diff options
Diffstat (limited to 'crypto/ecc.c')
| -rw-r--r-- | crypto/ecc.c | 266 |
1 files changed, 192 insertions, 74 deletions
diff --git a/crypto/ecc.c b/crypto/ecc.c index f6cef5a7942d..589831d82063 100644 --- a/crypto/ecc.c +++ b/crypto/ecc.c @@ -778,18 +778,133 @@ static void vli_mmod_fast_256(u64 *result, const u64 *product, } } +#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32) +#define AND64H(x64) (x64 & 0xffFFffFF00000000ull) +#define AND64L(x64) (x64 & 0x00000000ffFFffFFull) + +/* Computes result = product % curve_prime + * from "Mathematical routines for the NIST prime elliptic curves" + */ +static void vli_mmod_fast_384(u64 *result, const u64 *product, + const u64 *curve_prime, u64 *tmp) +{ + int carry; + const unsigned int ndigits = 6; + + /* t */ + vli_set(result, product, ndigits); + + /* s1 */ + tmp[0] = 0; // 0 || 0 + tmp[1] = 0; // 0 || 0 + tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 + tmp[3] = product[11]>>32; // 0 ||a23 + tmp[4] = 0; // 0 || 0 + tmp[5] = 0; // 0 || 0 + carry = vli_lshift(tmp, tmp, 1, ndigits); + carry += vli_add(result, result, tmp, ndigits); + + /* s2 */ + tmp[0] = product[6]; //a13||a12 + tmp[1] = product[7]; //a15||a14 + tmp[2] = product[8]; //a17||a16 + tmp[3] = product[9]; //a19||a18 + tmp[4] = product[10]; //a21||a20 + tmp[5] = product[11]; //a23||a22 + carry += vli_add(result, result, tmp, ndigits); + + /* s3 */ + tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 + tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 + tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13 + tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 + tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 + tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 + carry += vli_add(result, result, tmp, ndigits); + + /* s4 */ + tmp[0] = AND64H(product[11]); //a23|| 0 + tmp[1] = (product[10]<<32); //a20|| 0 + tmp[2] = product[6]; //a13||a12 + tmp[3] = product[7]; //a15||a14 + tmp[4] = product[8]; //a17||a16 + tmp[5] = product[9]; //a19||a18 + carry += vli_add(result, result, tmp, ndigits); + + /* s5 */ + tmp[0] = 0; // 0|| 0 + tmp[1] = 0; // 0|| 0 + tmp[2] = product[10]; //a21||a20 + tmp[3] = product[11]; //a23||a22 + tmp[4] = 0; // 0|| 0 + tmp[5] = 0; // 0|| 0 + carry += vli_add(result, result, tmp, ndigits); + + /* s6 */ + tmp[0] = AND64L(product[10]); // 0 ||a20 + tmp[1] = AND64H(product[10]); //a21|| 0 + tmp[2] = product[11]; //a23||a22 + tmp[3] = 0; // 0 || 0 + tmp[4] = 0; // 0 || 0 + tmp[5] = 0; // 0 || 0 + carry += vli_add(result, result, tmp, ndigits); + + /* d1 */ + tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 + tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13 + tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 + tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 + tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 + tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 + carry -= vli_sub(result, result, tmp, ndigits); + + /* d2 */ + tmp[0] = (product[10]<<32); //a20|| 0 + tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 + tmp[2] = (product[11]>>32); // 0 ||a23 + tmp[3] = 0; // 0 || 0 + tmp[4] = 0; // 0 || 0 + tmp[5] = 0; // 0 || 0 + carry -= vli_sub(result, result, tmp, ndigits); + + /* d3 */ + tmp[0] = 0; // 0 || 0 + tmp[1] = AND64H(product[11]); //a23|| 0 + tmp[2] = product[11]>>32; // 0 ||a23 + tmp[3] = 0; // 0 || 0 + tmp[4] = 0; // 0 || 0 + tmp[5] = 0; // 0 || 0 + carry -= vli_sub(result, result, tmp, ndigits); + + if (carry < 0) { + do { + carry += vli_add(result, result, curve_prime, ndigits); + } while (carry < 0); + } else { + while (carry || vli_cmp(curve_prime, result, ndigits) != 1) + carry -= vli_sub(result, result, curve_prime, ndigits); + } + +} + +#undef SL32OR32 +#undef AND64H +#undef AND64L + /* Computes result = product % curve_prime for different curve_primes. * * Note that curve_primes are distinguished just by heuristic check and * not by complete conformance check. */ static bool vli_mmod_fast(u64 *result, u64 *product, - const u64 *curve_prime, unsigned int ndigits) + const struct ecc_curve *curve) { u64 tmp[2 * ECC_MAX_DIGITS]; + const u64 *curve_prime = curve->p; + const unsigned int ndigits = curve->g.ndigits; - /* Currently, both NIST primes have -1 in lowest qword. */ - if (curve_prime[0] != -1ull) { + /* All NIST curves have name prefix 'nist_' */ + if (strncmp(curve->name, "nist_", 5) != 0) { /* Try to handle Pseudo-Marsenne primes. */ if (curve_prime[ndigits - 1] == -1ull) { vli_mmod_special(result, product, curve_prime, @@ -812,6 +927,9 @@ static bool vli_mmod_fast(u64 *result, u64 *product, case 4: vli_mmod_fast_256(result, product, curve_prime, tmp); break; + case 6: + vli_mmod_fast_384(result, product, curve_prime, tmp); + break; default: pr_err_ratelimited("ecc: unsupported digits size!