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@@ -0,0 +1,10780 @@
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+/* ge_448.c
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+ *
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+ * Copyright (C) 2006-2020 wolfSSL Inc.
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+ *
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+ * This file is part of wolfSSL.
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+ *
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+ * wolfSSL is free software; you can redistribute it and/or modify
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+ * it under the terms of the GNU General Public License as published by
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+ * the Free Software Foundation; either version 2 of the License, or
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+ * (at your option) any later version.
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+ *
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+ * wolfSSL is distributed in the hope that it will be useful,
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+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
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+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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+ * GNU General Public License for more details.
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+ *
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+ * You should have received a copy of the GNU General Public License
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+ * along with this program; if not, write to the Free Software
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+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
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+ */
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+
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+/* Based On Daniel J Bernstein's ed25519 Public Domain ref10 work.
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+ * Small implementation based on Daniel Beer's ed25519 public domain work.
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+ * Reworked for ed448 by Sean Parkinson.
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+ */
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+
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+#ifdef HAVE_CONFIG_H
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+ #include <config.h>
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+#endif
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+
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+#include <wolfssl/wolfcrypt/settings.h>
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+
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+#ifdef HAVE_ED448
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+
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+#include <wolfssl/wolfcrypt/ge_448.h>
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+#include <wolfssl/wolfcrypt/ed448.h>
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+#include <wolfssl/wolfcrypt/error-crypt.h>
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+#ifdef NO_INLINE
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+ #include <wolfssl/wolfcrypt/misc.h>
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+#else
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+ #define WOLFSSL_MISC_INCLUDED
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+ #include <wolfcrypt/src/misc.c>
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+#endif
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+
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+/*
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+sc means scalar.
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+ge means group element.
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+
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+Here the group is the set of pairs (x,y) of field elements (see ge_448.h)
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+satisfying -x^2 + y^2 = 1 + d x^2y^2
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+where d = -39081
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+
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+Representations:
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+ ge448_p2 (projective) : (X:Y:Z) satisfying x=X/Z, y=Y/Z
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+ ge448_precomp (affine): (X:Y)
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+*/
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+
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+
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+#ifdef ED448_SMALL
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+
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+/* Base point of ed448 */
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+static const ge448_p2 ed448_base = {
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+ { 0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26, 0x8e, 0x93, 0x00, 0x8b,
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+ 0xe1, 0x80, 0x3b, 0x43, 0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12,
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+ 0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea, 0x67, 0x17, 0x0f, 0x47,
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+ 0x70, 0x65, 0x14, 0x9e, 0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22,
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+ 0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f },
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+ { 0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98, 0xad, 0xc8, 0xd7, 0x4e,
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+ 0x2c, 0x13, 0xbd, 0xfd, 0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a,
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+ 0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87, 0x40, 0x98, 0xa3, 0x6c,
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+ 0x73, 0x73, 0xea, 0x4b, 0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88,
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+ 0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69 },
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+ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }
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+};
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+
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+/* Part of order of ed448 that needs tp be multiplied when reducing */
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+static const uint8_t ed448_order_mul[56] = {
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+ 0x0d, 0xbb, 0xa7, 0x54, 0x6d, 0x3d, 0x87, 0xdc, 0xaa, 0x70, 0x3a, 0x72,
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+ 0x8d, 0x3d, 0x93, 0xde, 0x6f, 0xc9, 0x29, 0x51, 0xb6, 0x24, 0xb1, 0x3b,
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+ 0x16, 0xdc, 0x35, 0x83,
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+};
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+
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+/* Reduce scalar mod the order of the curve.
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+ * Scalar Will be 114 bytes.
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+ *
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+ * b [in] Scalar to reduce.
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+ */
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+void sc448_reduce(uint8_t* b)
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+{
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+ int i, j;
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+ uint32_t t[114];
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+ uint8_t o;
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+
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+ for (i = 0; i < 86; i++) {
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+ t[i] = b[i];
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+ }
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+ for (i = 0; i < 58; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += b[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 54; i < 87; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ for (i = 0; i < 31; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += t[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 54; i < 60; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ for (i = 0; i < 4; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += t[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 0; i < 55; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ o = t[55] >> 6;
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+ t[55] &= 0x3f;
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+ for (j = 0; j < 28; j++)
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+ t[j] += o * (uint32_t)ed448_order_mul[j];
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+ for (i = 0; i < 55; i++) {
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+ t[i+1] += t[i] >> 8;
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+ b[i] = t[i] & 0xff;
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+ }
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+ b[i] = t[i] & 0xff;
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+ b[i+1] = 0;
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+}
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+
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+/* Multiply a by b and add d. r = (a * b + d) mod order
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+ *
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+ * r [in] Scalar to hold result.
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+ * a [in] Scalar to multiply.
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+ * b [in] Scalar to multiply.
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+ * d [in] Scalar to add to multiplicative result.
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+ */
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+void sc448_muladd(uint8_t* r, const uint8_t* a, const uint8_t* b,
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+ const uint8_t* d)
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+{
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+ int i, j;
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+ uint32_t t[112];
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+ uint8_t o;
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+
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+ /* a * b + d */
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+ for (i = 0; i < 56; i++)
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+ t[i] = d[i];
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+ for (i = 0; i < 56; i++) {
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+ for (j = 0; j < 56; j++)
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+ t[i+j] += (int16_t)a[i] * b[j];
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+ t[i+56] = 0;
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+ }
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+
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+ for (i = 0; i < 111; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ for (i = 0; i < 56; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += t[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 54; i < 85; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ for (i = 0; i < 29; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += t[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 54; i < 58; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ for (i = 0; i < 2; i++) {
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+ for (j = 0; j < 28; j++)
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+ t[i+j] += t[i+56] * ((uint32_t)ed448_order_mul[j] << 2);
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+ t[i+56] = 0;
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+ }
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+ for (i = 0; i < 55; i++) {
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+ t[i+1] += t[i] >> 8;
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+ t[i] &= 0xff;
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+ }
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+ o = t[55] >> 6;
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+ t[55] &= 0x3f;
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+ for (j = 0; j < 28; j++)
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+ t[j] += o * (uint32_t)ed448_order_mul[j];
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+ for (i = 0; i < 55; i++) {
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+ t[i+1] += t[i] >> 8;
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+ r[i] = t[i] & 0xff;
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+ }
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+ r[i] = t[i] & 0xff;
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+ r[i+1] = 0;
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+}
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+
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+/* Double the point on the Twisted Edwards curve. r = 2.p
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+ *
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+ * r [in] Point to hold result.
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+ * p [in] Point to double.
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+ */
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+static WC_INLINE void ge448_dbl(ge448_p2 *r,const ge448_p2 *p)
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+{
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+ ge448 t0[GE448_WORDS];
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+ ge448 t1[GE448_WORDS];
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+
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+ fe448_add(t0, p->X, p->Y); /* t0 = B1 = X1+Y1 */
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+ fe448_reduce(t0);
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+ fe448_sqr(t0, t0); /* t0 = B = (X1+Y1)^2 */
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+ fe448_sqr(r->X, p->X); /* r->X = C = X1^2 */
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+ fe448_sqr(r->Y, p->Y); /* r->Y = D = Y1^2 */
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+ fe448_add(t1, r->X, r->Y); /* t1 = E = C+D */
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+ fe448_reduce(t1);
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+ fe448_sub(r->Y, r->X, r->Y); /* r->Y = Y31 = C-D */
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+ fe448_sqr(r->Z, p->Z); /* r->Z = H = Z1^2 */
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+ fe448_add(r->Z, r->Z, r->Z); /* r->Z = J1 = 2*H */
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+ fe448_sub(r->Z, t1, r->Z); /* r->Z = J = E-2*H */
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+ fe448_reduce(r->Z);
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+ fe448_sub(r->X, t0, t1); /* r->X = X31 = B-E */
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+ fe448_mul(r->X, r->X, r->Z); /* r->X = X3 = (B-E)*J */
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+ fe448_mul(r->Y, r->Y, t1); /* r->Y = Y3 = E*(C-D) */
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+ fe448_mul(r->Z, t1, r->Z); /* r->Z = Z3 = E*J */
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+}
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+
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+/* Add two point on the Twisted Edwards curve. r = p + q
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+ *
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+ * r [in] Point to hold result.
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+ * p [in] Point to add.
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+ * q [in] Point to add.
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+ */
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+static WC_INLINE void ge448_add(ge448_p2* r, const ge448_p2* p,
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+ const ge448_p2* q)
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+{
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+ ge448 t0[GE448_WORDS];
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+ ge448 t1[GE448_WORDS];
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+ ge448 t2[GE448_WORDS];
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+ ge448 t3[GE448_WORDS];
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+ ge448 t4[GE448_WORDS];
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+
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+ fe448_mul(t1, p->X, q->X); /* t1 = C = X1*X2 */
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+ fe448_mul(t2, p->Y, q->Y); /* t2 = D = Y1*Y2 */
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+ fe448_mul(t3, t1, t2); /* t3 = E1 = C*D */
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+ fe448_mul39081(t3, t3); /* t3 = E = d*C*D */
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+ fe448_mul(r->Z, p->Z, q->Z); /* r->Z = A = Z1*Z2 */
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+ fe448_sqr(t0, r->Z); /* t0 = B = A^2 */
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+ fe448_add(t4, t0, t3); /* t4 = F = B-(-E) */
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+ fe448_sub(t0, t0, t3); /* t0 = G = B+(-E) */
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+ fe448_reduce(t0);
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+ fe448_add(r->X, p->X, p->Y); /* r->X = H1 = X1+Y1 */
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+ fe448_reduce(r->X);
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+ fe448_add(r->Y, q->X, q->Y); /* r->Y = H2 = X2+Y2 */
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+ fe448_reduce(r->Y);
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+ fe448_mul(r->X, r->X, r->Y); /* r->X = H = (X1+Y1)*(X2+Y2) */
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+ fe448_sub(r->X, r->X, t1); /* r->X = X31 = H-C */
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+ fe448_sub(r->X, r->X, t2); /* r->X = X32 = H-C-D */
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+ fe448_reduce(r->X);
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+ fe448_mul(r->X, r->X, t4); /* r->X = X33 = F*(H-C-D) */
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+ fe448_mul(r->X, r->X, r->Z); /* r->X = X3 = A*F*(H-C-D) */
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+ fe448_sub(r->Y, t2, t1); /* r->Y = Y31 = D-C */
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+ fe448_reduce(r->Y);
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+ fe448_mul(r->Y, r->Y, t0); /* r->Y = Y32 = G*(D-C) */
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+ fe448_mul(r->Y, r->Y, r->Z); /* r->Y = Y3 = A*F*(D-C) */
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+ fe448_mul(r->Z, t4, t0); /* r->Z = Z3 = F*G */
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+}
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+
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+/* Convert point to byte array assuming projective ordinates.
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+ *
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+ * b [in] Array of bytes to hold compressed point.
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+ * p [in] Point to convert.
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+ */
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+void ge448_to_bytes(uint8_t *s, const ge448_p2 *h)
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+{
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+ ge448 recip[56];
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+ ge448 x[56];
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+
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+ fe448_invert(recip, h->Z);
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+ fe448_mul(x, h->X, recip);
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+ fe448_mul(s, h->Y, recip);
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+ fe448_norm(x);
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+ fe448_norm(s);
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+ s[56] = (x[0] & 1) << 7;
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+}
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+
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+/* Compress the point to y-ordinate and negative bit.
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+ *
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+ * out [in] Array of bytes to hold compressed key.
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+ * xIn [in] The x-ordinate.
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+ * yIn [in] The y-ordinate.
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+ */
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+int ge448_compress_key(uint8_t* out, const uint8_t* xIn, const uint8_t* yIn)
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+{
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+ ge448 x[56];
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+
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+ fe448_copy(x, xIn);
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+ fe448_copy(out, yIn);
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+ fe448_norm(x);
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+ fe448_norm(out);
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+ out[56] = (x[0] & 1) << 7;
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+
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+ return 0;
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+}
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+
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+/* Perform a scalar multiplication of the a point. r = p * base
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+ *
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+ * r [in] Point to hold result.
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+ * a [in] Scalar to multiply by.
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+ */
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+static void ge448_scalarmult(ge448_p2* h, const ge448_p2* p, const uint8_t* a)
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+{
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+ ge448_p2 r;
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+ ge448_p2 s;
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+ int i;
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+
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+ XMEMSET(&r, 0, sizeof(r));
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+ r.Y[0] = 1;
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+ r.Z[0] = 1;
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+
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+ for (i = 447; i >= 0; i--) {
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+ const byte bit = (a[i >> 3] >> (i & 7)) & 1;
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+
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+ ge448_dbl(&r, &r);
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+ ge448_add(&s, &r, p);
|
|
|
+
|
|
|
+ fe448_cmov(r.X, s.X, bit);
|
|
|
+ fe448_cmov(r.Y, s.Y, bit);
|
|
|
+ fe448_cmov(r.Z, s.Z, bit);
|
|
|
+ }
|
|
|
+
|
|
|
+ XMEMCPY(h, &r, sizeof(r));
|
|
|
+}
|
|
|
+
|
|
|
+/* Perform a scalar multiplication of the base point. r = a * base
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * a [in] Scalar to multiply by.
|
|
|
+ */
|
|
|
+void ge448_scalarmult_base(ge448_p2* h, const uint8_t* a)
|
|
|
+{
|
|
|
+ ge448_scalarmult(h, &ed448_base, a);
|
|
|
+}
|
|
|
+
|
|
|
+/* Perform a scalar multplication of the base point and public point.
|
|
|
+ * r = a * p + b * base
|
|
|
+ * Uses a sliding window of 5 bits.
|
|
|
+ * Not constant time.
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * a [in] Scalar to multiply by.
|
|
|
+ */
|
|
|
+int ge448_double_scalarmult_vartime(ge448_p2 *r, const uint8_t *a,
|
|
|
+ const ge448_p2 *A, const uint8_t *b)
|
|
|
+{
|
|
|
+ ge448_p2 t;
|
|
|
+
|
|
|
+ ge448_scalarmult(&t, &ed448_base, b);
|
|
|
+ ge448_scalarmult(r, A, a);
|
|
|
+ ge448_add(r, r, &t);
|
|
|
+
|
|
|
+ return 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Convert compressed point to negative of affine point.
|
|
|
+ * Calculates x from the y and the negative bit.
|
|
|
+ * Not constant time.
|
|
|
+ *
|
|
|
+ * r [in] Uncompressed point.
|
|
|
+ * b [in] Array of bytes representing point.
|
|
|
+ * returns 0 on success and -1 on failure.
|
|
|
+ */
|
|
|
+int ge448_from_bytes_negate_vartime(ge448_p2 *r, const uint8_t *b)
|
|
|
+{
|
|
|
+ int ret = 0;
|
|
|
+ ge448 u[GE448_WORDS];
|
|
|
+ ge448 v[GE448_WORDS];
|
|
|
+ ge448 u3[GE448_WORDS];
|
|
|
+ ge448 vxx[GE448_WORDS];
|
|
|
+ ge448 check[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_copy(r->Y, b);
|
|
|
+ XMEMSET(r->Z, 0, sizeof(r->Z));
|
|
|
+ r->Z[0] = 1;
|
|
|
+ fe448_sqr(u, r->Y); /* u = y^2 */
|
|
|
+ fe448_mul39081(v, u); /* v = 39081.y^2 */
|
|
|
+ fe448_sub(u, u, r->Z); /* u = y^2-1 */
|
|
|
+ fe448_add(v, v, r->Z); /* v = 39081.y^2-1 */
|
|
|
+ fe448_neg(v, v); /* v = -39081.y^2-1 = d.y^2-1 */
|
|
|
+
|
|
|
+ fe448_sqr(r->X, v); /* x = v^2 */
|
|
|
+ fe448_mul(r->X, r->X, v); /* x = v^3 */
|
|
|
+ fe448_sqr(u3, u); /* x = u^2.v^3 */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^2.v^3 */
|
|
|
+ fe448_mul(u3, u3, u); /* u3 = u^3 */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^5.v^3 */
|
|
|
+
|
|
|
+ fe448_pow_2_446_222_1(r->X, r->X); /* x = (u^5.v^3)^((q-3)/4) */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^3(u^5.v^3)^((q-3)/4) */
|
|
|
+ fe448_mul(r->X, r->X, v); /* x = u^3.v(u^5.v^3)^((q-3)/4) */
|
|
|
+
|
|
|
+ fe448_sqr(vxx, r->X);
|
|
|
+ fe448_mul(vxx, vxx, v);
|
|
|
+ fe448_sub(check, vxx, u); /* check = v.x^2-u */
|
|
|
+ fe448_norm(check);
|
|
|
+ fe448_norm(r->X);
|
|
|
+ fe448_norm(r->Y);
|
|
|
+ /* Note; vx^2+u is NOT correct. */
|
|
|
+ if (fe448_isnonzero(check)) {
|
|
|
+ ret = -1;
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Calculating negative of point in bytes - negate only if X is correct. */
|
|
|
+ if ((r->X[0] & 1) == (b[56] >> 7)) {
|
|
|
+ fe448_neg(r->X, r->X);
|
|
|
+ }
|
|
|
+
|
|
|
+ return ret;
|
|
|
+}
|
|
|
+
|
|
|
+#else /* !ED448_SMALL */
|
|
|
+
|
|
|
+#if defined(CURVED448_128BIT)
|
|
|
+
|
|
|
+/* Reduce scalar mod the order of the curve.
|
|
|
+ * Scalar Will be 114 bytes.
|
|
|
+ *
|
|
|
+ * b [in] Scalar to reduce.
|
|
|
+ */
|
|
|
+void sc448_reduce(uint8_t* b)
|
|
|
+{
|
|
|
+ uint64_t d[8];
|
|
|
+ uint128_t t[17];
|
|
|
+ uint128_t c;
|
|
|
+ uint64_t o;
|
|
|
+
|
|
|
+ /* Load from bytes */
|
|
|
+ t[ 0] = ((int64_t) (b[ 0]) << 0)
|
|
|
+ | ((int64_t) (b[ 1]) << 8)
|
|
|
+ | ((int64_t) (b[ 2]) << 16)
|
|
|
+ | ((int64_t) (b[ 3]) << 24)
|
|
|
+ | ((int64_t) (b[ 4]) << 32)
|
|
|
+ | ((int64_t) (b[ 5]) << 40)
|
|
|
+ | ((int64_t) (b[ 6]) << 48);
|
|
|
+ t[ 1] = ((int64_t) (b[ 7]) << 0)
|
|
|
+ | ((int64_t) (b[ 8]) << 8)
|
|
|
+ | ((int64_t) (b[ 9]) << 16)
|
|
|
+ | ((int64_t) (b[10]) << 24)
|
|
|
+ | ((int64_t) (b[11]) << 32)
|
|
|
+ | ((int64_t) (b[12]) << 40)
|
|
|
+ | ((int64_t) (b[13]) << 48);
|
|
|
+ t[ 2] = ((int64_t) (b[14]) << 0)
|
|
|
+ | ((int64_t) (b[15]) << 8)
|
|
|
+ | ((int64_t) (b[16]) << 16)
|
|
|
+ | ((int64_t) (b[17]) << 24)
|
|
|
+ | ((int64_t) (b[18]) << 32)
|
|
|
+ | ((int64_t) (b[19]) << 40)
|
|
|
+ | ((int64_t) (b[20]) << 48);
|
|
|
+ t[ 3] = ((int64_t) (b[21]) << 0)
|
|
|
+ | ((int64_t) (b[22]) << 8)
|
|
|
+ | ((int64_t) (b[23]) << 16)
|
|
|
+ | ((int64_t) (b[24]) << 24)
|
|
|
+ | ((int64_t) (b[25]) << 32)
|
|
|
+ | ((int64_t) (b[26]) << 40)
|
|
|
+ | ((int64_t) (b[27]) << 48);
|
|
|
+ t[ 4] = ((int64_t) (b[28]) << 0)
|
|
|
+ | ((int64_t) (b[29]) << 8)
|
|
|
+ | ((int64_t) (b[30]) << 16)
|
|
|
+ | ((int64_t) (b[31]) << 24)
|
|
|
+ | ((int64_t) (b[32]) << 32)
|
|
|
+ | ((int64_t) (b[33]) << 40)
|
|
|
+ | ((int64_t) (b[34]) << 48);
|
|
|
+ t[ 5] = ((int64_t) (b[35]) << 0)
|
|
|
+ | ((int64_t) (b[36]) << 8)
|
|
|
+ | ((int64_t) (b[37]) << 16)
|
|
|
+ | ((int64_t) (b[38]) << 24)
|
|
|
+ | ((int64_t) (b[39]) << 32)
|
|
|
+ | ((int64_t) (b[40]) << 40)
|
|
|
+ | ((int64_t) (b[41]) << 48);
|
|
|
+ t[ 6] = ((int64_t) (b[42]) << 0)
|
|
|
+ | ((int64_t) (b[43]) << 8)
|
|
|
+ | ((int64_t) (b[44]) << 16)
|
|
|
+ | ((int64_t) (b[45]) << 24)
|
|
|
+ | ((int64_t) (b[46]) << 32)
|
|
|
+ | ((int64_t) (b[47]) << 40)
|
|
|
+ | ((int64_t) (b[48]) << 48);
|
|
|
+ t[ 7] = ((int64_t) (b[49]) << 0)
|
|
|
+ | ((int64_t) (b[50]) << 8)
|
|
|
+ | ((int64_t) (b[51]) << 16)
|
|
|
+ | ((int64_t) (b[52]) << 24)
|
|
|
+ | ((int64_t) (b[53]) << 32)
|
|
|
+ | ((int64_t) (b[54]) << 40)
|
|
|
+ | ((int64_t) (b[55]) << 48);
|
|
|
+ t[ 8] = ((int64_t) (b[56]) << 0)
|
|
|
+ | ((int64_t) (b[57]) << 8)
|
|
|
+ | ((int64_t) (b[58]) << 16)
|
|
|
+ | ((int64_t) (b[59]) << 24)
|
|
|
+ | ((int64_t) (b[60]) << 32)
|
|
|
+ | ((int64_t) (b[61]) << 40)
|
|
|
+ | ((int64_t) (b[62]) << 48);
|
|
|
+ t[ 9] = ((int64_t) (b[63]) << 0)
|
|
|
+ | ((int64_t) (b[64]) << 8)
|
|
|
+ | ((int64_t) (b[65]) << 16)
|
|
|
+ | ((int64_t) (b[66]) << 24)
|
|
|
+ | ((int64_t) (b[67]) << 32)
|
|
|
+ | ((int64_t) (b[68]) << 40)
|
|
|
+ | ((int64_t) (b[69]) << 48);
|
|
|
+ t[10] = ((int64_t) (b[70]) << 0)
|
|
|
+ | ((int64_t) (b[71]) << 8)
|
|
|
+ | ((int64_t) (b[72]) << 16)
|
|
|
+ | ((int64_t) (b[73]) << 24)
|
|
|
+ | ((int64_t) (b[74]) << 32)
|
|
|
+ | ((int64_t) (b[75]) << 40)
|
|
|
+ | ((int64_t) (b[76]) << 48);
|
|
|
+ t[11] = ((int64_t) (b[77]) << 0)
|
|
|
+ | ((int64_t) (b[78]) << 8)
|
|
|
+ | ((int64_t) (b[79]) << 16)
|
|
|
+ | ((int64_t) (b[80]) << 24)
|
|
|
+ | ((int64_t) (b[81]) << 32)
|
|
|
+ | ((int64_t) (b[82]) << 40)
|
|
|
+ | ((int64_t) (b[83]) << 48);
|
|
|
+ t[12] = ((int64_t) (b[84]) << 0)
|
|
|
+ | ((int64_t) (b[85]) << 8)
|
|
|
+ | ((int64_t) (b[86]) << 16)
|
|
|
+ | ((int64_t) (b[87]) << 24)
|
|
|
+ | ((int64_t) (b[88]) << 32)
|
|
|
+ | ((int64_t) (b[89]) << 40)
|
|
|
+ | ((int64_t) (b[90]) << 48);
|
|
|
+ t[13] = ((int64_t) (b[91]) << 0)
|
|
|
+ | ((int64_t) (b[92]) << 8)
|
|
|
+ | ((int64_t) (b[93]) << 16)
|
|
|
+ | ((int64_t) (b[94]) << 24)
|
|
|
+ | ((int64_t) (b[95]) << 32)
|
|
|
+ | ((int64_t) (b[96]) << 40)
|
|
|
+ | ((int64_t) (b[97]) << 48);
|
|
|
+ t[14] = ((int64_t) (b[98]) << 0)
|
|
|
+ | ((int64_t) (b[99]) << 8)
|
|
|
+ | ((int64_t) (b[100]) << 16)
|
|
|
+ | ((int64_t) (b[101]) << 24)
|
|
|
+ | ((int64_t) (b[102]) << 32)
|
|
|
+ | ((int64_t) (b[103]) << 40)
|
|
|
+ | ((int64_t) (b[104]) << 48);
|
|
|
+ t[15] = ((int64_t) (b[105]) << 0)
|
|
|
+ | ((int64_t) (b[106]) << 8)
|
|
|
+ | ((int64_t) (b[107]) << 16)
|
|
|
+ | ((int64_t) (b[108]) << 24)
|
|
|
+ | ((int64_t) (b[109]) << 32)
|
|
|
+ | ((int64_t) (b[110]) << 40)
|
|
|
+ | ((int64_t) (b[111]) << 48);
|
|
|
+ t[16] = ((int64_t) (b[112]) << 0)
|
|
|
+ | ((int64_t) (b[113]) << 8);
|
|
|
+
|
|
|
+ /* Mod curve order */
|
|
|
+ /* 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d */
|
|
|
+ /* Mod top half of extra words */
|
|
|
+ t[ 4] += (int128_t)0x21cf5b5529eec34L * t[12];
|
|
|
+ t[ 5] += (int128_t)0x0f635c8e9c2ab70L * t[12];
|
|
|
+ t[ 6] += (int128_t)0x2d944a725bf7a4cL * t[12];
|
|
|
+ t[ 7] += (int128_t)0x20cd77058eec490L * t[12];
|
|
|
+ t[ 5] += (int128_t)0x21cf5b5529eec34L * t[13];
|
|
|
+ t[ 6] += (int128_t)0x0f635c8e9c2ab70L * t[13];
|
|
|
+ t[ 7] += (int128_t)0x2d944a725bf7a4cL * t[13];
|
|
|
+ t[ 8] += (int128_t)0x20cd77058eec490L * t[13];
|
|
|
+ t[ 6] += (int128_t)0x21cf5b5529eec34L * t[14];
|
|
|
+ t[ 7] += (int128_t)0x0f635c8e9c2ab70L * t[14];
|
|
|
+ t[ 8] += (int128_t)0x2d944a725bf7a4cL * t[14];
|
|
|
+ t[ 9] += (int128_t)0x20cd77058eec490L * t[14];
|
|
|
+ t[ 7] += (int128_t)0x21cf5b5529eec34L * t[15];
|
|
|
+ t[ 8] += (int128_t)0x0f635c8e9c2ab70L * t[15];
|
|
|
+ t[ 9] += (int128_t)0x2d944a725bf7a4cL * t[15];
|
|
|
+ t[10] += (int128_t)0x20cd77058eec490L * t[15];
|
|
|
+ t[ 8] += (int128_t)0x21cf5b5529eec34L * t[16];
|
|
|
+ t[ 9] += (int128_t)0x0f635c8e9c2ab70L * t[16];
|
|
|
+ t[10] += (int128_t)0x2d944a725bf7a4cL * t[16];
|
|
|
+ t[11] += (int128_t)0x20cd77058eec490L * t[16];
|
|
|
+ t[12] = 0;
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; t[ 4] = t[ 4] & 0xffffffffffffff;
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; t[ 5] = t[ 5] & 0xffffffffffffff;
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; t[ 6] = t[ 6] & 0xffffffffffffff;
|
|
|
+ c = t[ 7] >> 56; t[ 8] += c; t[ 7] = t[ 7] & 0xffffffffffffff;
|
|
|
+ c = t[ 8] >> 56; t[ 9] += c; t[ 8] = t[ 8] & 0xffffffffffffff;
|
|
|
+ c = t[ 9] >> 56; t[10] += c; t[ 9] = t[ 9] & 0xffffffffffffff;
|
|
|
+ c = t[10] >> 56; t[11] += c; t[10] = t[10] & 0xffffffffffffff;
|
|
|
+ c = t[11] >> 56; t[12] += c; t[11] = t[11] & 0xffffffffffffff;
|
|
|
+ /* Mod bottom half of extra words */
|
|
|
+ t[ 0] += (int128_t)0x21cf5b5529eec34L * t[ 8];
|
|
|
+ t[ 1] += (int128_t)0x0f635c8e9c2ab70L * t[ 8];
|
|
|
+ t[ 2] += (int128_t)0x2d944a725bf7a4cL * t[ 8];
|
|
|
+ t[ 3] += (int128_t)0x20cd77058eec490L * t[ 8];
|
|
|
+ t[ 1] += (int128_t)0x21cf5b5529eec34L * t[ 9];
|
|
|
+ t[ 2] += (int128_t)0x0f635c8e9c2ab70L * t[ 9];
|
|
|
+ t[ 3] += (int128_t)0x2d944a725bf7a4cL * t[ 9];
|
|
|
+ t[ 4] += (int128_t)0x20cd77058eec490L * t[ 9];
|
|
|
+ t[ 2] += (int128_t)0x21cf5b5529eec34L * t[10];
|
|
|
+ t[ 3] += (int128_t)0x0f635c8e9c2ab70L * t[10];
|
|
|
+ t[ 4] += (int128_t)0x2d944a725bf7a4cL * t[10];
|
|
|
+ t[ 5] += (int128_t)0x20cd77058eec490L * t[10];
|
|
|
+ t[ 3] += (int128_t)0x21cf5b5529eec34L * t[11];
|
|
|
+ t[ 4] += (int128_t)0x0f635c8e9c2ab70L * t[11];
|
|
|
+ t[ 5] += (int128_t)0x2d944a725bf7a4cL * t[11];
|
|
|
+ t[ 6] += (int128_t)0x20cd77058eec490L * t[11];
|
|
|
+ t[ 4] += (int128_t)0x21cf5b5529eec34L * t[12];
|
|
|
+ t[ 5] += (int128_t)0x0f635c8e9c2ab70L * t[12];
|
|
|
+ t[ 6] += (int128_t)0x2d944a725bf7a4cL * t[12];
|
|
|
+ t[ 7] += (int128_t)0x20cd77058eec490L * t[12];
|
|
|
+ t[ 8] = 0;
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 56; t[ 1] += c; t[ 0] = t[ 0] & 0xffffffffffffff;
|
|
|
+ c = t[ 1] >> 56; t[ 2] += c; t[ 1] = t[ 1] & 0xffffffffffffff;
|
|
|
+ c = t[ 2] >> 56; t[ 3] += c; t[ 2] = t[ 2] & 0xffffffffffffff;
|
|
|
+ c = t[ 3] >> 56; t[ 4] += c; t[ 3] = t[ 3] & 0xffffffffffffff;
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; t[ 4] = t[ 4] & 0xffffffffffffff;
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; t[ 5] = t[ 5] & 0xffffffffffffff;
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; t[ 6] = t[ 6] & 0xffffffffffffff;
|
|
|
+ c = t[ 7] >> 56; t[ 8] += c; t[ 7] = t[ 7] & 0xffffffffffffff;
|
|
|
+ t[ 0] += (int128_t)0x21cf5b5529eec34L * t[ 8];
|
|
|
+ t[ 1] += (int128_t)0x0f635c8e9c2ab70L * t[ 8];
|
|
|
+ t[ 2] += (int128_t)0x2d944a725bf7a4cL * t[ 8];
|
|
|
+ t[ 3] += (int128_t)0x20cd77058eec490L * t[ 8];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 56; t[ 1] += c; d[ 0] = (int64_t)(t[ 0] & 0xffffffffffffff);
|
|
|
+ c = t[ 1] >> 56; t[ 2] += c; d[ 1] = (int64_t)(t[ 1] & 0xffffffffffffff);
|
|
|
+ c = t[ 2] >> 56; t[ 3] += c; d[ 2] = (int64_t)(t[ 2] & 0xffffffffffffff);
|
|
|
+ c = t[ 3] >> 56; t[ 4] += c; d[ 3] = (int64_t)(t[ 3] & 0xffffffffffffff);
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; d[ 4] = (int64_t)(t[ 4] & 0xffffffffffffff);
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; d[ 5] = (int64_t)(t[ 5] & 0xffffffffffffff);
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; d[ 6] = (int64_t)(t[ 6] & 0xffffffffffffff);
|
|
|
+ d[ 7] = t[7];
|
|
|
+ /* Mod bits over 56 in last word */
|
|
|
+ o = d[7] >> 54; d[ 7] &= 0x3fffffffffffff;
|
|
|
+ d[ 0] += 0x873d6d54a7bb0dL * o;
|
|
|
+ d[ 1] += 0x3d8d723a70aadcL * o;
|
|
|
+ d[ 2] += 0xb65129c96fde93L * o;
|
|
|
+ d[ 3] += 0x8335dc163bb124L * o;
|
|
|
+ /* Propagate carries */
|
|
|
+ o = d[ 0] >> 56; d[ 1] += o; d[ 0] = d[ 0] & 0xffffffffffffff;
|
|
|
+ o = d[ 1] >> 56; d[ 2] += o; d[ 1] = d[ 1] & 0xffffffffffffff;
|
|
|
+ o = d[ 2] >> 56; d[ 3] += o; d[ 2] = d[ 2] & 0xffffffffffffff;
|
|
|
+ o = d[ 3] >> 56; d[ 4] += o; d[ 3] = d[ 3] & 0xffffffffffffff;
|
|
|
+ o = d[ 4] >> 56; d[ 5] += o; d[ 4] = d[ 4] & 0xffffffffffffff;
|
|
|
+ o = d[ 5] >> 56; d[ 6] += o; d[ 5] = d[ 5] & 0xffffffffffffff;
|
|
|
+ o = d[ 6] >> 56; d[ 7] += o; d[ 6] = d[ 6] & 0xffffffffffffff;
|
|
|
+
|
|
|
+ /* Convert to bytes */
|
|
|
+ b[ 0] = (d[0 ] >> 0);
|
|
|
+ b[ 1] = (d[0 ] >> 8);
|
|
|
+ b[ 2] = (d[0 ] >> 16);
|
|
|
+ b[ 3] = (d[0 ] >> 24);
|
|
|
+ b[ 4] = (d[0 ] >> 32);
|
|
|
+ b[ 5] = (d[0 ] >> 40);
|
|
|
+ b[ 6] = (d[0 ] >> 48);
|
|
|
+ b[ 7] = (d[1 ] >> 0);
|
|
|
+ b[ 8] = (d[1 ] >> 8);
|
|
|
+ b[ 9] = (d[1 ] >> 16);
|
|
|
+ b[10] = (d[1 ] >> 24);
|
|
|
+ b[11] = (d[1 ] >> 32);
|
|
|
+ b[12] = (d[1 ] >> 40);
|
|
|
+ b[13] = (d[1 ] >> 48);
|
|
|
+ b[14] = (d[2 ] >> 0);
|
|
|
+ b[15] = (d[2 ] >> 8);
|
|
|
+ b[16] = (d[2 ] >> 16);
|
|
|
+ b[17] = (d[2 ] >> 24);
|
|
|
+ b[18] = (d[2 ] >> 32);
|
|
|
+ b[19] = (d[2 ] >> 40);
|
|
|
+ b[20] = (d[2 ] >> 48);
|
|
|
+ b[21] = (d[3 ] >> 0);
|
|
|
+ b[22] = (d[3 ] >> 8);
|
|
|
+ b[23] = (d[3 ] >> 16);
|
|
|
+ b[24] = (d[3 ] >> 24);
|
|
|
+ b[25] = (d[3 ] >> 32);
|
|
|
+ b[26] = (d[3 ] >> 40);
|
|
|
+ b[27] = (d[3 ] >> 48);
|
|
|
+ b[28] = (d[4 ] >> 0);
|
|
|
+ b[29] = (d[4 ] >> 8);
|
|
|
+ b[30] = (d[4 ] >> 16);
|
|
|
+ b[31] = (d[4 ] >> 24);
|
|
|
+ b[32] = (d[4 ] >> 32);
|
|
|
+ b[33] = (d[4 ] >> 40);
|
|
|
+ b[34] = (d[4 ] >> 48);
|
|
|
+ b[35] = (d[5 ] >> 0);
|
|
|
+ b[36] = (d[5 ] >> 8);
|
|
|
+ b[37] = (d[5 ] >> 16);
|
|
|
+ b[38] = (d[5 ] >> 24);
|
|
|
+ b[39] = (d[5 ] >> 32);
|
|
|
+ b[40] = (d[5 ] >> 40);
|
|
|
+ b[41] = (d[5 ] >> 48);
|
|
|
+ b[42] = (d[6 ] >> 0);
|
|
|
+ b[43] = (d[6 ] >> 8);
|
|
|
+ b[44] = (d[6 ] >> 16);
|
|
|
+ b[45] = (d[6 ] >> 24);
|
|
|
+ b[46] = (d[6 ] >> 32);
|
|
|
+ b[47] = (d[6 ] >> 40);
|
|
|
+ b[48] = (d[6 ] >> 48);
|
|
|
+ b[49] = (d[7 ] >> 0);
|
|
|
+ b[50] = (d[7 ] >> 8);
|
|
|
+ b[51] = (d[7 ] >> 16);
|
|
|
+ b[52] = (d[7 ] >> 24);
|
|
|
+ b[53] = (d[7 ] >> 32);
|
|
|
+ b[54] = (d[7 ] >> 40);
|
|
|
+ b[55] = (d[7 ] >> 48);
|
|
|
+ b[56] = 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Multiply a by b and add d. r = (a * b + d) mod order
|
|
|
+ *
|
|
|
+ * r [in] Scalar to hold result.
|
|
|
+ * a [in] Scalar to multiply.
|
|
|
+ * b [in] Scalar to multiply.
|
|
|
+ * d [in] Scalar to add to multiplicative result.
|
|
|
+ */
|
|
|
+void sc448_muladd(uint8_t* r, const uint8_t* a, const uint8_t* b,
|
|
|
+ const uint8_t* d)
|
|
|
+{
|
|
|
+ uint64_t ad[8], bd[8], dd[8], rd[8];
|
|
|
+ uint128_t t[16];
|
|
|
+ uint128_t c;
|
|
|
+ uint64_t o;
|
|
|
+
|
|
|
+ /* Load from bytes */
|
|
|
+ ad[ 0] = ((int64_t) (a[ 0]) << 0)
|
|
|
+ | ((int64_t) (a[ 1]) << 8)
|
|
|
+ | ((int64_t) (a[ 2]) << 16)
|
|
|
+ | ((int64_t) (a[ 3]) << 24)
|
|
|
+ | ((int64_t) (a[ 4]) << 32)
|
|
|
+ | ((int64_t) (a[ 5]) << 40)
|
|
|
+ | ((int64_t) (a[ 6]) << 48);
|
|
|
+ ad[ 1] = ((int64_t) (a[ 7]) << 0)
|
|
|
+ | ((int64_t) (a[ 8]) << 8)
|
|
|
+ | ((int64_t) (a[ 9]) << 16)
|
|
|
+ | ((int64_t) (a[10]) << 24)
|
|
|
+ | ((int64_t) (a[11]) << 32)
|
|
|
+ | ((int64_t) (a[12]) << 40)
|
|
|
+ | ((int64_t) (a[13]) << 48);
|
|
|
+ ad[ 2] = ((int64_t) (a[14]) << 0)
|
|
|
+ | ((int64_t) (a[15]) << 8)
|
|
|
+ | ((int64_t) (a[16]) << 16)
|
|
|
+ | ((int64_t) (a[17]) << 24)
|
|
|
+ | ((int64_t) (a[18]) << 32)
|
|
|
+ | ((int64_t) (a[19]) << 40)
|
|
|
+ | ((int64_t) (a[20]) << 48);
|
|
|
+ ad[ 3] = ((int64_t) (a[21]) << 0)
|
|
|
+ | ((int64_t) (a[22]) << 8)
|
|
|
+ | ((int64_t) (a[23]) << 16)
|
|
|
+ | ((int64_t) (a[24]) << 24)
|
|
|
+ | ((int64_t) (a[25]) << 32)
|
|
|
+ | ((int64_t) (a[26]) << 40)
|
|
|
+ | ((int64_t) (a[27]) << 48);
|
|
|
+ ad[ 4] = ((int64_t) (a[28]) << 0)
|
|
|
+ | ((int64_t) (a[29]) << 8)
|
|
|
+ | ((int64_t) (a[30]) << 16)
|
|
|
+ | ((int64_t) (a[31]) << 24)
|
|
|
+ | ((int64_t) (a[32]) << 32)
|
|
|
+ | ((int64_t) (a[33]) << 40)
|
|
|
+ | ((int64_t) (a[34]) << 48);
|
|
|
+ ad[ 5] = ((int64_t) (a[35]) << 0)
|
|
|
+ | ((int64_t) (a[36]) << 8)
|
|
|
+ | ((int64_t) (a[37]) << 16)
|
|
|
+ | ((int64_t) (a[38]) << 24)
|
|
|
+ | ((int64_t) (a[39]) << 32)
|
|
|
+ | ((int64_t) (a[40]) << 40)
|
|
|
+ | ((int64_t) (a[41]) << 48);
|
|
|
+ ad[ 6] = ((int64_t) (a[42]) << 0)
|
|
|
+ | ((int64_t) (a[43]) << 8)
|
|
|
+ | ((int64_t) (a[44]) << 16)
|
|
|
+ | ((int64_t) (a[45]) << 24)
|
|
|
+ | ((int64_t) (a[46]) << 32)
|
|
|
+ | ((int64_t) (a[47]) << 40)
|
|
|
+ | ((int64_t) (a[48]) << 48);
|
|
|
+ ad[ 7] = ((int64_t) (a[49]) << 0)
|
|
|
+ | ((int64_t) (a[50]) << 8)
|
|
|
+ | ((int64_t) (a[51]) << 16)
|
|
|
+ | ((int64_t) (a[52]) << 24)
|
|
|
+ | ((int64_t) (a[53]) << 32)
|
|
|
+ | ((int64_t) (a[54]) << 40)
|
|
|
+ | ((int64_t) (a[55]) << 48);
|
|
|
+ /* Load from bytes */
|
|
|
+ bd[ 0] = ((int64_t) (b[ 0]) << 0)
|
|
|
+ | ((int64_t) (b[ 1]) << 8)
|
|
|
+ | ((int64_t) (b[ 2]) << 16)
|
|
|
+ | ((int64_t) (b[ 3]) << 24)
|
|
|
+ | ((int64_t) (b[ 4]) << 32)
|
|
|
+ | ((int64_t) (b[ 5]) << 40)
|
|
|
+ | ((int64_t) (b[ 6]) << 48);
|
|
|
+ bd[ 1] = ((int64_t) (b[ 7]) << 0)
|
|
|
+ | ((int64_t) (b[ 8]) << 8)
|
|
|
+ | ((int64_t) (b[ 9]) << 16)
|
|
|
+ | ((int64_t) (b[10]) << 24)
|
|
|
+ | ((int64_t) (b[11]) << 32)
|
|
|
+ | ((int64_t) (b[12]) << 40)
|
|
|
+ | ((int64_t) (b[13]) << 48);
|
|
|
+ bd[ 2] = ((int64_t) (b[14]) << 0)
|
|
|
+ | ((int64_t) (b[15]) << 8)
|
|
|
+ | ((int64_t) (b[16]) << 16)
|
|
|
+ | ((int64_t) (b[17]) << 24)
|
|
|
+ | ((int64_t) (b[18]) << 32)
|
|
|
+ | ((int64_t) (b[19]) << 40)
|
|
|
+ | ((int64_t) (b[20]) << 48);
|
|
|
+ bd[ 3] = ((int64_t) (b[21]) << 0)
|
|
|
+ | ((int64_t) (b[22]) << 8)
|
|
|
+ | ((int64_t) (b[23]) << 16)
|
|
|
+ | ((int64_t) (b[24]) << 24)
|
|
|
+ | ((int64_t) (b[25]) << 32)
|
|
|
+ | ((int64_t) (b[26]) << 40)
|
|
|
+ | ((int64_t) (b[27]) << 48);
|
|
|
+ bd[ 4] = ((int64_t) (b[28]) << 0)
|
|
|
+ | ((int64_t) (b[29]) << 8)
|
|
|
+ | ((int64_t) (b[30]) << 16)
|
|
|
+ | ((int64_t) (b[31]) << 24)
|
|
|
+ | ((int64_t) (b[32]) << 32)
|
|
|
+ | ((int64_t) (b[33]) << 40)
|
|
|
+ | ((int64_t) (b[34]) << 48);
|
|
|
+ bd[ 5] = ((int64_t) (b[35]) << 0)
|
|
|
+ | ((int64_t) (b[36]) << 8)
|
|
|
+ | ((int64_t) (b[37]) << 16)
|
|
|
+ | ((int64_t) (b[38]) << 24)
|
|
|
+ | ((int64_t) (b[39]) << 32)
|
|
|
+ | ((int64_t) (b[40]) << 40)
|
|
|
+ | ((int64_t) (b[41]) << 48);
|
|
|
+ bd[ 6] = ((int64_t) (b[42]) << 0)
|
|
|
+ | ((int64_t) (b[43]) << 8)
|
|
|
+ | ((int64_t) (b[44]) << 16)
|
|
|
+ | ((int64_t) (b[45]) << 24)
|
|
|
+ | ((int64_t) (b[46]) << 32)
|
|
|
+ | ((int64_t) (b[47]) << 40)
|
|
|
+ | ((int64_t) (b[48]) << 48);
|
|
|
+ bd[ 7] = ((int64_t) (b[49]) << 0)
|
|
|
+ | ((int64_t) (b[50]) << 8)
|
|
|
+ | ((int64_t) (b[51]) << 16)
|
|
|
+ | ((int64_t) (b[52]) << 24)
|
|
|
+ | ((int64_t) (b[53]) << 32)
|
|
|
+ | ((int64_t) (b[54]) << 40)
|
|
|
+ | ((int64_t) (b[55]) << 48);
|
|
|
+ /* Load from bytes */
|
|
|
+ dd[ 0] = ((int64_t) (d[ 0]) << 0)
|
|
|
+ | ((int64_t) (d[ 1]) << 8)
|
|
|
+ | ((int64_t) (d[ 2]) << 16)
|
|
|
+ | ((int64_t) (d[ 3]) << 24)
|
|
|
+ | ((int64_t) (d[ 4]) << 32)
|
|
|
+ | ((int64_t) (d[ 5]) << 40)
|
|
|
+ | ((int64_t) (d[ 6]) << 48);
|
|
|
+ dd[ 1] = ((int64_t) (d[ 7]) << 0)
|
|
|
+ | ((int64_t) (d[ 8]) << 8)
|
|
|
+ | ((int64_t) (d[ 9]) << 16)
|
|
|
+ | ((int64_t) (d[10]) << 24)
|
|
|
+ | ((int64_t) (d[11]) << 32)
|
|
|
+ | ((int64_t) (d[12]) << 40)
|
|
|
+ | ((int64_t) (d[13]) << 48);
|
|
|
+ dd[ 2] = ((int64_t) (d[14]) << 0)
|
|
|
+ | ((int64_t) (d[15]) << 8)
|
|
|
+ | ((int64_t) (d[16]) << 16)
|
|
|
+ | ((int64_t) (d[17]) << 24)
|
|
|
+ | ((int64_t) (d[18]) << 32)
|
|
|
+ | ((int64_t) (d[19]) << 40)
|
|
|
+ | ((int64_t) (d[20]) << 48);
|
|
|
+ dd[ 3] = ((int64_t) (d[21]) << 0)
|
|
|
+ | ((int64_t) (d[22]) << 8)
|
|
|
+ | ((int64_t) (d[23]) << 16)
|
|
|
+ | ((int64_t) (d[24]) << 24)
|
|
|
+ | ((int64_t) (d[25]) << 32)
|
|
|
+ | ((int64_t) (d[26]) << 40)
|
|
|
+ | ((int64_t) (d[27]) << 48);
|
|
|
+ dd[ 4] = ((int64_t) (d[28]) << 0)
|
|
|
+ | ((int64_t) (d[29]) << 8)
|
|
|
+ | ((int64_t) (d[30]) << 16)
|
|
|
+ | ((int64_t) (d[31]) << 24)
|
|
|
+ | ((int64_t) (d[32]) << 32)
|
|
|
+ | ((int64_t) (d[33]) << 40)
|
|
|
+ | ((int64_t) (d[34]) << 48);
|
|
|
+ dd[ 5] = ((int64_t) (d[35]) << 0)
|
|
|
+ | ((int64_t) (d[36]) << 8)
|
|
|
+ | ((int64_t) (d[37]) << 16)
|
|
|
+ | ((int64_t) (d[38]) << 24)
|
|
|
+ | ((int64_t) (d[39]) << 32)
|
|
|
+ | ((int64_t) (d[40]) << 40)
|
|
|
+ | ((int64_t) (d[41]) << 48);
|
|
|
+ dd[ 6] = ((int64_t) (d[42]) << 0)
|
|
|
+ | ((int64_t) (d[43]) << 8)
|
|
|
+ | ((int64_t) (d[44]) << 16)
|
|
|
+ | ((int64_t) (d[45]) << 24)
|
|
|
+ | ((int64_t) (d[46]) << 32)
|
|
|
+ | ((int64_t) (d[47]) << 40)
|
|
|
+ | ((int64_t) (d[48]) << 48);
|
|
|
+ dd[ 7] = ((int64_t) (d[49]) << 0)
|
|
|
+ | ((int64_t) (d[50]) << 8)
|
|
|
+ | ((int64_t) (d[51]) << 16)
|
|
|
+ | ((int64_t) (d[52]) << 24)
|
|
|
+ | ((int64_t) (d[53]) << 32)
|
|
|
+ | ((int64_t) (d[54]) << 40)
|
|
|
+ | ((int64_t) (d[55]) << 48);
|
|
|
+
|
|
|
+ /* a * b + d */
|
|
|
+ t[ 0] = dd[ 0] + (int128_t)ad[ 0] * bd[ 0];
|
|
|
+ t[ 1] = dd[ 1] + (int128_t)ad[ 0] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 0];
|
|
|
+ t[ 2] = dd[ 2] + (int128_t)ad[ 0] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 0];
|
|
|
+ t[ 3] = dd[ 3] + (int128_t)ad[ 0] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 0];
|
|
|
+ t[ 4] = dd[ 4] + (int128_t)ad[ 0] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 0];
|
|
|
+ t[ 5] = dd[ 5] + (int128_t)ad[ 0] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 0];
|
|
|
+ t[ 6] = dd[ 6] + (int128_t)ad[ 0] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 0];
|
|
|
+ t[ 7] = dd[ 7] + (int128_t)ad[ 0] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 1] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 1]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 0];
|
|
|
+ t[ 8] = (int128_t)ad[ 1] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 2] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 2]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 1];
|
|
|
+ t[ 9] = (int128_t)ad[ 2] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 3] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 3]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 2];
|
|
|
+ t[10] = (int128_t)ad[ 3] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 4] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 4]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 3];
|
|
|
+ t[11] = (int128_t)ad[ 4] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 5] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 5]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 4];
|
|
|
+ t[12] = (int128_t)ad[ 5] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 6] * bd[ 6]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 5];
|
|
|
+ t[13] = (int128_t)ad[ 6] * bd[ 7]
|
|
|
+ + (int128_t)ad[ 7] * bd[ 6];
|
|
|
+ t[14] = (int128_t)ad[ 7] * bd[ 7];
|
|
|
+ t[15] = 0;
|
|
|
+
|
|
|
+ /* Mod curve order */
|
|
|
+ /* 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d */
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 56; t[ 1] += c; t[ 0] = t[ 0] & 0xffffffffffffff;
|
|
|
+ c = t[ 1] >> 56; t[ 2] += c; t[ 1] = t[ 1] & 0xffffffffffffff;
|
|
|
+ c = t[ 2] >> 56; t[ 3] += c; t[ 2] = t[ 2] & 0xffffffffffffff;
|
|
|
+ c = t[ 3] >> 56; t[ 4] += c; t[ 3] = t[ 3] & 0xffffffffffffff;
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; t[ 4] = t[ 4] & 0xffffffffffffff;
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; t[ 5] = t[ 5] & 0xffffffffffffff;
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; t[ 6] = t[ 6] & 0xffffffffffffff;
|
|
|
+ c = t[ 7] >> 56; t[ 8] += c; t[ 7] = t[ 7] & 0xffffffffffffff;
|
|
|
+ c = t[ 8] >> 56; t[ 9] += c; t[ 8] = t[ 8] & 0xffffffffffffff;
|
|
|
+ c = t[ 9] >> 56; t[10] += c; t[ 9] = t[ 9] & 0xffffffffffffff;
|
|
|
+ c = t[10] >> 56; t[11] += c; t[10] = t[10] & 0xffffffffffffff;
|
|
|
+ c = t[11] >> 56; t[12] += c; t[11] = t[11] & 0xffffffffffffff;
|
|
|
+ c = t[12] >> 56; t[13] += c; t[12] = t[12] & 0xffffffffffffff;
|
|
|
+ c = t[13] >> 56; t[14] += c; t[13] = t[13] & 0xffffffffffffff;
|
|
|
+ c = t[14] >> 56; t[15] += c; t[14] = t[14] & 0xffffffffffffff;
|
|
|
+ /* Mod top half of extra words */
|
|
|
+ t[ 4] += (int128_t)0x21cf5b5529eec34L * t[12];
|
|
|
+ t[ 5] += (int128_t)0x0f635c8e9c2ab70L * t[12];
|
|
|
+ t[ 6] += (int128_t)0x2d944a725bf7a4cL * t[12];
|
|
|
+ t[ 7] += (int128_t)0x20cd77058eec490L * t[12];
|
|
|
+ t[ 5] += (int128_t)0x21cf5b5529eec34L * t[13];
|
|
|
+ t[ 6] += (int128_t)0x0f635c8e9c2ab70L * t[13];
|
|
|
+ t[ 7] += (int128_t)0x2d944a725bf7a4cL * t[13];
|
|
|
+ t[ 8] += (int128_t)0x20cd77058eec490L * t[13];
|
|
|
+ t[ 6] += (int128_t)0x21cf5b5529eec34L * t[14];
|
|
|
+ t[ 7] += (int128_t)0x0f635c8e9c2ab70L * t[14];
|
|
|
+ t[ 8] += (int128_t)0x2d944a725bf7a4cL * t[14];
|
|
|
+ t[ 9] += (int128_t)0x20cd77058eec490L * t[14];
|
|
|
+ t[ 7] += (int128_t)0x21cf5b5529eec34L * t[15];
|
|
|
+ t[ 8] += (int128_t)0x0f635c8e9c2ab70L * t[15];
|
|
|
+ t[ 9] += (int128_t)0x2d944a725bf7a4cL * t[15];
|
|
|
+ t[10] += (int128_t)0x20cd77058eec490L * t[15];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; t[ 4] = t[ 4] & 0xffffffffffffff;
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; t[ 5] = t[ 5] & 0xffffffffffffff;
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; t[ 6] = t[ 6] & 0xffffffffffffff;
|
|
|
+ c = t[ 7] >> 56; t[ 8] += c; t[ 7] = t[ 7] & 0xffffffffffffff;
|
|
|
+ c = t[ 8] >> 56; t[ 9] += c; t[ 8] = t[ 8] & 0xffffffffffffff;
|
|
|
+ c = t[ 9] >> 56; t[10] += c; t[ 9] = t[ 9] & 0xffffffffffffff;
|
|
|
+ c = t[10] >> 56; t[11] += c; t[10] = t[10] & 0xffffffffffffff;
|
|
|
+ /* Mod bottom half of extra words */
|
|
|
+ t[ 0] += (int128_t)0x21cf5b5529eec34L * t[ 8];
|
|
|
+ t[ 1] += (int128_t)0x0f635c8e9c2ab70L * t[ 8];
|
|
|
+ t[ 2] += (int128_t)0x2d944a725bf7a4cL * t[ 8];
|
|
|
+ t[ 3] += (int128_t)0x20cd77058eec490L * t[ 8];
|
|
|
+ t[ 1] += (int128_t)0x21cf5b5529eec34L * t[ 9];
|
|
|
+ t[ 2] += (int128_t)0x0f635c8e9c2ab70L * t[ 9];
|
|
|
+ t[ 3] += (int128_t)0x2d944a725bf7a4cL * t[ 9];
|
|
|
+ t[ 4] += (int128_t)0x20cd77058eec490L * t[ 9];
|
|
|
+ t[ 2] += (int128_t)0x21cf5b5529eec34L * t[10];
|
|
|
+ t[ 3] += (int128_t)0x0f635c8e9c2ab70L * t[10];
|
|
|
+ t[ 4] += (int128_t)0x2d944a725bf7a4cL * t[10];
|
|
|
+ t[ 5] += (int128_t)0x20cd77058eec490L * t[10];
|
|
|
+ t[ 3] += (int128_t)0x21cf5b5529eec34L * t[11];
|
|
|
+ t[ 4] += (int128_t)0x0f635c8e9c2ab70L * t[11];
|
|
|
+ t[ 5] += (int128_t)0x2d944a725bf7a4cL * t[11];
|
|
|
+ t[ 6] += (int128_t)0x20cd77058eec490L * t[11];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 56; t[ 1] += c; rd[ 0] = (int64_t)(t[ 0] & 0xffffffffffffff);
|
|
|
+ c = t[ 1] >> 56; t[ 2] += c; rd[ 1] = (int64_t)(t[ 1] & 0xffffffffffffff);
|
|
|
+ c = t[ 2] >> 56; t[ 3] += c; rd[ 2] = (int64_t)(t[ 2] & 0xffffffffffffff);
|
|
|
+ c = t[ 3] >> 56; t[ 4] += c; rd[ 3] = (int64_t)(t[ 3] & 0xffffffffffffff);
|
|
|
+ c = t[ 4] >> 56; t[ 5] += c; rd[ 4] = (int64_t)(t[ 4] & 0xffffffffffffff);
|
|
|
+ c = t[ 5] >> 56; t[ 6] += c; rd[ 5] = (int64_t)(t[ 5] & 0xffffffffffffff);
|
|
|
+ c = t[ 6] >> 56; t[ 7] += c; rd[ 6] = (int64_t)(t[ 6] & 0xffffffffffffff);
|
|
|
+ rd[ 7] = t[7];
|
|
|
+ /* Mod bits over 56 in last word */
|
|
|
+ o = rd[7] >> 54; rd[ 7] &= 0x3fffffffffffff;
|
|
|
+ rd[ 0] += 0x873d6d54a7bb0dL * o;
|
|
|
+ rd[ 1] += 0x3d8d723a70aadcL * o;
|
|
|
+ rd[ 2] += 0xb65129c96fde93L * o;
|
|
|
+ rd[ 3] += 0x8335dc163bb124L * o;
|
|
|
+ /* Propagate carries */
|
|
|
+ o = rd[ 0] >> 56; rd[ 1] += o; rd[ 0] = rd[ 0] & 0xffffffffffffff;
|
|
|
+ o = rd[ 1] >> 56; rd[ 2] += o; rd[ 1] = rd[ 1] & 0xffffffffffffff;
|
|
|
+ o = rd[ 2] >> 56; rd[ 3] += o; rd[ 2] = rd[ 2] & 0xffffffffffffff;
|
|
|
+ o = rd[ 3] >> 56; rd[ 4] += o; rd[ 3] = rd[ 3] & 0xffffffffffffff;
|
|
|
+ o = rd[ 4] >> 56; rd[ 5] += o; rd[ 4] = rd[ 4] & 0xffffffffffffff;
|
|
|
+ o = rd[ 5] >> 56; rd[ 6] += o; rd[ 5] = rd[ 5] & 0xffffffffffffff;
|
|
|
+ o = rd[ 6] >> 56; rd[ 7] += o; rd[ 6] = rd[ 6] & 0xffffffffffffff;
|
|
|
+
|
|
|
+ /* Convert to bytes */
|
|
|
+ r[ 0] = (rd[0 ] >> 0);
|
|
|
+ r[ 1] = (rd[0 ] >> 8);
|
|
|
+ r[ 2] = (rd[0 ] >> 16);
|
|
|
+ r[ 3] = (rd[0 ] >> 24);
|
|
|
+ r[ 4] = (rd[0 ] >> 32);
|
|
|
+ r[ 5] = (rd[0 ] >> 40);
|
|
|
+ r[ 6] = (rd[0 ] >> 48);
|
|
|
+ r[ 7] = (rd[1 ] >> 0);
|
|
|
+ r[ 8] = (rd[1 ] >> 8);
|
|
|
+ r[ 9] = (rd[1 ] >> 16);
|
|
|
+ r[10] = (rd[1 ] >> 24);
|
|
|
+ r[11] = (rd[1 ] >> 32);
|
|
|
+ r[12] = (rd[1 ] >> 40);
|
|
|
+ r[13] = (rd[1 ] >> 48);
|
|
|
+ r[14] = (rd[2 ] >> 0);
|
|
|
+ r[15] = (rd[2 ] >> 8);
|
|
|
+ r[16] = (rd[2 ] >> 16);
|
|
|
+ r[17] = (rd[2 ] >> 24);
|
|
|
+ r[18] = (rd[2 ] >> 32);
|
|
|
+ r[19] = (rd[2 ] >> 40);
|
|
|
+ r[20] = (rd[2 ] >> 48);
|
|
|
+ r[21] = (rd[3 ] >> 0);
|
|
|
+ r[22] = (rd[3 ] >> 8);
|
|
|
+ r[23] = (rd[3 ] >> 16);
|
|
|
+ r[24] = (rd[3 ] >> 24);
|
|
|
+ r[25] = (rd[3 ] >> 32);
|
|
|
+ r[26] = (rd[3 ] >> 40);
|
|
|
+ r[27] = (rd[3 ] >> 48);
|
|
|
+ r[28] = (rd[4 ] >> 0);
|
|
|
+ r[29] = (rd[4 ] >> 8);
|
|
|
+ r[30] = (rd[4 ] >> 16);
|
|
|
+ r[31] = (rd[4 ] >> 24);
|
|
|
+ r[32] = (rd[4 ] >> 32);
|
|
|
+ r[33] = (rd[4 ] >> 40);
|
|
|
+ r[34] = (rd[4 ] >> 48);
|
|
|
+ r[35] = (rd[5 ] >> 0);
|
|
|
+ r[36] = (rd[5 ] >> 8);
|
|
|
+ r[37] = (rd[5 ] >> 16);
|
|
|
+ r[38] = (rd[5 ] >> 24);
|
|
|
+ r[39] = (rd[5 ] >> 32);
|
|
|
+ r[40] = (rd[5 ] >> 40);
|
|
|
+ r[41] = (rd[5 ] >> 48);
|
|
|
+ r[42] = (rd[6 ] >> 0);
|
|
|
+ r[43] = (rd[6 ] >> 8);
|
|
|
+ r[44] = (rd[6 ] >> 16);
|
|
|
+ r[45] = (rd[6 ] >> 24);
|
|
|
+ r[46] = (rd[6 ] >> 32);
|
|
|
+ r[47] = (rd[6 ] >> 40);
|
|
|
+ r[48] = (rd[6 ] >> 48);
|
|
|
+ r[49] = (rd[7 ] >> 0);
|
|
|
+ r[50] = (rd[7 ] >> 8);
|
|
|
+ r[51] = (rd[7 ] >> 16);
|
|
|
+ r[52] = (rd[7 ] >> 24);
|
|
|
+ r[53] = (rd[7 ] >> 32);
|
|
|
+ r[54] = (rd[7 ] >> 40);
|
|
|
+ r[55] = (rd[7 ] >> 48);
|
|
|
+ r[56] = 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Precomputed multiples of the base point. */
|
|
|
+static const ge448_precomp base[58][8] = {
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x26a82bc70cc05eL, 0x80e18b00938e26L, 0xf72ab66511433bL,
|
|
|
+ 0xa3d3a46412ae1aL, 0x0f1767ea6de324L, 0x36da9e14657047L,
|
|
|
+ 0xed221d15a622bfL, 0x4f1970c66bed0dL },
|
|
|
+ { 0x08795bf230fa14L, 0x132c4ed7c8ad98L, 0x1ce67c39c4fdbdL,
|
|
|
+ 0x05a0c2d73ad3ffL, 0xa3984087789c1eL, 0xc7624bea73736cL,
|
|
|
+ 0x248876203756c9L, 0x693f46716eb6bcL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x55555555555555L, 0x55555555555555L, 0x55555555555555L,
|
|
|
+ 0x55555555555555L, 0xaaaaaaaaaaaaa9L, 0xaaaaaaaaaaaaaaL,
|
|
|
+ 0xaaaaaaaaaaaaaaL, 0xaaaaaaaaaaaaaaL },
|
|
|
+ { 0xeafbcdea9386edL, 0xb2bed1cda06bdaL, 0x833a2a3098bbbcL,
|
|
|
+ 0x8ad8c4b80d6565L, 0x884dd7b7e36d72L, 0xc2b0036ed7a035L,
|
|
|
+ 0x8db359d6205086L, 0xae05e9634ad704L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x28173286ff2f8fL, 0xb769465da85757L, 0xf7f6271fd6e862L,
|
|
|
+ 0x4a3fcfe8daa9cbL, 0xda82c7e2ba077aL, 0x943332241b8b8cL,
|
|
|
+ 0x6455bd64316cb6L, 0x0865886b9108afL },
|
|
|
+ { 0x22ac13588ed6fcL, 0x9a68fed02dafb8L, 0x1bdb6767f0bffaL,
|
|
|
+ 0xec4e1d58bb3a33L, 0x56c3b9fce43c82L, 0xa6449a4a8d9523L,
|
|
|
+ 0xf706cbda7ad43aL, 0xe005a8dbd5125cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xce42ac48ba7f30L, 0xe1798949e120e2L, 0xf1515dd8ba21aeL,
|
|
|
+ 0x70c74cc301b7bdL, 0x0891c693fda4beL, 0x29ea255a09cf4eL,
|
|
|
+ 0x2c1419a17226f9L, 0x49dcbc5c6c0cceL },
|
|
|
+ { 0xe236f86de51839L, 0x44285d0d4f5b32L, 0x7ea1ca9472b5d4L,
|
|
|
+ 0x7b8a5bc1c0d8f9L, 0x57d845c90dc322L, 0x1b979cb7c02f04L,
|
|
|
+ 0x27164b33a5de02L, 0xd49077e4accde5L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xa99d1092030034L, 0x2d8cefc6f950d0L, 0x7a920c3c96f07bL,
|
|
|
+ 0x958812808bc0d5L, 0x62ada756d761e8L, 0x0def80cbcf7285L,
|
|
|
+ 0x0e2ba7601eedb5L, 0x7a9f9335a48dcbL },
|
|
|
+ { 0xb4731472f435ebL, 0x5512881f225443L, 0xee59d2b33c5840L,
|
|
|
+ 0xb698017127d7a4L, 0xb18fced86551f7L, 0x0ade260ca1823aL,
|
|
|
+ 0xd3b9109ce4fd58L, 0xadfd751a2517edL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x7fd7652abef79cL, 0x6c20a07443a878L, 0x5c1840d12a7109L,
|
|
|
+ 0x4a06e4a876451cL, 0x3bed0b4ad95f65L, 0x25d2e673fb0260L,
|
|
|
+ 0x2e00349aebd971L, 0x54523e04498b72L },
|
|
|
+ { 0xea5d1da07c7bccL, 0xcce776938ea98cL, 0x80284e861d2b3eL,
|
|
|
+ 0x48de76b6e1ff1bL, 0x7b121869c58522L, 0xbfd053a2765a1aL,
|
|
|
+ 0x2d743ec056c667L, 0x3f99b9cd8ab61cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xdf9567ceb5eaf7L, 0x110a6b478ac7d7L, 0x2d335014706e0bL,
|
|
|
+ 0x0df9c7b0b5a209L, 0xba4223d568e684L, 0xd78af2d8c3719bL,
|
|
|
+ 0x77467b9a5291b6L, 0x079748e5c89befL },
|
|
|
+ { 0xe20d3fadac377fL, 0x34e866972b5c09L, 0xd8687a3c40bbb7L,
|
|
|
+ 0x7b3946fd2f84c9L, 0xd00e40ca78f50eL, 0xb87594417e7179L,
|
|
|
+ 0x9c7373bcb23583L, 0x7ddeda3c90fd69L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x2538a67153bde0L, 0x223aca9406b696L, 0xf9080dc1ad713eL,
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|
|
+ { 0x6fb627760a0aa8L, 0xe046843cbe04f0L, 0xc01d120e6ad443L,
|
|
|
+ 0xa42a05cabef2fcL, 0x6b793f112ff09cL, 0x5734ea8a3e5854L,
|
|
|
+ 0xe482b36775f0adL, 0x2f4f60df864a34L },
|
|
|
+ { 0xf521c5884f2449L, 0x58734a99186a71L, 0x157f5d5ac5eaccL,
|
|
|
+ 0x858d9a4248ee61L, 0x0727e6d48149c3L, 0xd5c3eaaac9ec50L,
|
|
|
+ 0xa63a64a20ee9b5L, 0x3f0dfc487be9deL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x836349db13e3f4L, 0xebdd0263e9316dL, 0x3fd61e8324fd6cL,
|
|
|
+ 0x85dddfa0964f41L, 0x06e72de52add1bL, 0xb752cff8c4a9e2L,
|
|
|
+ 0x53b0894fdf09f7L, 0xd5220ab0bc24fdL },
|
|
|
+ { 0x8442b35fb1981aL, 0xa733a373edd701L, 0x42b60c3d0ef089L,
|
|
|
+ 0xa1b16ec46e7bcaL, 0xc0df179a09aaf4L, 0xcd4f187638f3a1L,
|
|
|
+ 0x9af64f79eab1c2L, 0x86fed79d1d78e3L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x42c8d86fe29980L, 0x6657b816575660L, 0x82d52c680f92caL,
|
|
|
+ 0x8587af102d42beL, 0xb5151316e8bdf0L, 0x706e2d9c333495L,
|
|
|
+ 0xd53601a9673064L, 0x27b1fbb8219099L },
|
|
|
+ { 0x3f0929d705f7c8L, 0xff40b10f3d6e6fL, 0x673c703026af5cL,
|
|
|
+ 0x2c1dce4e25a422L, 0x5348bd73dad8b6L, 0xc39b6b6be2c329L,
|
|
|
+ 0x47854ffb921084L, 0xb347b8bb391f20L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x79fc841eb9b774L, 0xf32da25b4b6c1dL, 0xcbba76bfe492cbL,
|
|
|
+ 0x76c51fcd623903L, 0x114cf6fcf0705aL, 0x6b720497815dafL,
|
|
|
+ 0x630b362473382eL, 0xbf40c3a9704db5L },
|
|
|
+ { 0xa8a9ddcc5456ebL, 0x2b4472a72f2dc1L, 0x9874444d6d6ef3L,
|
|
|
+ 0x27e8d85a0ba5edL, 0x5d225b4194849fL, 0xe852cd6ebaa40dL,
|
|
|
+ 0xb669c248d4bf3fL, 0xa8601eb2343991L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x8a0485459502d3L, 0xcab27eee269a7bL, 0x41793074875adaL,
|
|
|
+ 0x179e685e2405f9L, 0x0d7b6987b28963L, 0x80c9db8422a43eL,
|
|
|
+ 0xf5ff318a0f43eeL, 0x7a928054ba7aa7L },
|
|
|
+ { 0xa5c79fe0c0834eL, 0x837ca0d1f849ecL, 0xfe0d7fa628ab7bL,
|
|
|
+ 0x94bcb956edd19aL, 0xa18bc932226fbfL, 0x2795379aad54a3L,
|
|
|
+ 0xceeacf8371129eL, 0x65ca57fa588be5L }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x7a578b52caa330L, 0x7c21944d8ca34aL, 0x6c0fbbb6447282L,
|
|
|
+ 0xa8a9957f90b2e5L, 0xbbe10666586b71L, 0x716a90249138a2L,
|
|
|
+ 0x2fa6034e7ed66dL, 0x56f77ed2b9916aL },
|
|
|
+ { 0x69f1e26bddefb3L, 0xa4978098c08420L, 0xc3377eb09bc184L,
|
|
|
+ 0x796ce0cbe6dadeL, 0x3be0625d103bbbL, 0x01be27c992685cL,
|
|
|
+ 0xc0e25597755f9fL, 0x165c40d1c0dbfaL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xc63a397659c761L, 0x10a0e5b630fbadL, 0xf21e8a6655ac56L,
|
|
|
+ 0xe8580fac1181e2L, 0xbfc2d9c0a84b5cL, 0x2cdbaff7afd5d1L,
|
|
|
+ 0x95f1182f61e85aL, 0x1173e96719eaf4L },
|
|
|
+ { 0xc06d55ec6de8b9L, 0x1b4c8ebafcbcaaL, 0x52af5cbbc2bbcdL,
|
|
|
+ 0x564fab877bcd10L, 0xfd53a18ae85a6eL, 0x225785994c712fL,
|
|
|
+ 0x29b11d71352121L, 0xab1cb76c40491aL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xb4e8ca8ce32eb4L, 0x7e484acb250b49L, 0x062c6f7a3e31a2L,
|
|
|
+ 0x497fd83625d1fcL, 0x98f821c362dda7L, 0xcae1f8f6be3111L,
|
|
|
+ 0x9077e955d4fa42L, 0xa589971a65855aL },
|
|
|
+ { 0xda6321d28832a9L, 0xf9ef5dc3936e9eL, 0xa37f117c9797efL,
|
|
|
+ 0x0eb3c80db581beL, 0x207c5c4baa0002L, 0xc0401b5f38faa0L,
|
|
|
+ 0xceee523d0f1e6eL, 0x8d27a5fd1f0045L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x9411063cf0af29L, 0x304385789a6693L, 0x9a9fb8f640145eL,
|
|
|
+ 0x7d82fe954832ebL, 0xf2789e1898c520L, 0x448b402f948dc0L,
|
|
|
+ 0xeca8fdf68996ddL, 0x22227e9a149b2fL },
|
|
|
+ { 0x63509ff8e62d6aL, 0xe98d81c8c9c57fL, 0xd3874071fe3bedL,
|
|
|
+ 0xf1db013539538fL, 0xb04092e48418ceL, 0xbbf8e76d6d9d4dL,
|
|
|
+ 0x2ea9cda2cec5aeL, 0x8414b3e5078fa9L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x5ad1cdbd68a073L, 0xd4cedafc18b591L, 0x78267078e4c1c9L,
|
|
|
+ 0x9b8d9209ca302aL, 0x3101bd2326115bL, 0x6f154b54c2717aL,
|
|
|
+ 0x618c31b263e84bL, 0x12c4138bbd6942L },
|
|
|
+ { 0xf9ead2580da426L, 0xe748e9947d9680L, 0x9b396a38a4210eL,
|
|
|
+ 0xfaf03ddf4b8f72L, 0xbd94a5266159e7L, 0x5e730491d4c7cbL,
|
|
|
+ 0x31d1f9a7910f38L, 0x4fd10ca08d6dd1L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x4f510ac9f2331eL, 0xee872dc7e3dcc2L, 0x4a11a32a0a0c73L,
|
|
|
+ 0x27e5803aa5a630L, 0xe5ae5037af4a8aL, 0x2dcdeba9fffeb0L,
|
|
|
+ 0x8c27748719d91fL, 0xd3b5b62b9cc61cL },
|
|
|
+ { 0x998ac90cca7939L, 0xc22b59864514e5L, 0x950aaa1b35738aL,
|
|
|
+ 0x4b208bbdab0264L, 0x6677931a557d2eL, 0x2c696d8f7c17d3L,
|
|
|
+ 0x1672d4a3e15c51L, 0x95fab663db0e82L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x3d427346ff205eL, 0x7f187d90ea9fbeL, 0xbd9367f466b2afL,
|
|
|
+ 0x188e53203daf2fL, 0xefe132927b54d8L, 0x14faf85ef70435L,
|
|
|
+ 0xa5061281ec95c4L, 0xad01705c22cba7L },
|
|
|
+ { 0x7d2dfa66197333L, 0xedd7f078b4f6edL, 0xe0cb68575df105L,
|
|
|
+ 0x47c9ddb80f76bcL, 0x49ab5319073c54L, 0x845255ae607f44L,
|
|
|
+ 0x0b4ed9fcc74b7cL, 0xcfb52d50f5c3a6L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x545c7c6c278776L, 0x92a39ae98c30f0L, 0x8aa8c01d2f4680L,
|
|
|
+ 0xa5409ed6b7f840L, 0x0c450acdcb24e7L, 0x5da6fb2c5770d9L,
|
|
|
+ 0x5b8e8be8658333L, 0xb26bf4a67ea4adL },
|
|
|
+ { 0x2e30c81c7d91faL, 0x6e50a490eeb69fL, 0x9458c2bee4bc26L,
|
|
|
+ 0x419acf233be250L, 0x79d6f8187881abL, 0x694565d403b1beL,
|
|
|
+ 0x34b3990234fe1dL, 0x60997d72132b38L }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x00a974126975dcL, 0x42161c46cf94e7L, 0xcc9fe4bc64ed99L,
|
|
|
+ 0x020019a4680570L, 0x885595a698da0dL, 0x008444b77dd962L,
|
|
|
+ 0xbf3c22da4fea0eL, 0xc4630482c81245L },
|
|
|
+ { 0xcb248c5793ab18L, 0x4dc7a20eb4320bL, 0x9a0906f1572b7dL,
|
|
|
+ 0xd5b3019f9ac20fL, 0x79b1bf534520a3L, 0x788dfe869b5322L,
|
|
|
+ 0x9a05298455b7e2L, 0x2f4aecb016bca9L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x414d3798745618L, 0x64ba22eb7c983cL, 0x9a5d19f9f9d532L,
|
|
|
+ 0x81a00d844a80c8L, 0xb9e24f5cae98d6L, 0x6c3769caca965aL,
|
|
|
+ 0x50d6081f6e4e6dL, 0x0d9698054422a6L },
|
|
|
+ { 0xbd7e7925cdd790L, 0xcff65da6a35219L, 0x40dc3638b60ebeL,
|
|
|
+ 0x84bee7492a50dcL, 0x57d4be415ad65eL, 0xc54256b1a6d1d3L,
|
|
|
+ 0x141c64945717ccL, 0x05eb609cd1c736L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xfd52eab1e3c7ecL, 0xa4a5eca9f24895L, 0xaaa2a8d79fdb83L,
|
|
|
+ 0xd105e6072bdfdaL, 0x59e6ae2681d97eL, 0xfedf8e08e8077fL,
|
|
|
+ 0xb06d0ad629e462L, 0x8c7c2d096fa863L },
|
|
|
+ { 0x5eecc4cee8fc91L, 0x5e83ab29e61174L, 0x1fd8925b28c02dL,
|
|
|
+ 0x93be5382072864L, 0xda0c88624c984eL, 0xdcf9f0ca008286L,
|
|
|
+ 0x1ecb5a6a58ba75L, 0x1d9b890c2e3c83L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x19e866eeeee062L, 0x31c1c7f4f7b387L, 0x9be60181c06652L,
|
|
|
+ 0xc00a93a2b68bbbL, 0x54c65d69d52b2bL, 0x4591416e8b744aL,
|
|
|
+ 0x641bcca9a64ab6L, 0xf22bcb1ab08098L },
|
|
|
+ { 0x3c0db8ff1f726cL, 0x4f5739e9d2e6a6L, 0x5cb669b45c9530L,
|
|
|
+ 0x861b04e7b472d0L, 0x3e30515894da77L, 0x3344685c9ac39bL,
|
|
|
+ 0x9e1730573bdd29L, 0x9cac12c808dc85L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xf152b865e27087L, 0x267bd8590a580eL, 0xba79cec8baafc1L,
|
|
|
+ 0x6140ab19442686L, 0xa67090c5b31693L, 0x50a103a28b4117L,
|
|
|
+ 0x7722e610ddc08fL, 0x5d19d43e6569b2L },
|
|
|
+ { 0x70e0c525962bf6L, 0x808e316fb5fb02L, 0x3fb80da5b667beL,
|
|
|
+ 0x8aa366efcfacecL, 0xcb0b3e7134280eL, 0x0bf1de4cd7d944L,
|
|
|
+ 0x0cd23bed092df5L, 0xc9a6a79a153a0cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x1c69ad02d5a4b7L, 0x4bb28d0d9e6f4aL, 0x815308ca984fc6L,
|
|
|
+ 0x40929c79037ca5L, 0x0ea2b491bd0357L, 0xec17e5b42aad4eL,
|
|
|
+ 0x1f32ade18e7235L, 0xbc60b05a96a9d3L },
|
|
|
+ { 0x3b0229ae20f707L, 0xd63505056bdfadL, 0xac2d922d8b2e1eL,
|
|
|
+ 0x92b2998235c748L, 0x6002c3ad766f97L, 0x99198001a2a862L,
|
|
|
+ 0x2af7567b58b684L, 0xd8fe707aaafce5L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x54487ab5df7a4bL, 0x51cccdec57ccc2L, 0x23943277510b53L,
|
|
|
+ 0x3a09f02f555de3L, 0xa696aec1be484dL, 0x56f459f37817a2L,
|
|
|
+ 0x8d8f61c623dcb4L, 0xc52223c5335656L },
|
|
|
+ { 0xf634111b49914aL, 0xbf8e1ab8e4f9bbL, 0x2f59578f4dba02L,
|
|
|
+ 0x2a94199e004319L, 0x87931f0654d005L, 0x7df57d96fa0814L,
|
|
|
+ 0xc8da316a154031L, 0x2a44ac041f658bL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xfb5f4f89e34ac6L, 0x0a1b10b97790f2L, 0x58fe4e74b8a06cL,
|
|
|
+ 0x10c1710955f27cL, 0x77b798ad5ebe19L, 0xaf1c35b1f1c2dcL,
|
|
|
+ 0xc25b8e6a1f8d69L, 0x49cf751f76bf23L },
|
|
|
+ { 0x15cb2db436f7b7L, 0x186d7c27e74d1aL, 0x60731dec00a415L,
|
|
|
+ 0xea1e15615f0772L, 0xf02d591714463fL, 0x26a0c6451adeb1L,
|
|
|
+ 0x20174cdcc5229eL, 0xb817e50efd512aL }
|
|
|
+ },
|
|
|
+},
|
|
|
+};
|
|
|
+
|
|
|
+static const ge448_precomp base_i[16] = {
|
|
|
+ {
|
|
|
+ { 0x26a82bc70cc05eL, 0x80e18b00938e26L, 0xf72ab66511433bL,
|
|
|
+ 0xa3d3a46412ae1aL, 0x0f1767ea6de324L, 0x36da9e14657047L,
|
|
|
+ 0xed221d15a622bfL, 0x4f1970c66bed0dL },
|
|
|
+ { 0x08795bf230fa14L, 0x132c4ed7c8ad98L, 0x1ce67c39c4fdbdL,
|
|
|
+ 0x05a0c2d73ad3ffL, 0xa3984087789c1eL, 0xc7624bea73736cL,
|
|
|
+ 0x248876203756c9L, 0x693f46716eb6bcL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x28173286ff2f8fL, 0xb769465da85757L, 0xf7f6271fd6e862L,
|
|
|
+ 0x4a3fcfe8daa9cbL, 0xda82c7e2ba077aL, 0x943332241b8b8cL,
|
|
|
+ 0x6455bd64316cb6L, 0x0865886b9108afL },
|
|
|
+ { 0x22ac13588ed6fcL, 0x9a68fed02dafb8L, 0x1bdb6767f0bffaL,
|
|
|
+ 0xec4e1d58bb3a33L, 0x56c3b9fce43c82L, 0xa6449a4a8d9523L,
|
|
|
+ 0xf706cbda7ad43aL, 0xe005a8dbd5125cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xa99d1092030034L, 0x2d8cefc6f950d0L, 0x7a920c3c96f07bL,
|
|
|
+ 0x958812808bc0d5L, 0x62ada756d761e8L, 0x0def80cbcf7285L,
|
|
|
+ 0x0e2ba7601eedb5L, 0x7a9f9335a48dcbL },
|
|
|
+ { 0xb4731472f435ebL, 0x5512881f225443L, 0xee59d2b33c5840L,
|
|
|
+ 0xb698017127d7a4L, 0xb18fced86551f7L, 0x0ade260ca1823aL,
|
|
|
+ 0xd3b9109ce4fd58L, 0xadfd751a2517edL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xdf9567ceb5eaf7L, 0x110a6b478ac7d7L, 0x2d335014706e0bL,
|
|
|
+ 0x0df9c7b0b5a209L, 0xba4223d568e684L, 0xd78af2d8c3719bL,
|
|
|
+ 0x77467b9a5291b6L, 0x079748e5c89befL },
|
|
|
+ { 0xe20d3fadac377fL, 0x34e866972b5c09L, 0xd8687a3c40bbb7L,
|
|
|
+ 0x7b3946fd2f84c9L, 0xd00e40ca78f50eL, 0xb87594417e7179L,
|
|
|
+ 0x9c7373bcb23583L, 0x7ddeda3c90fd69L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x3d0def76ab686bL, 0x1a467ec49f7c79L, 0x3e53f4fc8989edL,
|
|
|
+ 0x101e344430a0d9L, 0xa3ae7318ad44eeL, 0xaefa6cdae1d134L,
|
|
|
+ 0xaa8cd7d824ad4dL, 0xef1650ced584fcL },
|
|
|
+ { 0xa74df674f4754fL, 0xf52cea8ef3fb8bL, 0x47c32d42971140L,
|
|
|
+ 0x391c15da256fbbL, 0xc165faba605671L, 0xf2518c687993b9L,
|
|
|
+ 0x2daf7acbd5a84dL, 0x1560b6298f12aeL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xef4da0254dc10aL, 0x63118655940db8L, 0xe20b14982f2948L,
|
|
|
+ 0x67b93775581dbaL, 0x422ee7104f5029L, 0x5d440db5122d34L,
|
|
|
+ 0xb1e56d71a4c640L, 0xbf12abbc2408eeL },
|
|
|
+ { 0x0cc9f86016af01L, 0x88366abf3d8cabL, 0x85dda13a2efe12L,
|
|
|
+ 0x390df605d00674L, 0xf18f5806d187f7L, 0x28c900ff0c5d20L,
|
|
|
+ 0xad308123e01733L, 0x42d35b554bf2fdL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x009135f2ffb1f1L, 0x099fc7e8f9c605L, 0xcc67da626bfa5aL,
|
|
|
+ 0xc186d12344552bL, 0xb5232501b339e1L, 0x70a544fc9708c5L,
|
|
|
+ 0x06baaec1e928e7L, 0x0baedd2ef0f50fL },
|
|
|
+ { 0x535d6d8bf479e5L, 0x156e536e4ec3e9L, 0x3165741ddb9be2L,
|
|
|
+ 0x988af7159fd736L, 0x13d8a782e33dddL, 0x54604214e69002L,
|
|
|
+ 0x34d56e0804a268L, 0xc59b84f0e52a4cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x525d45f24729d9L, 0x5768aba8712327L, 0xa25e43b43035dbL,
|
|
|
+ 0x15a1ee8927ef21L, 0xa785d216056112L, 0x45e2fbfd508af9L,
|
|
|
+ 0xb6f721a37ba969L, 0x30d6d8c216d8d3L },
|
|
|
+ { 0x3065e0852074c3L, 0xfa40b4a2a0684eL, 0x851325a763f955L,
|
|
|
+ 0xd4ef19c9f25900L, 0x799c869f665756L, 0x7b052223312990L,
|
|
|
+ 0xc986c2b28db802L, 0xf48fb8f28ade0aL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x1e461731649b68L, 0xa96e5d65beb9dcL, 0x765ddff481935dL,
|
|
|
+ 0x6cf132c9f3bf2aL, 0x9f6c5c97c35658L, 0x99cd1394696e60L,
|
|
|
+ 0x99fa9249c0d5e4L, 0x1acd0638845a95L },
|
|
|
+ { 0x0b065413636087L, 0xea20e78ea17b7fL, 0x20afc5f6161967L,
|
|
|
+ 0xfd6c8a2dc81028L, 0x4ef1357e32c8fdL, 0x8aa400400e4a88L,
|
|
|
+ 0xd6fcaef48cb82fL, 0x7ba7c6db3cd4faL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xf843473d19c7abL, 0x968e76dc655c4dL, 0x52c87d9c4b9c2fL,
|
|
|
+ 0x65f641ae4aa082L, 0x491a39733c3603L, 0xa606ffe5810098L,
|
|
|
+ 0x09920e68bf8ad4L, 0x691a0c86db7882L },
|
|
|
+ { 0x5205883a4d3ef5L, 0xee839b7acf2efeL, 0x4b78e2ac00ca66L,
|
|
|
+ 0xbe3f071f9fcb91L, 0x61e66c9bf6943aL, 0xe9b4e57061b79dL,
|
|
|
+ 0x8d1b01b56c06bdL, 0x0dfa315df76ae5L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x803df65f1fd093L, 0x1cd6523489b77eL, 0x2cd2e15c20e295L,
|
|
|
+ 0xcd490be9b912d1L, 0xdd9a2ff2e886d2L, 0xa3c836dfe9d72aL,
|
|
|
+ 0xfcad5f2298e0c1L, 0xed126e24bcf067L },
|
|
|
+ { 0x1e339533dc81bcL, 0xbea4d76ece6a08L, 0x1d15de3991b252L,
|
|
|
+ 0x74cc5cfe6daf97L, 0x5ad343f0826493L, 0x2d38a471064049L,
|
|
|
+ 0xf7f47b9ffcfa4dL, 0xef14490418066cL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x4e7f86b9bb55abL, 0x310d7853f496a3L, 0xbd682fc0dec42cL,
|
|
|
+ 0xbde047a411d32aL, 0xea639b4c5a5ea2L, 0x5052078ba08fa1L,
|
|
|
+ 0xc968b2307729f2L, 0x567b5a623d3e28L },
|
|
|
+ { 0x171e825977fbf7L, 0x0319c70be990aaL, 0x8f65023e12cd69L,
|
|
|
+ 0x1fb9b19f5015e6L, 0x0083f603568a7cL, 0xba3d30b1f3c5acL,
|
|
|
+ 0xe7b509d3d7a988L, 0x2318b99cd0f6b6L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x54d3b8793ab2cfL, 0x366abead2d8306L, 0x66e8eb6d7a4977L,
|
|
|
+ 0xa61888cae0072eL, 0x9eeeef5dbc3315L, 0x93f09db163e7f5L,
|
|
|
+ 0xee9095959ade9aL, 0xaf7f578ce59be0L },
|
|
|
+ { 0x24bfd8d5ece59eL, 0x8aa698b3689523L, 0xa9a65de2de92cfL,
|
|
|
+ 0xec11dbca6ad300L, 0x217f3fa09f88caL, 0xf6c33e3b4d6af7L,
|
|
|
+ 0xcd3bfa21d86d2dL, 0x1497f835f13f25L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xa579568cd03d1dL, 0xd717cdae158af6L, 0x59eda97389a19fL,
|
|
|
+ 0xb32c370099e99cL, 0xa2dba91dabb591L, 0x6d697d577c2c97L,
|
|
|
+ 0x5423fc2d43fa6dL, 0x56ea8a50b382bfL },
|
|
|
+ { 0x4a987bad80c11aL, 0xe4cde217d590a5L, 0x3dd8860f97e559L,
|
|
|
+ 0xff45e2543b593cL, 0x00eb4535343cb5L, 0x06b9b997bbfbddL,
|
|
|
+ 0x4da36b716aea24L, 0x247651757a624eL }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x32207d03474e0dL, 0x3ffbf04b41cc73L, 0x5c4dc45319eb39L,
|
|
|
+ 0xfee29be758b463L, 0xcc8a381c30c7a7L, 0x147f4e49fe0e53L,
|
|
|
+ 0x05b2e26e35a2deL, 0x4362f0292f3666L },
|
|
|
+ { 0x0476d0c8474b85L, 0x9d8c65fccaf108L, 0xf58d4041d54b6aL,
|
|
|
+ 0x3ee6862f38e4b0L, 0x7c7c9d53b44f54L, 0x36a3fd80fb0db5L,
|
|
|
+ 0xfcd94ba18a8ac8L, 0xc1b1d568f35c05L }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x16539fc1bdd30dL, 0x1356e538df4afbL, 0xc0545d85a1aedbL,
|
|
|
+ 0xeb2037a489396bL, 0x897fcbd5660894L, 0x02a58a9b7d104aL,
|
|
|
+ 0x57fa24cc96b980L, 0xf6448e35bd8946L },
|
|
|
+ { 0xee727418805c83L, 0x10fa274992cfc6L, 0x95141939e66b21L,
|
|
|
+ 0xe0ffa44bd08009L, 0x174332220da22bL, 0x4891ff359e6831L,
|
|
|
+ 0x407ed73a7d687bL, 0x2fb4e0751d99cfL }
|
|
|
+ },
|
|
|
+};
|
|
|
+#else
|
|
|
+
|
|
|
+/* Reduce scalar mod the order of the curve.
|
|
|
+ * Scalar Will be 114 bytes.
|
|
|
+ *
|
|
|
+ * b [in] Scalar to reduce.
|
|
|
+ */
|
|
|
+void sc448_reduce(uint8_t* b)
|
|
|
+{
|
|
|
+ uint32_t d[16];
|
|
|
+ uint64_t t[33];
|
|
|
+ uint64_t c;
|
|
|
+ uint32_t o;
|
|
|
+
|
|
|
+ /* Load from bytes */
|
|
|
+ t[ 0] = (((int32_t)((b[ 0] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[ 1] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[ 2] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[ 3] & 0xf )) >> 0)) << 24);
|
|
|
+ t[ 1] = (((int32_t)((b[ 3] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[ 4] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[ 5] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[ 6] ) >> 0)) << 20);
|
|
|
+ t[ 2] = (((int32_t)((b[ 7] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[ 8] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[ 9] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[10] & 0xf )) >> 0)) << 24);
|
|
|
+ t[ 3] = (((int32_t)((b[10] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[11] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[12] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[13] ) >> 0)) << 20);
|
|
|
+ t[ 4] = (((int32_t)((b[14] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[15] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[16] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[17] & 0xf )) >> 0)) << 24);
|
|
|
+ t[ 5] = (((int32_t)((b[17] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[18] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[19] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[20] ) >> 0)) << 20);
|
|
|
+ t[ 6] = (((int32_t)((b[21] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[22] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[23] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[24] & 0xf )) >> 0)) << 24);
|
|
|
+ t[ 7] = (((int32_t)((b[24] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[25] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[26] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[27] ) >> 0)) << 20);
|
|
|
+ t[ 8] = (((int32_t)((b[28] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[29] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[30] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[31] & 0xf )) >> 0)) << 24);
|
|
|
+ t[ 9] = (((int32_t)((b[31] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[32] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[33] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[34] ) >> 0)) << 20);
|
|
|
+ t[10] = (((int32_t)((b[35] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[36] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[37] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[38] & 0xf )) >> 0)) << 24);
|
|
|
+ t[11] = (((int32_t)((b[38] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[39] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[40] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[41] ) >> 0)) << 20);
|
|
|
+ t[12] = (((int32_t)((b[42] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[43] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[44] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[45] & 0xf )) >> 0)) << 24);
|
|
|
+ t[13] = (((int32_t)((b[45] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[46] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[47] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[48] ) >> 0)) << 20);
|
|
|
+ t[14] = (((int32_t)((b[49] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[50] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[51] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[52] & 0xf )) >> 0)) << 24);
|
|
|
+ t[15] = (((int32_t)((b[52] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[53] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[54] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[55] ) >> 0)) << 20);
|
|
|
+ t[16] = (((int32_t)((b[56] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[57] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[58] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[59] & 0xf )) >> 0)) << 24);
|
|
|
+ t[17] = (((int32_t)((b[59] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[60] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[61] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[62] ) >> 0)) << 20);
|
|
|
+ t[18] = (((int32_t)((b[63] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[64] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[65] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[66] & 0xf )) >> 0)) << 24);
|
|
|
+ t[19] = (((int32_t)((b[66] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[67] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[68] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[69] ) >> 0)) << 20);
|
|
|
+ t[20] = (((int32_t)((b[70] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[71] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[72] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[73] & 0xf )) >> 0)) << 24);
|
|
|
+ t[21] = (((int32_t)((b[73] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[74] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[75] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[76] ) >> 0)) << 20);
|
|
|
+ t[22] = (((int32_t)((b[77] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[78] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[79] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[80] & 0xf )) >> 0)) << 24);
|
|
|
+ t[23] = (((int32_t)((b[80] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[81] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[82] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[83] ) >> 0)) << 20);
|
|
|
+ t[24] = (((int32_t)((b[84] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[85] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[86] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[87] & 0xf )) >> 0)) << 24);
|
|
|
+ t[25] = (((int32_t)((b[87] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[88] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[89] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[90] ) >> 0)) << 20);
|
|
|
+ t[26] = (((int32_t)((b[91] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[92] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[93] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[94] & 0xf )) >> 0)) << 24);
|
|
|
+ t[27] = (((int32_t)((b[94] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[95] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[96] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[97] ) >> 0)) << 20);
|
|
|
+ t[28] = (((int32_t)((b[98] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[99] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[100] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[101] & 0xf )) >> 0)) << 24);
|
|
|
+ t[29] = (((int32_t)((b[101] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[102] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[103] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[104] ) >> 0)) << 20);
|
|
|
+ t[30] = (((int32_t)((b[105] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[106] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[107] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[108] & 0xf )) >> 0)) << 24);
|
|
|
+ t[31] = (((int32_t)((b[108] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[109] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[110] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[111] ) >> 0)) << 20);
|
|
|
+ t[32] = (((int32_t)((b[112] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[113] ) >> 0)) << 8);
|
|
|
+
|
|
|
+ /* Mod curve order */
|
|
|
+ /* 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d */
|
|
|
+ /* Mod top half of extra words */
|
|
|
+ t[ 8] += (int64_t)0x129eec34 * t[24];
|
|
|
+ t[ 9] += (int64_t)0x21cf5b54 * t[24];
|
|
|
+ t[10] += (int64_t)0x29c2ab70 * t[24];
|
|
|
+ t[11] += (int64_t)0x0f635c8c * t[24];
|
|
|
+ t[12] += (int64_t)0x25bf7a4c * t[24];
|
|
|
+ t[13] += (int64_t)0x2d944a70 * t[24];
|
|
|
+ t[14] += (int64_t)0x18eec490 * t[24];
|
|
|
+ t[15] += (int64_t)0x20cd7704 * t[24];
|
|
|
+ t[ 9] += (int64_t)0x129eec34 * t[25];
|
|
|
+ t[10] += (int64_t)0x21cf5b54 * t[25];
|
|
|
+ t[11] += (int64_t)0x29c2ab70 * t[25];
|
|
|
+ t[12] += (int64_t)0x0f635c8c * t[25];
|
|
|
+ t[13] += (int64_t)0x25bf7a4c * t[25];
|
|
|
+ t[14] += (int64_t)0x2d944a70 * t[25];
|
|
|
+ t[15] += (int64_t)0x18eec490 * t[25];
|
|
|
+ t[16] += (int64_t)0x20cd7704 * t[25];
|
|
|
+ t[10] += (int64_t)0x129eec34 * t[26];
|
|
|
+ t[11] += (int64_t)0x21cf5b54 * t[26];
|
|
|
+ t[12] += (int64_t)0x29c2ab70 * t[26];
|
|
|
+ t[13] += (int64_t)0x0f635c8c * t[26];
|
|
|
+ t[14] += (int64_t)0x25bf7a4c * t[26];
|
|
|
+ t[15] += (int64_t)0x2d944a70 * t[26];
|
|
|
+ t[16] += (int64_t)0x18eec490 * t[26];
|
|
|
+ t[17] += (int64_t)0x20cd7704 * t[26];
|
|
|
+ t[11] += (int64_t)0x129eec34 * t[27];
|
|
|
+ t[12] += (int64_t)0x21cf5b54 * t[27];
|
|
|
+ t[13] += (int64_t)0x29c2ab70 * t[27];
|
|
|
+ t[14] += (int64_t)0x0f635c8c * t[27];
|
|
|
+ t[15] += (int64_t)0x25bf7a4c * t[27];
|
|
|
+ t[16] += (int64_t)0x2d944a70 * t[27];
|
|
|
+ t[17] += (int64_t)0x18eec490 * t[27];
|
|
|
+ t[18] += (int64_t)0x20cd7704 * t[27];
|
|
|
+ t[12] += (int64_t)0x129eec34 * t[28];
|
|
|
+ t[13] += (int64_t)0x21cf5b54 * t[28];
|
|
|
+ t[14] += (int64_t)0x29c2ab70 * t[28];
|
|
|
+ t[15] += (int64_t)0x0f635c8c * t[28];
|
|
|
+ t[16] += (int64_t)0x25bf7a4c * t[28];
|
|
|
+ t[17] += (int64_t)0x2d944a70 * t[28];
|
|
|
+ t[18] += (int64_t)0x18eec490 * t[28];
|
|
|
+ t[19] += (int64_t)0x20cd7704 * t[28];
|
|
|
+ t[13] += (int64_t)0x129eec34 * t[29];
|
|
|
+ t[14] += (int64_t)0x21cf5b54 * t[29];
|
|
|
+ t[15] += (int64_t)0x29c2ab70 * t[29];
|
|
|
+ t[16] += (int64_t)0x0f635c8c * t[29];
|
|
|
+ t[17] += (int64_t)0x25bf7a4c * t[29];
|
|
|
+ t[18] += (int64_t)0x2d944a70 * t[29];
|
|
|
+ t[19] += (int64_t)0x18eec490 * t[29];
|
|
|
+ t[20] += (int64_t)0x20cd7704 * t[29];
|
|
|
+ t[14] += (int64_t)0x129eec34 * t[30];
|
|
|
+ t[15] += (int64_t)0x21cf5b54 * t[30];
|
|
|
+ t[16] += (int64_t)0x29c2ab70 * t[30];
|
|
|
+ t[17] += (int64_t)0x0f635c8c * t[30];
|
|
|
+ t[18] += (int64_t)0x25bf7a4c * t[30];
|
|
|
+ t[19] += (int64_t)0x2d944a70 * t[30];
|
|
|
+ t[20] += (int64_t)0x18eec490 * t[30];
|
|
|
+ t[21] += (int64_t)0x20cd7704 * t[30];
|
|
|
+ t[15] += (int64_t)0x129eec34 * t[31];
|
|
|
+ t[16] += (int64_t)0x21cf5b54 * t[31];
|
|
|
+ t[17] += (int64_t)0x29c2ab70 * t[31];
|
|
|
+ t[18] += (int64_t)0x0f635c8c * t[31];
|
|
|
+ t[19] += (int64_t)0x25bf7a4c * t[31];
|
|
|
+ t[20] += (int64_t)0x2d944a70 * t[31];
|
|
|
+ t[21] += (int64_t)0x18eec490 * t[31];
|
|
|
+ t[22] += (int64_t)0x20cd7704 * t[31];
|
|
|
+ t[16] += (int64_t)0x129eec34 * t[32];
|
|
|
+ t[17] += (int64_t)0x21cf5b54 * t[32];
|
|
|
+ t[18] += (int64_t)0x29c2ab70 * t[32];
|
|
|
+ t[19] += (int64_t)0x0f635c8c * t[32];
|
|
|
+ t[20] += (int64_t)0x25bf7a4c * t[32];
|
|
|
+ t[21] += (int64_t)0x2d944a70 * t[32];
|
|
|
+ t[22] += (int64_t)0x18eec490 * t[32];
|
|
|
+ t[23] += (int64_t)0x20cd7704 * t[32];
|
|
|
+ t[24] = 0;
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; t[ 8] = t[ 8] & 0xfffffff;
|
|
|
+ c = t[ 9] >> 28; t[10] += c; t[ 9] = t[ 9] & 0xfffffff;
|
|
|
+ c = t[10] >> 28; t[11] += c; t[10] = t[10] & 0xfffffff;
|
|
|
+ c = t[11] >> 28; t[12] += c; t[11] = t[11] & 0xfffffff;
|
|
|
+ c = t[12] >> 28; t[13] += c; t[12] = t[12] & 0xfffffff;
|
|
|
+ c = t[13] >> 28; t[14] += c; t[13] = t[13] & 0xfffffff;
|
|
|
+ c = t[14] >> 28; t[15] += c; t[14] = t[14] & 0xfffffff;
|
|
|
+ c = t[15] >> 28; t[16] += c; t[15] = t[15] & 0xfffffff;
|
|
|
+ c = t[16] >> 28; t[17] += c; t[16] = t[16] & 0xfffffff;
|
|
|
+ c = t[17] >> 28; t[18] += c; t[17] = t[17] & 0xfffffff;
|
|
|
+ c = t[18] >> 28; t[19] += c; t[18] = t[18] & 0xfffffff;
|
|
|
+ c = t[19] >> 28; t[20] += c; t[19] = t[19] & 0xfffffff;
|
|
|
+ c = t[20] >> 28; t[21] += c; t[20] = t[20] & 0xfffffff;
|
|
|
+ c = t[21] >> 28; t[22] += c; t[21] = t[21] & 0xfffffff;
|
|
|
+ c = t[22] >> 28; t[23] += c; t[22] = t[22] & 0xfffffff;
|
|
|
+ c = t[23] >> 28; t[24] += c; t[23] = t[23] & 0xfffffff;
|
|
|
+ /* Mod bottom half of extra words */
|
|
|
+ t[ 0] += (int64_t)0x129eec34 * t[16];
|
|
|
+ t[ 1] += (int64_t)0x21cf5b54 * t[16];
|
|
|
+ t[ 2] += (int64_t)0x29c2ab70 * t[16];
|
|
|
+ t[ 3] += (int64_t)0x0f635c8c * t[16];
|
|
|
+ t[ 4] += (int64_t)0x25bf7a4c * t[16];
|
|
|
+ t[ 5] += (int64_t)0x2d944a70 * t[16];
|
|
|
+ t[ 6] += (int64_t)0x18eec490 * t[16];
|
|
|
+ t[ 7] += (int64_t)0x20cd7704 * t[16];
|
|
|
+ t[ 1] += (int64_t)0x129eec34 * t[17];
|
|
|
+ t[ 2] += (int64_t)0x21cf5b54 * t[17];
|
|
|
+ t[ 3] += (int64_t)0x29c2ab70 * t[17];
|
|
|
+ t[ 4] += (int64_t)0x0f635c8c * t[17];
|
|
|
+ t[ 5] += (int64_t)0x25bf7a4c * t[17];
|
|
|
+ t[ 6] += (int64_t)0x2d944a70 * t[17];
|
|
|
+ t[ 7] += (int64_t)0x18eec490 * t[17];
|
|
|
+ t[ 8] += (int64_t)0x20cd7704 * t[17];
|
|
|
+ t[ 2] += (int64_t)0x129eec34 * t[18];
|
|
|
+ t[ 3] += (int64_t)0x21cf5b54 * t[18];
|
|
|
+ t[ 4] += (int64_t)0x29c2ab70 * t[18];
|
|
|
+ t[ 5] += (int64_t)0x0f635c8c * t[18];
|
|
|
+ t[ 6] += (int64_t)0x25bf7a4c * t[18];
|
|
|
+ t[ 7] += (int64_t)0x2d944a70 * t[18];
|
|
|
+ t[ 8] += (int64_t)0x18eec490 * t[18];
|
|
|
+ t[ 9] += (int64_t)0x20cd7704 * t[18];
|
|
|
+ t[ 3] += (int64_t)0x129eec34 * t[19];
|
|
|
+ t[ 4] += (int64_t)0x21cf5b54 * t[19];
|
|
|
+ t[ 5] += (int64_t)0x29c2ab70 * t[19];
|
|
|
+ t[ 6] += (int64_t)0x0f635c8c * t[19];
|
|
|
+ t[ 7] += (int64_t)0x25bf7a4c * t[19];
|
|
|
+ t[ 8] += (int64_t)0x2d944a70 * t[19];
|
|
|
+ t[ 9] += (int64_t)0x18eec490 * t[19];
|
|
|
+ t[10] += (int64_t)0x20cd7704 * t[19];
|
|
|
+ t[ 4] += (int64_t)0x129eec34 * t[20];
|
|
|
+ t[ 5] += (int64_t)0x21cf5b54 * t[20];
|
|
|
+ t[ 6] += (int64_t)0x29c2ab70 * t[20];
|
|
|
+ t[ 7] += (int64_t)0x0f635c8c * t[20];
|
|
|
+ t[ 8] += (int64_t)0x25bf7a4c * t[20];
|
|
|
+ t[ 9] += (int64_t)0x2d944a70 * t[20];
|
|
|
+ t[10] += (int64_t)0x18eec490 * t[20];
|
|
|
+ t[11] += (int64_t)0x20cd7704 * t[20];
|
|
|
+ t[ 5] += (int64_t)0x129eec34 * t[21];
|
|
|
+ t[ 6] += (int64_t)0x21cf5b54 * t[21];
|
|
|
+ t[ 7] += (int64_t)0x29c2ab70 * t[21];
|
|
|
+ t[ 8] += (int64_t)0x0f635c8c * t[21];
|
|
|
+ t[ 9] += (int64_t)0x25bf7a4c * t[21];
|
|
|
+ t[10] += (int64_t)0x2d944a70 * t[21];
|
|
|
+ t[11] += (int64_t)0x18eec490 * t[21];
|
|
|
+ t[12] += (int64_t)0x20cd7704 * t[21];
|
|
|
+ t[ 6] += (int64_t)0x129eec34 * t[22];
|
|
|
+ t[ 7] += (int64_t)0x21cf5b54 * t[22];
|
|
|
+ t[ 8] += (int64_t)0x29c2ab70 * t[22];
|
|
|
+ t[ 9] += (int64_t)0x0f635c8c * t[22];
|
|
|
+ t[10] += (int64_t)0x25bf7a4c * t[22];
|
|
|
+ t[11] += (int64_t)0x2d944a70 * t[22];
|
|
|
+ t[12] += (int64_t)0x18eec490 * t[22];
|
|
|
+ t[13] += (int64_t)0x20cd7704 * t[22];
|
|
|
+ t[ 7] += (int64_t)0x129eec34 * t[23];
|
|
|
+ t[ 8] += (int64_t)0x21cf5b54 * t[23];
|
|
|
+ t[ 9] += (int64_t)0x29c2ab70 * t[23];
|
|
|
+ t[10] += (int64_t)0x0f635c8c * t[23];
|
|
|
+ t[11] += (int64_t)0x25bf7a4c * t[23];
|
|
|
+ t[12] += (int64_t)0x2d944a70 * t[23];
|
|
|
+ t[13] += (int64_t)0x18eec490 * t[23];
|
|
|
+ t[14] += (int64_t)0x20cd7704 * t[23];
|
|
|
+ t[ 8] += (int64_t)0x129eec34 * t[24];
|
|
|
+ t[ 9] += (int64_t)0x21cf5b54 * t[24];
|
|
|
+ t[10] += (int64_t)0x29c2ab70 * t[24];
|
|
|
+ t[11] += (int64_t)0x0f635c8c * t[24];
|
|
|
+ t[12] += (int64_t)0x25bf7a4c * t[24];
|
|
|
+ t[13] += (int64_t)0x2d944a70 * t[24];
|
|
|
+ t[14] += (int64_t)0x18eec490 * t[24];
|
|
|
+ t[15] += (int64_t)0x20cd7704 * t[24];
|
|
|
+ t[16] = 0;
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 28; t[ 1] += c; t[ 0] = t[ 0] & 0xfffffff;
|
|
|
+ c = t[ 1] >> 28; t[ 2] += c; t[ 1] = t[ 1] & 0xfffffff;
|
|
|
+ c = t[ 2] >> 28; t[ 3] += c; t[ 2] = t[ 2] & 0xfffffff;
|
|
|
+ c = t[ 3] >> 28; t[ 4] += c; t[ 3] = t[ 3] & 0xfffffff;
|
|
|
+ c = t[ 4] >> 28; t[ 5] += c; t[ 4] = t[ 4] & 0xfffffff;
|
|
|
+ c = t[ 5] >> 28; t[ 6] += c; t[ 5] = t[ 5] & 0xfffffff;
|
|
|
+ c = t[ 6] >> 28; t[ 7] += c; t[ 6] = t[ 6] & 0xfffffff;
|
|
|
+ c = t[ 7] >> 28; t[ 8] += c; t[ 7] = t[ 7] & 0xfffffff;
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; t[ 8] = t[ 8] & 0xfffffff;
|
|
|
+ c = t[ 9] >> 28; t[10] += c; t[ 9] = t[ 9] & 0xfffffff;
|
|
|
+ c = t[10] >> 28; t[11] += c; t[10] = t[10] & 0xfffffff;
|
|
|
+ c = t[11] >> 28; t[12] += c; t[11] = t[11] & 0xfffffff;
|
|
|
+ c = t[12] >> 28; t[13] += c; t[12] = t[12] & 0xfffffff;
|
|
|
+ c = t[13] >> 28; t[14] += c; t[13] = t[13] & 0xfffffff;
|
|
|
+ c = t[14] >> 28; t[15] += c; t[14] = t[14] & 0xfffffff;
|
|
|
+ c = t[15] >> 28; t[16] += c; t[15] = t[15] & 0xfffffff;
|
|
|
+ t[ 0] += (int64_t)0x129eec34 * t[16];
|
|
|
+ t[ 1] += (int64_t)0x21cf5b54 * t[16];
|
|
|
+ t[ 2] += (int64_t)0x29c2ab70 * t[16];
|
|
|
+ t[ 3] += (int64_t)0x0f635c8c * t[16];
|
|
|
+ t[ 4] += (int64_t)0x25bf7a4c * t[16];
|
|
|
+ t[ 5] += (int64_t)0x2d944a70 * t[16];
|
|
|
+ t[ 6] += (int64_t)0x18eec490 * t[16];
|
|
|
+ t[ 7] += (int64_t)0x20cd7704 * t[16];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 28; t[ 1] += c; d[ 0] = (int32_t)(t[ 0] & 0xfffffff);
|
|
|
+ c = t[ 1] >> 28; t[ 2] += c; d[ 1] = (int32_t)(t[ 1] & 0xfffffff);
|
|
|
+ c = t[ 2] >> 28; t[ 3] += c; d[ 2] = (int32_t)(t[ 2] & 0xfffffff);
|
|
|
+ c = t[ 3] >> 28; t[ 4] += c; d[ 3] = (int32_t)(t[ 3] & 0xfffffff);
|
|
|
+ c = t[ 4] >> 28; t[ 5] += c; d[ 4] = (int32_t)(t[ 4] & 0xfffffff);
|
|
|
+ c = t[ 5] >> 28; t[ 6] += c; d[ 5] = (int32_t)(t[ 5] & 0xfffffff);
|
|
|
+ c = t[ 6] >> 28; t[ 7] += c; d[ 6] = (int32_t)(t[ 6] & 0xfffffff);
|
|
|
+ c = t[ 7] >> 28; t[ 8] += c; d[ 7] = (int32_t)(t[ 7] & 0xfffffff);
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; d[ 8] = (int32_t)(t[ 8] & 0xfffffff);
|
|
|
+ c = t[ 9] >> 28; t[10] += c; d[ 9] = (int32_t)(t[ 9] & 0xfffffff);
|
|
|
+ c = t[10] >> 28; t[11] += c; d[10] = (int32_t)(t[10] & 0xfffffff);
|
|
|
+ c = t[11] >> 28; t[12] += c; d[11] = (int32_t)(t[11] & 0xfffffff);
|
|
|
+ c = t[12] >> 28; t[13] += c; d[12] = (int32_t)(t[12] & 0xfffffff);
|
|
|
+ c = t[13] >> 28; t[14] += c; d[13] = (int32_t)(t[13] & 0xfffffff);
|
|
|
+ c = t[14] >> 28; t[15] += c; d[14] = (int32_t)(t[14] & 0xfffffff);
|
|
|
+ d[15] = t[15];
|
|
|
+ /* Mod bits over 28 in last word */
|
|
|
+ o = d[15] >> 26; d[15] &= 0x3ffffff;
|
|
|
+ d[ 0] += 0x4a7bb0d * o;
|
|
|
+ d[ 1] += 0x873d6d5 * o;
|
|
|
+ d[ 2] += 0xa70aadc * o;
|
|
|
+ d[ 3] += 0x3d8d723 * o;
|
|
|
+ d[ 4] += 0x96fde93 * o;
|
|
|
+ d[ 5] += 0xb65129c * o;
|
|
|
+ d[ 6] += 0x63bb124 * o;
|
|
|
+ d[ 7] += 0x8335dc1 * o;
|
|
|
+ /* Propagate carries */
|
|
|
+ o = d[ 0] >> 28; d[ 1] += o; d[ 0] = d[ 0] & 0xfffffff;
|
|
|
+ o = d[ 1] >> 28; d[ 2] += o; d[ 1] = d[ 1] & 0xfffffff;
|
|
|
+ o = d[ 2] >> 28; d[ 3] += o; d[ 2] = d[ 2] & 0xfffffff;
|
|
|
+ o = d[ 3] >> 28; d[ 4] += o; d[ 3] = d[ 3] & 0xfffffff;
|
|
|
+ o = d[ 4] >> 28; d[ 5] += o; d[ 4] = d[ 4] & 0xfffffff;
|
|
|
+ o = d[ 5] >> 28; d[ 6] += o; d[ 5] = d[ 5] & 0xfffffff;
|
|
|
+ o = d[ 6] >> 28; d[ 7] += o; d[ 6] = d[ 6] & 0xfffffff;
|
|
|
+ o = d[ 7] >> 28; d[ 8] += o; d[ 7] = d[ 7] & 0xfffffff;
|
|
|
+ o = d[ 8] >> 28; d[ 9] += o; d[ 8] = d[ 8] & 0xfffffff;
|
|
|
+ o = d[ 9] >> 28; d[10] += o; d[ 9] = d[ 9] & 0xfffffff;
|
|
|
+ o = d[10] >> 28; d[11] += o; d[10] = d[10] & 0xfffffff;
|
|
|
+ o = d[11] >> 28; d[12] += o; d[11] = d[11] & 0xfffffff;
|
|
|
+ o = d[12] >> 28; d[13] += o; d[12] = d[12] & 0xfffffff;
|
|
|
+ o = d[13] >> 28; d[14] += o; d[13] = d[13] & 0xfffffff;
|
|
|
+ o = d[14] >> 28; d[15] += o; d[14] = d[14] & 0xfffffff;
|
|
|
+
|
|
|
+ /* Convert to bytes */
|
|
|
+ b[ 0] = (d[0 ] >> 0);
|
|
|
+ b[ 1] = (d[0 ] >> 8);
|
|
|
+ b[ 2] = (d[0 ] >> 16);
|
|
|
+ b[ 3] = (d[0 ] >> 24) + ((d[1 ] >> 0) << 4);
|
|
|
+ b[ 4] = (d[1 ] >> 4);
|
|
|
+ b[ 5] = (d[1 ] >> 12);
|
|
|
+ b[ 6] = (d[1 ] >> 20);
|
|
|
+ b[ 7] = (d[2 ] >> 0);
|
|
|
+ b[ 8] = (d[2 ] >> 8);
|
|
|
+ b[ 9] = (d[2 ] >> 16);
|
|
|
+ b[10] = (d[2 ] >> 24) + ((d[3 ] >> 0) << 4);
|
|
|
+ b[11] = (d[3 ] >> 4);
|
|
|
+ b[12] = (d[3 ] >> 12);
|
|
|
+ b[13] = (d[3 ] >> 20);
|
|
|
+ b[14] = (d[4 ] >> 0);
|
|
|
+ b[15] = (d[4 ] >> 8);
|
|
|
+ b[16] = (d[4 ] >> 16);
|
|
|
+ b[17] = (d[4 ] >> 24) + ((d[5 ] >> 0) << 4);
|
|
|
+ b[18] = (d[5 ] >> 4);
|
|
|
+ b[19] = (d[5 ] >> 12);
|
|
|
+ b[20] = (d[5 ] >> 20);
|
|
|
+ b[21] = (d[6 ] >> 0);
|
|
|
+ b[22] = (d[6 ] >> 8);
|
|
|
+ b[23] = (d[6 ] >> 16);
|
|
|
+ b[24] = (d[6 ] >> 24) + ((d[7 ] >> 0) << 4);
|
|
|
+ b[25] = (d[7 ] >> 4);
|
|
|
+ b[26] = (d[7 ] >> 12);
|
|
|
+ b[27] = (d[7 ] >> 20);
|
|
|
+ b[28] = (d[8 ] >> 0);
|
|
|
+ b[29] = (d[8 ] >> 8);
|
|
|
+ b[30] = (d[8 ] >> 16);
|
|
|
+ b[31] = (d[8 ] >> 24) + ((d[9 ] >> 0) << 4);
|
|
|
+ b[32] = (d[9 ] >> 4);
|
|
|
+ b[33] = (d[9 ] >> 12);
|
|
|
+ b[34] = (d[9 ] >> 20);
|
|
|
+ b[35] = (d[10] >> 0);
|
|
|
+ b[36] = (d[10] >> 8);
|
|
|
+ b[37] = (d[10] >> 16);
|
|
|
+ b[38] = (d[10] >> 24) + ((d[11] >> 0) << 4);
|
|
|
+ b[39] = (d[11] >> 4);
|
|
|
+ b[40] = (d[11] >> 12);
|
|
|
+ b[41] = (d[11] >> 20);
|
|
|
+ b[42] = (d[12] >> 0);
|
|
|
+ b[43] = (d[12] >> 8);
|
|
|
+ b[44] = (d[12] >> 16);
|
|
|
+ b[45] = (d[12] >> 24) + ((d[13] >> 0) << 4);
|
|
|
+ b[46] = (d[13] >> 4);
|
|
|
+ b[47] = (d[13] >> 12);
|
|
|
+ b[48] = (d[13] >> 20);
|
|
|
+ b[49] = (d[14] >> 0);
|
|
|
+ b[50] = (d[14] >> 8);
|
|
|
+ b[51] = (d[14] >> 16);
|
|
|
+ b[52] = (d[14] >> 24) + ((d[15] >> 0) << 4);
|
|
|
+ b[53] = (d[15] >> 4);
|
|
|
+ b[54] = (d[15] >> 12);
|
|
|
+ b[55] = (d[15] >> 20);
|
|
|
+ b[56] = 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Multiply a by b and add d. r = (a * b + d) mod order
|
|
|
+ *
|
|
|
+ * r [in] Scalar to hold result.
|
|
|
+ * a [in] Scalar to multiply.
|
|
|
+ * b [in] Scalar to multiply.
|
|
|
+ * d [in] Scalar to add to multiplicative result.
|
|
|
+ */
|
|
|
+void sc448_muladd(uint8_t* r, const uint8_t* a, const uint8_t* b,
|
|
|
+ const uint8_t* d)
|
|
|
+{
|
|
|
+ uint32_t ad[16], bd[16], dd[16], rd[16];
|
|
|
+ uint64_t t[32];
|
|
|
+ uint64_t c;
|
|
|
+ uint32_t o;
|
|
|
+
|
|
|
+ /* Load from bytes */
|
|
|
+ ad[ 0] = (((int32_t)((a[ 0] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[ 1] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[ 2] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[ 3] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[ 1] = (((int32_t)((a[ 3] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[ 4] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[ 5] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[ 6] ) >> 0)) << 20);
|
|
|
+ ad[ 2] = (((int32_t)((a[ 7] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[ 8] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[ 9] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[10] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[ 3] = (((int32_t)((a[10] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[11] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[12] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[13] ) >> 0)) << 20);
|
|
|
+ ad[ 4] = (((int32_t)((a[14] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[15] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[16] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[17] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[ 5] = (((int32_t)((a[17] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[18] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[19] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[20] ) >> 0)) << 20);
|
|
|
+ ad[ 6] = (((int32_t)((a[21] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[22] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[23] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[24] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[ 7] = (((int32_t)((a[24] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[25] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[26] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[27] ) >> 0)) << 20);
