t1); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp6_free(t0); fp6_free(t1); fp6_free(t2); } }
/** * 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 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 fp6_copy(fp6_t c, fp6_t a) { fp2_copy(c[0], a[0]); fp2_copy(c[1], a[1]); fp2_copy(c[2], a[2]); }
void ep2_copy(ep2_t r, ep2_t p) { fp2_copy(r->x, p->x); fp2_copy(r->y, p->y); fp2_copy(r->z, p->z); r->norm = p->norm; }