\n"); return false; @@ -835,22 +953,22 @@ EXPORT_SYMBOL(vli_mod_mult_slow); /* Computes result = (left * right) % curve_prime. */ static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, - const u64 *curve_prime, unsigned int ndigits) + const struct ecc_curve *curve) { u64 product[2 * ECC_MAX_DIGITS]; - vli_mult(product, left, right, ndigits); - vli_mmod_fast(result, product, curve_prime, ndigits); + vli_mult(product, left, right, curve->g.ndigits); + vli_mmod_fast(result, product, curve); } /* Computes result = left^2 % curve_prime. */ static void vli_mod_square_fast(u64 *result, const u64 *left, - const u64 *curve_prime, unsigned int ndigits) + const struct ecc_curve *curve) { u64 product[2 * ECC_MAX_DIGITS]; - vli_square(product, left, ndigits); - vli_mmod_fast(result, product, curve_prime, ndigits); + vli_square(product, left, curve->g.ndigits); + vli_mmod_fast(result, product, curve); } #define EVEN(vli) (!(vli[0] & 1)) @@ -948,25 +1066,27 @@ static bool ecc_point_is_zero(const struct ecc_point *point) /* Double in place */ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, - u64 *curve_prime, unsigned int ndigits) + const struct ecc_curve *curve) { /* t1 = x, t2 = y, t3 = z */ u64 t4[ECC_MAX_DIGITS]; u64 t5[ECC_MAX_DIGITS]; + const u64 *curve_prime = curve->p; + const unsigned int ndigits = curve->g.ndigits; if (vli_is_zero(z1, ndigits)) return; /* t4 = y1^2 */ - vli_mod_square_fast(t4, y1, curve_prime, ndigits); + vli_mod_square_fast(t4, y1, curve); /* t5 = x1*y1^2 = A */ - vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits); + vli_mod_mult_fast(t5, x1, t4, curve); /* t4 = y1^4 */ - vli_mod_square_fast(t4, t4, curve_prime, ndigits); + vli_mod_square_fast(t4, t4, curve); /* t2 = y1*z1 = z3 */ - vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits); + vli_mod_mult_fast(y1, y1, z1, curve); /* t3 = z1^2 */ - vli_mod_square_fast(z1, z1, curve_prime, ndigits); + vli_mod_square_fast(z1, z1, curve); /* t1 = x1 + z1^2 */ vli_mod_add(x1, x1, z1, curve_prime, ndigits); @@ -975,7 +1095,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, /* t3 = x1 - z1^2 */ vli_mod_sub(z1, x1, z1, curve_prime, ndigits); /* t1 = x1^2 - z1^4 */ - vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits); + vli_mod_mult_fast(x1, x1, z1, curve); /* t3 = 2*(x1^2 - z1^4) */ vli_mod_add(z1, x1, x1, curve_prime, ndigits); @@ -992,7 +1112,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, /* t1 = 3/2*(x1^2 - z1^4) = B */ /* t3 = B^2 */ - vli_mod_square_fast(z1, x1, curve_prime, ndigits); + vli_mod_square_fast(z1, x1, curve); /* t3 = B^2 - A */ vli_mod_sub(z1, z1, t5, curve_prime, ndigits); /* t3 = B^2 - 2A = x3 */ @@ -1000,7 +1120,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, /* t5 = A - x3 */ vli_mod_sub(t5, t5, z1, curve_prime, ndigits); /* t1 = B * (A - x3) */ - vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + vli_mod_mult_fast(x1, x1, t5, curve); /* t4 = B * (A - x3) - y1^4 = y3 */ vli_mod_sub(t4, x1, t4, curve_prime, ndigits); @@ -1010,23 +1130,22 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, } /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ -static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime, - unsigned int ndigits) +static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve) { u64 t1[ECC_MAX_DIGITS]; - vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */ - vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */ - vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */ - vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */ + vli_mod_square_fast(t1, z, curve); /* z^2 */ + vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */ + vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */ + vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */ } /* P = (x1, y1) => 2P, (x2, y2) => P' */ static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, - u64 *p_initial_z, u64 *curve_prime, - unsigned int ndigits) + u64 *p_initial_z, const struct ecc_curve *curve) { u64 z[ECC_MAX_DIGITS]; + const unsigned int ndigits = curve->g.ndigits; vli_set(x2, x1, ndigits); vli_set(y2, y1, ndigits); @@ -1037,35 +1156,37 @@ static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, if (p_initial_z) vli_set(z, p_initial_z, ndigits); - apply_z(x1, y1, z, curve_prime, ndigits); + apply_z(x1, y1, z, curve); - ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits); + ecc_point_double_jacobian(x1, y1, z, curve); - apply_z(x2, y2, z, curve_prime, ndigits); + apply_z(x2, y2, z, curve); } /* Input P = (x1, y1, Z), Q = (x2, y2, Z) * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) * or P => P', Q => P + Q */ -static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, - unsigned int ndigits) +static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, + const struct ecc_curve *curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ u64 t5[ECC_MAX_DIGITS]; + const u64 *curve_prime = curve->p; + const unsigned int ndigits = curve->g.ndigits; /* t5 = x2 - x1 */ vli_mod_sub(t5, x2, x1, curve_prime, ndigits); /* t5 = (x2 - x1)^2 = A */ - vli_mod_square_fast(t5, t5, curve_prime, ndigits); + vli_mod_square_fast(t5, t5, curve); /* t1 = x1*A = B */ - vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + vli_mod_mult_fast(x1, x1, t5, curve); /* t3 = x2*A = C */ - vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); + vli_mod_mult_fast(x2, x2, t5, curve); /* t4 = y2 - y1 */ vli_mod_sub(y2, y2, y1, curve_prime, ndigits); /* t5 = (y2 - y1)^2 = D */ - vli_mod_square_fast(t5, y2, curve_prime, ndigits); + vli_mod_square_fast(t5, y2, curve); /* t5 = D - B */ vli_mod_sub(t5, t5, x1, curve_prime, ndigits); @@ -1074,11 +1195,11 @@ static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, /* t3 = C - B */ vli_mod_sub(x2, x2, x1, curve_prime, ndigits); /* t2 = y1*(C - B) */ - vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits); + vli_mod_mult_fast(y1, y1, x2, curve); /* t3 = B - x3 */ vli_mod_sub(x2, x1, t5, curve_prime, ndigits); /* t4 = (y2 - y1)*(B - x3) */ - vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits); + vli_mod_mult_fast(y2, y2, x2, curve); /* t4 = y3 */ vli_mod_sub(y2, y2, y1, curve_prime, ndigits); @@ -1089,22 +1210,24 @@ static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) * or P => P - Q, Q => P + Q */ -static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, - unsigned int ndigits) +static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, + const struct ecc_curve *curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ u64 t5[ECC_MAX_DIGITS]; u64 t6[ECC_MAX_DIGITS]; u64 t7[ECC_MAX_DIGITS]; + const u64 *curve_prime = curve->p; + const unsigned int ndigits = curve->g.ndigits; /* t5 = x2 - x1 */ vli_mod_sub(t5, x2, x1, curve_prime, ndigits); /* t5 = (x2 - x1)^2 = A */ - vli_mod_square_fast(t5, t5, curve_prime, ndigits); + vli_mod_square_fast(t5, t5, curve); /* t1 = x1*A = B */ - vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + vli_mod_mult_fast(x1, x1, t5, curve); /* t3 = x2*A = C */ - vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); + vli_mod_mult_fast(x2, x2, t5, curve); /* t4 = y2 + y1 */ vli_mod_add(t5, y2, y1, curve_prime, ndigits); /* t4 = y2 - y1 */ @@ -1113,29 +1236,29 @@ static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, /* t6 = C - B */ vli_mod_sub(t6, x2, x1, curve_prime, ndigits); /* t2 = y1 * (C - B) */ - vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits); + vli_mod_mult_fast(y1, y1, t6, curve); /* t6 = B + C */ vli_mod_add(t6, x1, x2, curve_prime, ndigits); /* t3 = (y2 - y1)^2 */ - vli_mod_square_fast(x2, y2, curve_prime, ndigits); + vli_mod_square_fast(x2, y2, curve); /* t3 = x3 */ vli_mod_sub(x2, x2, t6, curve_prime, ndigits); /* t7 = B - x3 */ vli_mod_sub(t7, x1, x2, curve_prime, ndigits); /* t4 = (y2 - y1)*(B - x3) */ - vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits); + vli_mod_mult_fast(y2, y2, t7, curve); /* t4 = y3 */ vli_mod_sub(y2, y2, y1, curve_prime, ndigits); /* t7 = (y2 + y1)^2 = F */ - vli_mod_square_fast(t7, t5, curve_prime, ndigits); + vli_mod_square_fast(t7, t5, curve); /* t7 = x3' */ vli_mod_sub(t7, t7, t6, curve_prime, ndigits); /* t6 = x3' - B */ vli_mod_sub(t6, t7, x1, curve_prime, ndigits); /* t6 = (y2 + y1)*(x3' - B) */ - vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits); + vli_mod_mult_fast(t6, t6, t5, curve); /* t2 = y3' */ vli_mod_sub(y1, t6, y1, curve_prime, ndigits); @@ -1165,41 +1288,37 @@ static void ecc_point_mult(struct ecc_point *result, vli_set(rx[1], point->x, ndigits); vli_set(ry[1], point->y, ndigits); - xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime, - ndigits); + xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve); for (i = num_bits - 2; i > 0; i--) { nb = !vli_test_bit(scalar, i); - xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime, - ndigits); - xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, - ndigits); + xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); } nb = !vli_test_bit(scalar, 0); - xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime, - ndigits); + xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); /* Find final 1/Z value. */ /* X1 - X0 */ vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); /* Yb * (X1 - X0) */ - vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits); + vli_mod_mult_fast(z, z, ry[1 - nb], curve); /* xP * Yb * (X1 - X0) */ - vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits); + vli_mod_mult_fast(z, z, point->x, curve); /* 1 / (xP * Yb * (X1 - X0)) */ vli_mod_inv(z, z, curve_prime, point->ndigits); /* yP / (xP * Yb * (X1 - X0)) */ - vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits); + vli_mod_mult_fast(z, z, point->y, curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */ - vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits); + vli_mod_mult_fast(z, z, rx[1 - nb], curve); /* End 1/Z calculation */ - xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits); + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); - apply_z(rx[0], ry[0], z, curve_prime, ndigits); + apply_z(rx[0], ry[0], z, curve); vli_set(result->x, rx[0], ndigits); vli_set(result->y, ry[0], ndigits); @@ -1220,9 +1339,9 @@ static void ecc_point_add(const struct ecc_point *result, vli_mod_sub(z, result->x, p->x, curve->p, ndigits); vli_set(px, p->x, ndigits); vli_set(py, p->y, ndigits); - xycz_add(px, py, result->x, result->y, curve->p, ndigits); + xycz_add(px, py, result->x, result->y, curve); vli_mod_inv(z, z, curve->p, ndigits); - apply_z(result->x, result->y, z, curve->p, ndigits); + apply_z(result->x, result->y, z, curve); } /* Computes R = u1P + u2Q mod p using Shamir's trick. @@ -1251,8 +1370,7 @@ void ecc_point_mult_shamir(const struct ecc_point *result, points[2] = q; points[3] = ∑ - num_bits = max(vli_num_bits(u1, ndigits), - vli_num_bits(u2, ndigits)); + num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits)); i = num_bits - 1; idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); point = points[idx]; @@ -1263,7 +1381,7 @@ void ecc_point_mult_shamir(const struct ecc_point *result, z[0] = 1; for (--i; i >= 0; i--) { - ecc_point_double_jacobian(rx, ry, z, curve->p, ndigits); + ecc_point_double_jacobian(rx, ry, z, curve); idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); point = points[idx]; if (point) { @@ -1273,14 +1391,14 @@ void ecc_point_mult_shamir(const struct ecc_point *result, vli_set(tx, point->x, ndigits); vli_set(ty, point->y, ndigits); - apply_z(tx, ty, z, curve->p, ndigits); + apply_z(tx, ty, z, curve); vli_mod_sub(tz, rx, tx, curve->p, ndigits); - xycz_add(tx, ty, rx, ry, curve->p, ndigits); - vli_mod_mult_fast(z, z, tz, curve->p, ndigits); + xycz_add(tx, ty, rx, ry, curve); + vli_mod_mult_fast(z, z, tz, curve); } } vli_mod_inv(z, z, curve->p, ndigits); - apply_z(rx, ry, z, curve->p, ndigits); + apply_z(rx, ry, z, curve); } EXPORT_SYMBOL(ecc_point_mult_shamir); @@ -1434,10 +1552,10 @@ int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, return -EINVAL; /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */ - vli_mod_square_fast(yy, pk->y, curve->p, pk->ndigits); /* y^2 */ - vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */ - vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */ - vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* a·x */ + vli_mod_square_fast(yy, pk->y, curve); /* y^2 */ + vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */ + vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */ + vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */ vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */ vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */ if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */ |