--- /dev/null
+/*
+ * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+/******************************************************************************
+ * *
+ * Copyright 2014 Intel Corporation *
+ * *
+ * Licensed under the Apache License, Version 2.0 (the "License"); *
+ * you may not use this file except in compliance with the License. *
+ * You may obtain a copy of the License at *
+ * *
+ * http://www.apache.org/licenses/LICENSE-2.0 *
+ * *
+ * Unless required by applicable law or agreed to in writing, software *
+ * distributed under the License is distributed on an "AS IS" BASIS, *
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
+ * See the License for the specific language governing permissions and *
+ * limitations under the License. *
+ * *
+ ******************************************************************************
+ * *
+ * Developers and authors: *
+ * Shay Gueron (1, 2), and Vlad Krasnov (1) *
+ * (1) Intel Corporation, Israel Development Center *
+ * (2) University of Haifa *
+ * Reference: *
+ * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
+ * 256 Bit Primes" *
+ * *
+ ******************************************************************************/
+
+#include <string.h>
+
+#include "internal/cryptlib.h"
+#include "internal/bn_int.h"
+#include "ec_lcl.h"
+
+#if BN_BITS2 != 64
+# define TOBN(hi,lo) lo,hi
+#else
+# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
+#endif
+
+#if defined(__GNUC__)
+# define ALIGN32 __attribute((aligned(32)))
+#elif defined(_MSC_VER)
+# define ALIGN32 __declspec(align(32))
+#else
+# define ALIGN32
+#endif
+
+#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
+#define P256_LIMBS (256/BN_BITS2)
+
+typedef unsigned short u16;
+
+typedef struct {
+ BN_ULONG X[P256_LIMBS];
+ BN_ULONG Y[P256_LIMBS];
+ BN_ULONG Z[P256_LIMBS];
+} P256_POINT;
+
+typedef struct {
+ BN_ULONG X[P256_LIMBS];
+ BN_ULONG Y[P256_LIMBS];
+} P256_POINT_AFFINE;
+
+typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
+
+/* structure for precomputed multiples of the generator */
+struct nistz256_pre_comp_st {
+ const EC_GROUP *group; /* Parent EC_GROUP object */
+ size_t w; /* Window size */
+ /*
+ * Constant time access to the X and Y coordinates of the pre-computed,
+ * generator multiplies, in the Montgomery domain. Pre-calculated
+ * multiplies are stored in affine form.
+ */
+ PRECOMP256_ROW *precomp;
+ void *precomp_storage;
+ int references;
+ CRYPTO_RWLOCK *lock;
+};
+
+/* Functions implemented in assembly */
+/*
+ * Most of below mentioned functions *preserve* the property of inputs
+ * being fully reduced, i.e. being in [0, modulus) range. Simply put if
+ * inputs are fully reduced, then output is too. Note that reverse is
+ * not true, in sense that given partially reduced inputs output can be
+ * either, not unlikely reduced. And "most" in first sentence refers to
+ * the fact that given the calculations flow one can tolerate that
+ * addition, 1st function below, produces partially reduced result *if*
+ * multiplications by 2 and 3, which customarily use addition, fully
+ * reduce it. This effectively gives two options: a) addition produces
+ * fully reduced result [as long as inputs are, just like remaining
+ * functions]; b) addition is allowed to produce partially reduced
+ * result, but multiplications by 2 and 3 perform additional reduction
+ * step. Choice between the two can be platform-specific, but it was a)
+ * in all cases so far...
+ */
+/* Modular add: res = a+b mod P */
+void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS],
+ const BN_ULONG b[P256_LIMBS]);
+/* Modular mul by 2: res = 2*a mod P */
+void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS]);
+/* Modular mul by 3: res = 3*a mod P */
+void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS]);
+
+/* Modular div by 2: res = a/2 mod P */
+void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS]);
+/* Modular sub: res = a-b mod P */
+void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS],
+ const BN_ULONG b[P256_LIMBS]);
+/* Modular neg: res = -a mod P */
+void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
+/* Montgomery mul: res = a*b*2^-256 mod P */
+void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS],
+ const BN_ULONG b[P256_LIMBS]);
+/* Montgomery sqr: res = a*a*2^-256 mod P */
+void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS]);
+/* Convert a number from Montgomery domain, by multiplying with 1 */
+void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG in[P256_LIMBS]);
+/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
+void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG in[P256_LIMBS]);
+/* Functions that perform constant time access to the precomputed tables */
+void ecp_nistz256_scatter_w5(P256_POINT *val,
+ const P256_POINT *in_t, int idx);
+void ecp_nistz256_gather_w5(P256_POINT *val,
+ const P256_POINT *in_t, int idx);
+void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
+ const P256_POINT_AFFINE *in_t, int idx);
+void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
+ const P256_POINT_AFFINE *in_t, int idx);
+
+/* One converted into the Montgomery domain */
+static const BN_ULONG ONE[P256_LIMBS] = {
+ TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
+ TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
+};
+
+static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
+
+/* Precomputed tables for the default generator */
+extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
+
+/* Recode window to a signed digit, see ecp_nistputil.c for details */
+static unsigned int _booth_recode_w5(unsigned int in)
+{
+ unsigned int s, d;
+
+ s = ~((in >> 5) - 1);
+ d = (1 << 6) - in - 1;
+ d = (d & s) | (in & ~s);
+ d = (d >> 1) + (d & 1);
+
+ return (d << 1) + (s & 1);
+}
+
+static unsigned int _booth_recode_w7(unsigned int in)
+{
+ unsigned int s, d;
+
+ s = ~((in >> 7) - 1);
+ d = (1 << 8) - in - 1;
+ d = (d & s) | (in & ~s);
+ d = (d >> 1) + (d & 1);
+
+ return (d << 1) + (s & 1);
+}
+
+static void copy_conditional(BN_ULONG dst[P256_LIMBS],
+ const BN_ULONG src[P256_LIMBS], BN_ULONG move)
+{
+ BN_ULONG mask1 = 0-move;
+ BN_ULONG mask2 = ~mask1;
+
+ dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
+ dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
+ dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
+ dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
+ if (P256_LIMBS == 8) {
+ dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
+ dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
+ dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
+ dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
+ }
+}
+
+static BN_ULONG is_zero(BN_ULONG in)
+{
+ in |= (0 - in);
+ in = ~in;
+ in >>= BN_BITS2 - 1;
+ return in;
+}
+
+static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
+ const BN_ULONG b[P256_LIMBS])
+{
+ BN_ULONG res;
+
+ res = a[0] ^ b[0];
+ res |= a[1] ^ b[1];
+ res |= a[2] ^ b[2];
+ res |= a[3] ^ b[3];
+ if (P256_LIMBS == 8) {
+ res |= a[4] ^ b[4];
+ res |= a[5] ^ b[5];
+ res |= a[6] ^ b[6];
+ res |= a[7] ^ b[7];
+ }
+
+ return is_zero(res);
+}
+
+static BN_ULONG is_one(const BIGNUM *z)
+{
+ BN_ULONG res = 0;
+ BN_ULONG *a = bn_get_words(z);
+
+ if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
+ res = a[0] ^ ONE[0];
+ res |= a[1] ^ ONE[1];
+ res |= a[2] ^ ONE[2];
+ res |= a[3] ^ ONE[3];
+ if (P256_LIMBS == 8) {
+ res |= a[4] ^ ONE[4];
+ res |= a[5] ^ ONE[5];
+ res |= a[6] ^ ONE[6];
+ /*
+ * no check for a[7] (being zero) on 32-bit platforms,
+ * because value of "one" takes only 7 limbs.
+ */
+ }
+ res = is_zero(res);
+ }
+
+ return res;
+}
+
+#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
+void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
+void ecp_nistz256_point_add(P256_POINT *r,
+ const P256_POINT *a, const P256_POINT *b);
+void ecp_nistz256_point_add_affine(P256_POINT *r,
+ const P256_POINT *a,
+ const P256_POINT_AFFINE *b);
+#else
+/* Point double: r = 2*a */
+static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
+{
+ BN_ULONG S[P256_LIMBS];
+ BN_ULONG M[P256_LIMBS];
+ BN_ULONG Zsqr[P256_LIMBS];
+ BN_ULONG tmp0[P256_LIMBS];
+
+ const BN_ULONG *in_x = a->X;
+ const BN_ULONG *in_y = a->Y;
+ const BN_ULONG *in_z = a->Z;
+
+ BN_ULONG *res_x = r->X;
+ BN_ULONG *res_y = r->Y;
+ BN_ULONG *res_z = r->Z;
+
+ ecp_nistz256_mul_by_2(S, in_y);
+
+ ecp_nistz256_sqr_mont(Zsqr, in_z);
+
+ ecp_nistz256_sqr_mont(S, S);
+
+ ecp_nistz256_mul_mont(res_z, in_z, in_y);
+ ecp_nistz256_mul_by_2(res_z, res_z);
+
+ ecp_nistz256_add(M, in_x, Zsqr);
+ ecp_nistz256_sub(Zsqr, in_x, Zsqr);
+
+ ecp_nistz256_sqr_mont(res_y, S);
+ ecp_nistz256_div_by_2(res_y, res_y);
+
+ ecp_nistz256_mul_mont(M, M, Zsqr);
+ ecp_nistz256_mul_by_3(M, M);
+
+ ecp_nistz256_mul_mont(S, S, in_x);
+ ecp_nistz256_mul_by_2(tmp0, S);
+
+ ecp_nistz256_sqr_mont(res_x, M);
+
+ ecp_nistz256_sub(res_x, res_x, tmp0);
+ ecp_nistz256_sub(S, S, res_x);
+
+ ecp_nistz256_mul_mont(S, S, M);
+ ecp_nistz256_sub(res_y, S, res_y);
+}
+
+/* Point addition: r = a+b */
+static void ecp_nistz256_point_add(P256_POINT *r,
+ const P256_POINT *a, const P256_POINT *b)
+{
+ BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
+ BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
+ BN_ULONG Z1sqr[P256_LIMBS];
+ BN_ULONG Z2sqr[P256_LIMBS];
+ BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
+ BN_ULONG Hsqr[P256_LIMBS];
+ BN_ULONG Rsqr[P256_LIMBS];
+ BN_ULONG Hcub[P256_LIMBS];
+
+ BN_ULONG res_x[P256_LIMBS];
+ BN_ULONG res_y[P256_LIMBS];
+ BN_ULONG res_z[P256_LIMBS];
+
+ BN_ULONG in1infty, in2infty;
+
+ const BN_ULONG *in1_x = a->X;
+ const BN_ULONG *in1_y = a->Y;
+ const BN_ULONG *in1_z = a->Z;
+
+ const BN_ULONG *in2_x = b->X;
+ const BN_ULONG *in2_y = b->Y;
+ const BN_ULONG *in2_z = b->Z;
+
+ /*
+ * Infinity in encoded as (,,0)
+ */
+ in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
+ if (P256_LIMBS == 8)
+ in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
+
+ in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
+ if (P256_LIMBS == 8)
+ in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
+
+ in1infty = is_zero(in1infty);
+ in2infty = is_zero(in2infty);
+
+ ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
+ ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
+
+ ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
+ ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
+
+ ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
+ ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
+ ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
+
+ ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
+ ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
+ ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
+
+ /*
+ * This should not happen during sign/ecdh, so no constant time violation
+ */
+ if (is_equal(U1, U2) && !in1infty && !in2infty) {
+ if (is_equal(S1, S2)) {
+ ecp_nistz256_point_double(r, a);
+ return;
+ } else {
+ memset(r, 0, sizeof(*r));
+ return;
+ }
+ }
+
+ ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
+ ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
+ ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
+ ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
+ ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
+
+ ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
+ ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
+
+ ecp_nistz256_sub(res_x, Rsqr, Hsqr);
+ ecp_nistz256_sub(res_x, res_x, Hcub);
+
+ ecp_nistz256_sub(res_y, U2, res_x);
+
+ ecp_nistz256_mul_mont(S2, S1, Hcub);
+ ecp_nistz256_mul_mont(res_y, R, res_y);
+ ecp_nistz256_sub(res_y, res_y, S2);
+
+ copy_conditional(res_x, in2_x, in1infty);
+ copy_conditional(res_y, in2_y, in1infty);
+ copy_conditional(res_z, in2_z, in1infty);
+
+ copy_conditional(res_x, in1_x, in2infty);
+ copy_conditional(res_y, in1_y, in2infty);
+ copy_conditional(res_z, in1_z, in2infty);
+
+ memcpy(r->X, res_x, sizeof(res_x));
+ memcpy(r->Y, res_y, sizeof(res_y));
+ memcpy(r->Z, res_z, sizeof(res_z));
+}
+
+/* Point addition when b is known to be affine: r = a+b */
+static void ecp_nistz256_point_add_affine(P256_POINT *r,
+ const P256_POINT *a,
+ const P256_POINT_AFFINE *b)
+{
+ BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
+ BN_ULONG Z1sqr[P256_LIMBS];
+ BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
+ BN_ULONG Hsqr[P256_LIMBS];
+ BN_ULONG Rsqr[P256_LIMBS];
+ BN_ULONG Hcub[P256_LIMBS];
+
+ BN_ULONG res_x[P256_LIMBS];
+ BN_ULONG res_y[P256_LIMBS];
+ BN_ULONG res_z[P256_LIMBS];
+
+ BN_ULONG in1infty, in2infty;
+
+ const BN_ULONG *in1_x = a->X;
+ const BN_ULONG *in1_y = a->Y;
+ const BN_ULONG *in1_z = a->Z;
+
+ const BN_ULONG *in2_x = b->X;
+ const BN_ULONG *in2_y = b->Y;
+
+ /*
+ * Infinity in encoded as (,,0)
+ */
+ in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
+ if (P256_LIMBS == 8)
+ in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
+
+ /*
+ * In affine representation we encode infinity as (0,0), which is
+ * not on the curve, so it is OK
+ */
+ in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
+ in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
+ if (P256_LIMBS == 8)
+ in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
+ in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
+
+ in1infty = is_zero(in1infty);
+ in2infty = is_zero(in2infty);
+
+ ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
+
+ ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
+ ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
+
+ ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
+
+ ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
+
+ ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
+ ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
+
+ ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
+ ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
+ ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
+
+ ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
+ ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
+
+ ecp_nistz256_sub(res_x, Rsqr, Hsqr);
+ ecp_nistz256_sub(res_x, res_x, Hcub);
+ ecp_nistz256_sub(H, U2, res_x);
+
+ ecp_nistz256_mul_mont(S2, in1_y, Hcub);
+ ecp_nistz256_mul_mont(H, H, R);
+ ecp_nistz256_sub(res_y, H, S2);
+
+ copy_conditional(res_x, in2_x, in1infty);
+ copy_conditional(res_x, in1_x, in2infty);
+
+ copy_conditional(res_y, in2_y, in1infty);
+ copy_conditional(res_y, in1_y, in2infty);
+
+ copy_conditional(res_z, ONE, in1infty);
+ copy_conditional(res_z, in1_z, in2infty);
+
+ memcpy(r->X, res_x, sizeof(res_x));
+ memcpy(r->Y, res_y, sizeof(res_y));
+ memcpy(r->Z, res_z, sizeof(res_z));
+}
+#endif
+
+/* r = in^-1 mod p */
+static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
+ const BN_ULONG in[P256_LIMBS])
+{
+ /*
+ * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
+ * ffffffff ffffffff We use FLT and used poly-2 as exponent
+ */
+ BN_ULONG p2[P256_LIMBS];
+ BN_ULONG p4[P256_LIMBS];
+ BN_ULONG p8[P256_LIMBS];
+ BN_ULONG p16[P256_LIMBS];
+ BN_ULONG p32[P256_LIMBS];
+ BN_ULONG res[P256_LIMBS];
+ int i;
+
+ ecp_nistz256_sqr_mont(res, in);
+ ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
+
+ ecp_nistz256_sqr_mont(res, p2);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
+
+ ecp_nistz256_sqr_mont(res, p4);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
+
+ ecp_nistz256_sqr_mont(res, p8);
+ for (i = 0; i < 7; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
+
+ ecp_nistz256_sqr_mont(res, p16);
+ for (i = 0; i < 15; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
+
+ ecp_nistz256_sqr_mont(res, p32);
+ for (i = 0; i < 31; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, in);
+
+ for (i = 0; i < 32 * 4; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p32);
+
+ for (i = 0; i < 32; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p32);
+
+ for (i = 0; i < 16; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p16);
+
+ for (i = 0; i < 8; i++)
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p8);
+
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p4);
+
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, p2);
+
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_sqr_mont(res, res);
+ ecp_nistz256_mul_mont(res, res, in);
+
+ memcpy(r, res, sizeof(res));
+}
+
+/*
+ * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
+ * returns one if it fits. Otherwise it returns zero.
+ */
+__owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
+ const BIGNUM *in)
+{
+ return bn_copy_words(out, in, P256_LIMBS);
+}
+
+/* r = sum(scalar[i]*point[i]) */
+__owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
+ P256_POINT *r,
+ const BIGNUM **scalar,
+ const EC_POINT **point,
+ size_t num, BN_CTX *ctx)
+{
+ size_t i;
+ int j, ret = 0;
+ unsigned int idx;
+ unsigned char (*p_str)[33] = NULL;
+ const unsigned int window_size = 5;
+ const unsigned int mask = (1 << (window_size + 1)) - 1;
+ unsigned int wvalue;
+ P256_POINT *temp; /* place for 5 temporary points */
+ const BIGNUM **scalars = NULL;
+ P256_POINT (*table)[16] = NULL;
+ void *table_storage = NULL;
+
+ if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
+ || (table_storage =
+ OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
+ || (p_str =
+ OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
+ || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ table = (void *)ALIGNPTR(table_storage, 64);
+ temp = (P256_POINT *)(table + num);
+
+ for (i = 0; i < num; i++) {
+ P256_POINT *row = table[i];
+
+ /* This is an unusual input, we don't guarantee constant-timeness. */
+ if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
+ BIGNUM *mod;
+
+ if ((mod = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
+ ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
+ goto err;
+ }
+ scalars[i] = mod;
+ } else
+ scalars[i] = scalar[i];
+
+ for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
+ BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
+
+ p_str[i][j + 0] = (unsigned char)d;
+ p_str[i][j + 1] = (unsigned char)(d >> 8);
+ p_str[i][j + 2] = (unsigned char)(d >> 16);
+ p_str[i][j + 3] = (unsigned char)(d >>= 24);
+ if (BN_BYTES == 8) {
+ d >>= 8;
+ p_str[i][j + 4] = (unsigned char)d;
+ p_str[i][j + 5] = (unsigned char)(d >> 8);
+ p_str[i][j + 6] = (unsigned char)(d >> 16);
+ p_str[i][j + 7] = (unsigned char)(d >> 24);
+ }
+ }
+ for (; j < 33; j++)
+ p_str[i][j] = 0;
+
+ if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
+ || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
+ || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
+ ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
+ EC_R_COORDINATES_OUT_OF_RANGE);
+ goto err;
+ }
+
+ /*
+ * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
+ * is not stored. All other values are actually stored with an offset
+ * of -1 in table.
+ */
+
+ ecp_nistz256_scatter_w5 (row, &temp[0], 1);
+ ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
+ ecp_nistz256_scatter_w5 (row, &temp[1], 2);
+ ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
+ ecp_nistz256_scatter_w5 (row, &temp[2], 3);
+ ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
+ ecp_nistz256_scatter_w5 (row, &temp[1], 4);
+ ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
+ ecp_nistz256_scatter_w5 (row, &temp[2], 6);
+ ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
+ ecp_nistz256_scatter_w5 (row, &temp[3], 5);
+ ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
+ ecp_nistz256_scatter_w5 (row, &temp[4], 7);
+ ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
+ ecp_nistz256_scatter_w5 (row, &temp[1], 8);
+ ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
+ ecp_nistz256_scatter_w5 (row, &temp[2], 12);
+ ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
+ ecp_nistz256_scatter_w5 (row, &temp[3], 10);
+ ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
+ ecp_nistz256_scatter_w5 (row, &temp[4], 14);
+ ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
+ ecp_nistz256_scatter_w5 (row, &temp[2], 13);
+ ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
+ ecp_nistz256_scatter_w5 (row, &temp[3], 11);
+ ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
+ ecp_nistz256_scatter_w5 (row, &temp[4], 15);
+ ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
+ ecp_nistz256_scatter_w5 (row, &temp[2], 9);
+ ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
+ ecp_nistz256_scatter_w5 (row, &temp[1], 16);
+ }
+
+ idx = 255;
+
+ wvalue = p_str[0][(idx - 1) / 8];
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+
+ /*
+ * We gather to temp[0], because we know it's position relative
+ * to table
+ */
+ ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
+ memcpy(r, &temp[0], sizeof(temp[0]));
+
+ while (idx >= 5) {
+ for (i = (idx == 255 ? 1 : 0); i < num; i++) {
+ unsigned int off = (idx - 1) / 8;
+
+ wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+
+ wvalue = _booth_recode_w5(wvalue);
+
+ ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
+
+ ecp_nistz256_neg(temp[1].Y, temp[0].Y);
+ copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
+
+ ecp_nistz256_point_add(r, r, &temp[0]);
+ }
+
+ idx -= window_size;
+
+ ecp_nistz256_point_double(r, r);
+ ecp_nistz256_point_double(r, r);
+ ecp_nistz256_point_double(r, r);
+ ecp_nistz256_point_double(r, r);
+ ecp_nistz256_point_double(r, r);
+ }
+
+ /* Final window */
+ for (i = 0; i < num; i++) {
+ wvalue = p_str[i][0];
+ wvalue = (wvalue << 1) & mask;
+
+ wvalue = _booth_recode_w5(wvalue);
+
+ ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
+
+ ecp_nistz256_neg(temp[1].Y, temp[0].Y);
+ copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
+
+ ecp_nistz256_point_add(r, r, &temp[0]);
+ }
+
+ ret = 1;
+ err:
+ OPENSSL_free(table_storage);
+ OPENSSL_free(p_str);
+ OPENSSL_free(scalars);
+ return ret;
+}
+
+/* Coordinates of G, for which we have precomputed tables */
+const static BN_ULONG def_xG[P256_LIMBS] = {
+ TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
+ TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
+};
+
+const static BN_ULONG def_yG[P256_LIMBS] = {
+ TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
+ TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
+};
+
+/*
+ * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
+ * generator.
+ */
+static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
+{
+ return (bn_get_top(generator->X) == P256_LIMBS) &&
+ (bn_get_top(generator->Y) == P256_LIMBS) &&
+ is_equal(bn_get_words(generator->X), def_xG) &&
+ is_equal(bn_get_words(generator->Y), def_yG) &&
+ is_one(generator->Z);
+}
+
+__owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
+{
+ /*
+ * We precompute a table for a Booth encoded exponent (wNAF) based
+ * computation. Each table holds 64 values for safe access, with an
+ * implicit value of infinity at index zero. We use window of size 7, and
+ * therefore require ceil(256/7) = 37 tables.
+ */
+ const BIGNUM *order;
+ EC_POINT *P = NULL, *T = NULL;
+ const EC_POINT *generator;
+ NISTZ256_PRE_COMP *pre_comp;
+ BN_CTX *new_ctx = NULL;
+ int i, j, k, ret = 0;
+ size_t w;
+
+ PRECOMP256_ROW *preComputedTable = NULL;
+ unsigned char *precomp_storage = NULL;
+
+ /* if there is an old NISTZ256_PRE_COMP object, throw it away */
+ EC_pre_comp_free(group);
+ generator = EC_GROUP_get0_generator(group);
+ if (generator == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
+ return 0;
+ }
+
+ if (ecp_nistz256_is_affine_G(generator)) {
+ /*
+ * No need to calculate tables for the standard generator because we
+ * have them statically.
+ */
+ return 1;
+ }
+
+ if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
+ return 0;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ goto err;
+ }
+
+ BN_CTX_start(ctx);
+
+ order = EC_GROUP_get0_order(group);
+ if (order == NULL)
+ goto err;
+
+ if (BN_is_zero(order)) {
+ ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
+ goto err;
+ }
+
+ w = 7;
+
+ if ((precomp_storage =
+ OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
+
+ P = EC_POINT_new(group);
+ T = EC_POINT_new(group);
+ if (P == NULL || T == NULL)
+ goto err;
+
+ /*
+ * The zero entry is implicitly infinity, and we skip it, storing other
+ * values with -1 offset.
+ */
+ if (!EC_POINT_copy(T, generator))
+ goto err;
+
+ for (k = 0; k < 64; k++) {
+ if (!EC_POINT_copy(P, T))
+ goto err;
+ for (j = 0; j < 37; j++) {
+ P256_POINT_AFFINE temp;
+ /*
+ * It would be faster to use EC_POINTs_make_affine and
+ * make multiple points affine at the same time.
+ */
+ if (!EC_POINT_make_affine(group, P, ctx))
+ goto err;
+ if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
+ !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
+ ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
+ EC_R_COORDINATES_OUT_OF_RANGE);
+ goto err;
+ }
+ ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
+ for (i = 0; i < 7; i++) {
+ if (!EC_POINT_dbl(group, P, P, ctx))
+ goto err;
+ }
+ }
+ if (!EC_POINT_add(group, T, T, generator, ctx))
+ goto err;
+ }
+
+ pre_comp->group = group;
+ pre_comp->w = w;
+ pre_comp->precomp = preComputedTable;
+ pre_comp->precomp_storage = precomp_storage;
+ precomp_storage = NULL;
+ SETPRECOMP(group, nistz256, pre_comp);
+ pre_comp = NULL;
+ ret = 1;
+
+ err:
+ if (ctx != NULL)
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+
+ EC_nistz256_pre_comp_free(pre_comp);
+ OPENSSL_free(precomp_storage);
+ EC_POINT_free(P);
+ EC_POINT_free(T);
+ return ret;
+}
+
+/*
+ * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
+ * code processing 4 points in parallel, corresponding serial operation
+ * is several times slower, because it uses 29x29=58-bit multiplication
+ * as opposite to 64x64=128-bit in integer-only scalar case. As result
+ * it doesn't provide *significant* performance improvement. Note that
+ * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
+ * you'd need to compile even asm/ecp_nistz256-avx.pl module.
+ */
+#if defined(ECP_NISTZ256_AVX2)
+# if !(defined(__x86_64) || defined(__x86_64__) || \
+ defined(_M_AMD64) || defined(_MX64)) || \
+ !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
+# undef ECP_NISTZ256_AVX2
+# else
+/* Constant time access, loading four values, from four consecutive tables */
+void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
+ int index0, int index1, int index2,
+ int index3);
+void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
+void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
+void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
+ const void *Bx4);
+void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
+ const void *Bx4);
+void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
+void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
+void ecp_nistz256_avx2_set1(void *RESULTx4);
+int ecp_nistz_avx2_eligible(void);
+
+static void booth_recode_w7(unsigned char *sign,
+ unsigned char *digit, unsigned char in)
+{
+ unsigned char s, d;
+
+ s = ~((in >> 7) - 1);
+ d = (1 << 8) - in - 1;
+ d = (d & s) | (in & ~s);
+ d = (d >> 1) + (d & 1);
+
+ *sign = s & 1;
+ *digit = d;
+}
+
+/*
+ * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
+ * precomputed table. It does 4 affine point additions in parallel,
+ * significantly speeding up point multiplication for a fixed value.
+ */
+static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
+ unsigned char p_str[33],
+ const P256_POINT_AFFINE(*preComputedTable)[64])
+{
+ const unsigned int window_size = 7;
+ const unsigned int mask = (1 << (window_size + 1)) - 1;
+ unsigned int wvalue;
+ /* Using 4 windows at a time */
+ unsigned char sign0, digit0;
+ unsigned char sign1, digit1;
+ unsigned char sign2, digit2;
+ unsigned char sign3, digit3;
+ unsigned int idx = 0;
+ BN_ULONG tmp[P256_LIMBS];
+ int i;
+
+ ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
+ ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
+ ALIGN32 P256_POINT_AFFINE point_arr[4];
+ ALIGN32 P256_POINT res_point_arr[4];
+
+ /* Initial four windows */
+ wvalue = *((u16 *) & p_str[0]);
+ wvalue = (wvalue << 1) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign0, &digit0, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign1, &digit1, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign2, &digit2, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign3, &digit3, wvalue);
+
+ ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
+ digit0, digit1, digit2, digit3);
+
+ ecp_nistz256_neg(tmp, point_arr[0].Y);
+ copy_conditional(point_arr[0].Y, tmp, sign0);
+ ecp_nistz256_neg(tmp, point_arr[1].Y);
+ copy_conditional(point_arr[1].Y, tmp, sign1);
+ ecp_nistz256_neg(tmp, point_arr[2].Y);
+ copy_conditional(point_arr[2].Y, tmp, sign2);
+ ecp_nistz256_neg(tmp, point_arr[3].Y);
+ copy_conditional(point_arr[3].Y, tmp, sign3);
+
+ ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
+ ecp_nistz256_avx2_to_mont(aX4, aX4);
+ ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
+ ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
+
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign0, &digit0, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign1, &digit1, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign2, &digit2, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign3, &digit3, wvalue);
+
+ ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
+ digit0, digit1, digit2, digit3);
+
+ ecp_nistz256_neg(tmp, point_arr[0].Y);
+ copy_conditional(point_arr[0].Y, tmp, sign0);
+ ecp_nistz256_neg(tmp, point_arr[1].Y);
+ copy_conditional(point_arr[1].Y, tmp, sign1);
+ ecp_nistz256_neg(tmp, point_arr[2].Y);
+ copy_conditional(point_arr[2].Y, tmp, sign2);
+ ecp_nistz256_neg(tmp, point_arr[3].Y);
+ copy_conditional(point_arr[3].Y, tmp, sign3);
+
+ ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
+ ecp_nistz256_avx2_to_mont(bX4, bX4);
+ ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
+ /* Optimized when both inputs are affine */
+ ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
+
+ for (i = 2; i < 9; i++) {
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign0, &digit0, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign1, &digit1, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign2, &digit2, wvalue);
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+ booth_recode_w7(&sign3, &digit3, wvalue);
+
+ ecp_nistz256_avx2_multi_gather_w7(point_arr,
+ preComputedTable[4 * i],
+ digit0, digit1, digit2, digit3);
+
+ ecp_nistz256_neg(tmp, point_arr[0].Y);
+ copy_conditional(point_arr[0].Y, tmp, sign0);
+ ecp_nistz256_neg(tmp, point_arr[1].Y);
+ copy_conditional(point_arr[1].Y, tmp, sign1);
+ ecp_nistz256_neg(tmp, point_arr[2].Y);
+ copy_conditional(point_arr[2].Y, tmp, sign2);
+ ecp_nistz256_neg(tmp, point_arr[3].Y);
+ copy_conditional(point_arr[3].Y, tmp, sign3);
+
+ ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
+ ecp_nistz256_avx2_to_mont(bX4, bX4);
+ ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
+
+ ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
+ }
+
+ ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
+ ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
+ ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
+
+ ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
+ /* Last window is performed serially */
+ wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ booth_recode_w7(&sign0, &digit0, wvalue);
+ ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
+ preComputedTable[36], digit0);
+ ecp_nistz256_neg(tmp, r->Y);
+ copy_conditional(r->Y, tmp, sign0);
+ memcpy(r->Z, ONE, sizeof(ONE));
+ /* Sum the four windows */
+ ecp_nistz256_point_add(r, r, &res_point_arr[0]);
+ ecp_nistz256_point_add(r, r, &res_point_arr[1]);
+ ecp_nistz256_point_add(r, r, &res_point_arr[2]);
+ ecp_nistz256_point_add(r, r, &res_point_arr[3]);
+}
+# endif
+#endif
+
+__owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
+ const P256_POINT_AFFINE *in,
+ BN_CTX *ctx)
+{
+ BIGNUM *x, *y;
+ BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
+ int ret = 0;
+
+ x = BN_new();
+ if (x == NULL)
+ return 0;
+ y = BN_new();
+ if (y == NULL) {
+ BN_free(x);
+ return 0;
+ }
+ memcpy(d_x, in->X, sizeof(d_x));
+ bn_set_static_words(x, d_x, P256_LIMBS);
+
+ memcpy(d_y, in->Y, sizeof(d_y));
+ bn_set_static_words(y, d_y, P256_LIMBS);
+
+ ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
+
+ BN_free(x);
+ BN_free(y);
+
+ return ret;
+}
+
+/* r = scalar*G + sum(scalars[i]*points[i]) */
+__owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
+ EC_POINT *r,
+ const BIGNUM *scalar,
+ size_t num,
+ const EC_POINT *points[],
+ const BIGNUM *scalars[], BN_CTX *ctx)
+{
+ int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
+ size_t j;
+ unsigned char p_str[33] = { 0 };
+ const PRECOMP256_ROW *preComputedTable = NULL;
+ const NISTZ256_PRE_COMP *pre_comp = NULL;
+ const EC_POINT *generator = NULL;
+ BN_CTX *new_ctx = NULL;
+ const BIGNUM **new_scalars = NULL;
+ const EC_POINT **new_points = NULL;
+ unsigned int idx = 0;
+ const unsigned int window_size = 7;
+ const unsigned int mask = (1 << (window_size + 1)) - 1;
+ unsigned int wvalue;
+ ALIGN32 union {
+ P256_POINT p;
+ P256_POINT_AFFINE a;
+ } t, p;
+ BIGNUM *tmp_scalar;
+
+ if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+ return 0;
+ }
+
+ if (group->meth != r->meth) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+ return 0;
+ }
+
+ if ((scalar == NULL) && (num == 0))
+ return EC_POINT_set_to_infinity(group, r);
+
+ for (j = 0; j < num; j++) {
+ if (group->meth != points[j]->meth) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+ return 0;
+ }
+ }
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ goto err;
+ }
+
+ BN_CTX_start(ctx);
+
+ if (scalar) {
+ generator = EC_GROUP_get0_generator(group);
+ if (generator == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
+ goto err;
+ }
+
+ /* look if we can use precomputed multiples of generator */
+ pre_comp = group->pre_comp.nistz256;
+
+ if (pre_comp) {
+ /*
+ * If there is a precomputed table for the generator, check that
+ * it was generated with the same generator.
+ */
+ EC_POINT *pre_comp_generator = EC_POINT_new(group);
+ if (pre_comp_generator == NULL)
+ goto err;
+
+ if (!ecp_nistz256_set_from_affine(pre_comp_generator,
+ group, pre_comp->precomp[0],
+ ctx)) {
+ EC_POINT_free(pre_comp_generator);
+ goto err;
+ }
+
+ if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
+ preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
+
+ EC_POINT_free(pre_comp_generator);
+ }
+
+ if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
+ /*
+ * If there is no precomputed data, but the generator is the
+ * default, a hardcoded table of precomputed data is used. This
+ * is because applications, such as Apache, do not use
+ * EC_KEY_precompute_mult.
+ */
+ preComputedTable = ecp_nistz256_precomputed;
+ }
+
+ if (preComputedTable) {
+ if ((BN_num_bits(scalar) > 256)
+ || BN_is_negative(scalar)) {
+ if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
+ goto err;
+ }
+ scalar = tmp_scalar;
+ }
+
+ for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
+ BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
+
+ p_str[i + 0] = (unsigned char)d;
+ p_str[i + 1] = (unsigned char)(d >> 8);
+ p_str[i + 2] = (unsigned char)(d >> 16);
+ p_str[i + 3] = (unsigned char)(d >>= 24);
+ if (BN_BYTES == 8) {
+ d >>= 8;
+ p_str[i + 4] = (unsigned char)d;
+ p_str[i + 5] = (unsigned char)(d >> 8);
+ p_str[i + 6] = (unsigned char)(d >> 16);
+ p_str[i + 7] = (unsigned char)(d >> 24);
+ }
+ }
+
+ for (; i < 33; i++)
+ p_str[i] = 0;
+
+#if defined(ECP_NISTZ256_AVX2)
+ if (ecp_nistz_avx2_eligible()) {
+ ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
+ } else
+#endif
+ {
+ BN_ULONG infty;
+
+ /* First window */
+ wvalue = (p_str[0] << 1) & mask;
+ idx += window_size;
+
+ wvalue = _booth_recode_w7(wvalue);
+
+ ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
+ wvalue >> 1);
+
+ ecp_nistz256_neg(p.p.Z, p.p.Y);
+ copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
+
+ /*
+ * Since affine infinity is encoded as (0,0) and
+ * Jacobian ias (,,0), we need to harmonize them
+ * by assigning "one" or zero to Z.
+ */
+ infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
+ p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
+ if (P256_LIMBS == 8)
+ infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
+ p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
+
+ infty = 0 - is_zero(infty);
+ infty = ~infty;
+
+ p.p.Z[0] = ONE[0] & infty;
+ p.p.Z[1] = ONE[1] & infty;
+ p.p.Z[2] = ONE[2] & infty;
+ p.p.Z[3] = ONE[3] & infty;
+ if (P256_LIMBS == 8) {
+ p.p.Z[4] = ONE[4] & infty;
+ p.p.Z[5] = ONE[5] & infty;
+ p.p.Z[6] = ONE[6] & infty;
+ p.p.Z[7] = ONE[7] & infty;
+ }
+
+ for (i = 1; i < 37; i++) {
+ unsigned int off = (idx - 1) / 8;
+ wvalue = p_str[off] | p_str[off + 1] << 8;
+ wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
+ idx += window_size;
+
+ wvalue = _booth_recode_w7(wvalue);
+
+ ecp_nistz256_gather_w7(&t.a,
+ preComputedTable[i], wvalue >> 1);
+
+ ecp_nistz256_neg(t.p.Z, t.a.Y);
+ copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
+
+ ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
+ }
+ }
+ } else {
+ p_is_infinity = 1;
+ no_precomp_for_generator = 1;
+ }
+ } else
+ p_is_infinity = 1;
+
+ if (no_precomp_for_generator) {
+ /*
+ * Without a precomputed table for the generator, it has to be
+ * handled like a normal point.
+ */
+ new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
+ if (new_scalars == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
+ if (new_points == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
+ new_scalars[num] = scalar;
+ memcpy(new_points, points, num * sizeof(EC_POINT *));
+ new_points[num] = generator;
+
+ scalars = new_scalars;
+ points = new_points;
+ num++;
+ }
+
+ if (num) {
+ P256_POINT *out = &t.p;
+ if (p_is_infinity)
+ out = &p.p;
+
+ if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
+ goto err;
+
+ if (!p_is_infinity)
+ ecp_nistz256_point_add(&p.p, &p.p, out);
+ }
+
+ /* Not constant-time, but we're only operating on the public output. */
+ if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
+ !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
+ !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
+ goto err;
+ }
+ r->Z_is_one = is_one(r->Z) & 1;
+
+ ret = 1;
+
+err:
+ if (ctx)
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ OPENSSL_free(new_points);
+ OPENSSL_free(new_scalars);
+ return ret;
+}
+
+__owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
+ const EC_POINT *point,
+ BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
+{
+ BN_ULONG z_inv2[P256_LIMBS];
+ BN_ULONG z_inv3[P256_LIMBS];
+ BN_ULONG x_aff[P256_LIMBS];
+ BN_ULONG y_aff[P256_LIMBS];
+ BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
+ BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
+
+ if (EC_POINT_is_at_infinity(group, point)) {
+ ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
+ return 0;
+ }
+
+ if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
+ !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
+ !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
+ ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
+ return 0;
+ }
+
+ ecp_nistz256_mod_inverse(z_inv3, point_z);
+ ecp_nistz256_sqr_mont(z_inv2, z_inv3);
+ ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
+
+ if (x != NULL) {
+ ecp_nistz256_from_mont(x_ret, x_aff);
+ if (!bn_set_words(x, x_ret, P256_LIMBS))
+ return 0;
+ }
+
+ if (y != NULL) {
+ ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
+ ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
+ ecp_nistz256_from_mont(y_ret, y_aff);
+ if (!bn_set_words(y, y_ret, P256_LIMBS))
+ return 0;
+ }
+
+ return 1;
+}
+
+static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
+{
+ NISTZ256_PRE_COMP *ret = NULL;
+
+ if (!group)
+ return NULL;
+
+ ret = OPENSSL_zalloc(sizeof(*ret));
+
+ if (ret == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
+ return ret;
+ }
+
+ ret->group = group;
+ ret->w = 6; /* default */
+ ret->references = 1;
+
+ ret->lock = CRYPTO_THREAD_lock_new();
+ if (ret->lock == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
+ OPENSSL_free(ret);
+ return NULL;
+ }
+ return ret;
+}
+
+NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
+{
+ int i;
+ if (p != NULL)
+ CRYPTO_atomic_add(&p->references, 1, &i, p->lock);
+ return p;
+}
+
+void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
+{
+ int i;
+
+ if (pre == NULL)
+ return;
+
+ CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock);
+ REF_PRINT_COUNT("EC_nistz256", x);
+ if (i > 0)
+ return;
+ REF_ASSERT_ISNT(i < 0);
+
+ OPENSSL_free(pre->precomp_storage);
+ CRYPTO_THREAD_lock_free(pre->lock);
+ OPENSSL_free(pre);
+}
+
+
+static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
+{
+ /* There is a hard-coded table for the default generator. */
+ const EC_POINT *generator = EC_GROUP_get0_generator(group);
+
+ if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
+ /* There is a hard-coded table for the default generator. */
+ return 1;
+ }
+
+ return HAVEPRECOMP(group, nistz256);
+}
+
+const EC_METHOD *EC_GFp_nistz256_method(void)
+{
+ static const EC_METHOD ret = {
+ EC_FLAGS_DEFAULT_OCT,
+ NID_X9_62_prime_field,
+ ec_GFp_mont_group_init,
+ ec_GFp_mont_group_finish,
+ ec_GFp_mont_group_clear_finish,
+ ec_GFp_mont_group_copy,
+ ec_GFp_mont_group_set_curve,
+ ec_GFp_simple_group_get_curve,
+ ec_GFp_simple_group_get_degree,
+ ec_group_simple_order_bits,
+ ec_GFp_simple_group_check_discriminant,
+ ec_GFp_simple_point_init,
+ ec_GFp_simple_point_finish,
+ ec_GFp_simple_point_clear_finish,
+ ec_GFp_simple_point_copy,
+ ec_GFp_simple_point_set_to_infinity,
+ ec_GFp_simple_set_Jprojective_coordinates_GFp,
+ ec_GFp_simple_get_Jprojective_coordinates_GFp,
+ ec_GFp_simple_point_set_affine_coordinates,
+ ecp_nistz256_get_affine,
+ 0, 0, 0,
+ ec_GFp_simple_add,
+ ec_GFp_simple_dbl,
+ ec_GFp_simple_invert,
+ ec_GFp_simple_is_at_infinity,
+ ec_GFp_simple_is_on_curve,
+ ec_GFp_simple_cmp,
+ ec_GFp_simple_make_affine,
+ ec_GFp_simple_points_make_affine,
+ ecp_nistz256_points_mul, /* mul */
+ ecp_nistz256_mult_precompute, /* precompute_mult */
+ ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
+ ec_GFp_mont_field_mul,
+ ec_GFp_mont_field_sqr,
+ 0, /* field_div */
+ ec_GFp_mont_field_encode,
+ ec_GFp_mont_field_decode,
+ ec_GFp_mont_field_set_to_one,
+ ec_key_simple_priv2oct,
+ ec_key_simple_oct2priv,
+ 0, /* set private */
+ ec_key_simple_generate_key,
+ ec_key_simple_check_key,
+ ec_key_simple_generate_public_key,
+ 0, /* keycopy */
+ 0, /* keyfinish */
+ ecdh_simple_compute_key
+ };
+
+ return &ret;
+}
projects / cassiopeia.git / blobdiff