|
|
|
+ ad[ 8] = (((int32_t)((a[28] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[29] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[30] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[31] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[ 9] = (((int32_t)((a[31] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[32] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[33] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[34] ) >> 0)) << 20);
|
|
|
+ ad[10] = (((int32_t)((a[35] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[36] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[37] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[38] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[11] = (((int32_t)((a[38] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[39] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[40] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[41] ) >> 0)) << 20);
|
|
|
+ ad[12] = (((int32_t)((a[42] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[43] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[44] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[45] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[13] = (((int32_t)((a[45] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[46] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[47] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[48] ) >> 0)) << 20);
|
|
|
+ ad[14] = (((int32_t)((a[49] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((a[50] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((a[51] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((a[52] & 0xf )) >> 0)) << 24);
|
|
|
+ ad[15] = (((int32_t)((a[52] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((a[53] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((a[54] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((a[55] ) >> 0)) << 20);
|
|
|
+ /* Load from bytes */
|
|
|
+ bd[ 0] = (((int32_t)((b[ 0] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[ 1] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[ 2] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[ 3] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[ 1] = (((int32_t)((b[ 3] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[ 4] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[ 5] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[ 6] ) >> 0)) << 20);
|
|
|
+ bd[ 2] = (((int32_t)((b[ 7] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[ 8] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[ 9] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[10] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[ 3] = (((int32_t)((b[10] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[11] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[12] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[13] ) >> 0)) << 20);
|
|
|
+ bd[ 4] = (((int32_t)((b[14] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[15] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[16] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[17] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[ 5] = (((int32_t)((b[17] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[18] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[19] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[20] ) >> 0)) << 20);
|
|
|
+ bd[ 6] = (((int32_t)((b[21] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[22] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[23] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[24] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[ 7] = (((int32_t)((b[24] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[25] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[26] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[27] ) >> 0)) << 20);
|
|
|
+ bd[ 8] = (((int32_t)((b[28] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[29] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[30] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[31] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[ 9] = (((int32_t)((b[31] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[32] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[33] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[34] ) >> 0)) << 20);
|
|
|
+ bd[10] = (((int32_t)((b[35] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[36] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[37] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[38] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[11] = (((int32_t)((b[38] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[39] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[40] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[41] ) >> 0)) << 20);
|
|
|
+ bd[12] = (((int32_t)((b[42] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[43] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[44] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[45] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[13] = (((int32_t)((b[45] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[46] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[47] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[48] ) >> 0)) << 20);
|
|
|
+ bd[14] = (((int32_t)((b[49] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((b[50] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((b[51] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((b[52] & 0xf )) >> 0)) << 24);
|
|
|
+ bd[15] = (((int32_t)((b[52] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((b[53] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((b[54] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((b[55] ) >> 0)) << 20);
|
|
|
+ /* Load from bytes */
|
|
|
+ dd[ 0] = (((int32_t)((d[ 0] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[ 1] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[ 2] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[ 3] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[ 1] = (((int32_t)((d[ 3] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[ 4] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[ 5] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[ 6] ) >> 0)) << 20);
|
|
|
+ dd[ 2] = (((int32_t)((d[ 7] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[ 8] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[ 9] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[10] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[ 3] = (((int32_t)((d[10] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[11] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[12] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[13] ) >> 0)) << 20);
|
|
|
+ dd[ 4] = (((int32_t)((d[14] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[15] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[16] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[17] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[ 5] = (((int32_t)((d[17] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[18] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[19] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[20] ) >> 0)) << 20);
|
|
|
+ dd[ 6] = (((int32_t)((d[21] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[22] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[23] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[24] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[ 7] = (((int32_t)((d[24] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[25] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[26] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[27] ) >> 0)) << 20);
|
|
|
+ dd[ 8] = (((int32_t)((d[28] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[29] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[30] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[31] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[ 9] = (((int32_t)((d[31] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[32] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[33] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[34] ) >> 0)) << 20);
|
|
|
+ dd[10] = (((int32_t)((d[35] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[36] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[37] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[38] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[11] = (((int32_t)((d[38] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[39] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[40] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[41] ) >> 0)) << 20);
|
|
|
+ dd[12] = (((int32_t)((d[42] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[43] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[44] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[45] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[13] = (((int32_t)((d[45] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[46] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[47] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[48] ) >> 0)) << 20);
|
|
|
+ dd[14] = (((int32_t)((d[49] ) >> 0)) << 0)
|
|
|
+ | (((int32_t)((d[50] ) >> 0)) << 8)
|
|
|
+ | (((int32_t)((d[51] ) >> 0)) << 16)
|
|
|
+ | ((((int32_t)((d[52] & 0xf )) >> 0)) << 24);
|
|
|
+ dd[15] = (((int32_t)((d[52] ) >> 4)) << 0)
|
|
|
+ | (((int32_t)((d[53] ) >> 0)) << 4)
|
|
|
+ | (((int32_t)((d[54] ) >> 0)) << 12)
|
|
|
+ | (((int32_t)((d[55] ) >> 0)) << 20);
|
|
|
+
|
|
|
+ /* a * b + d */
|
|
|
+ t[ 0] = dd[ 0] + (int64_t)ad[ 0] * bd[ 0];
|
|
|
+ t[ 1] = dd[ 1] + (int64_t)ad[ 0] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 0];
|
|
|
+ t[ 2] = dd[ 2] + (int64_t)ad[ 0] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 0];
|
|
|
+ t[ 3] = dd[ 3] + (int64_t)ad[ 0] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 0];
|
|
|
+ t[ 4] = dd[ 4] + (int64_t)ad[ 0] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 0];
|
|
|
+ t[ 5] = dd[ 5] + (int64_t)ad[ 0] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 0];
|
|
|
+ t[ 6] = dd[ 6] + (int64_t)ad[ 0] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 0];
|
|
|
+ t[ 7] = dd[ 7] + (int64_t)ad[ 0] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 0];
|
|
|
+ t[ 8] = dd[ 8] + (int64_t)ad[ 0] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 0];
|
|
|
+ t[ 9] = dd[ 9] + (int64_t)ad[ 0] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 1]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 0];
|
|
|
+ t[10] = dd[10] + (int64_t)ad[ 0] * bd[10]
|
|
|
+ + (int64_t)ad[ 1] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 2]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 1]
|
|
|
+ + (int64_t)ad[10] * bd[ 0];
|
|
|
+ t[11] = dd[11] + (int64_t)ad[ 0] * bd[11]
|
|
|
+ + (int64_t)ad[ 1] * bd[10]
|
|
|
+ + (int64_t)ad[ 2] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 3]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 2]
|
|
|
+ + (int64_t)ad[10] * bd[ 1]
|
|
|
+ + (int64_t)ad[11] * bd[ 0];
|
|
|
+ t[12] = dd[12] + (int64_t)ad[ 0] * bd[12]
|
|
|
+ + (int64_t)ad[ 1] * bd[11]
|
|
|
+ + (int64_t)ad[ 2] * bd[10]
|
|
|
+ + (int64_t)ad[ 3] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 4]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 3]
|
|
|
+ + (int64_t)ad[10] * bd[ 2]
|
|
|
+ + (int64_t)ad[11] * bd[ 1]
|
|
|
+ + (int64_t)ad[12] * bd[ 0];
|
|
|
+ t[13] = dd[13] + (int64_t)ad[ 0] * bd[13]
|
|
|
+ + (int64_t)ad[ 1] * bd[12]
|
|
|
+ + (int64_t)ad[ 2] * bd[11]
|
|
|
+ + (int64_t)ad[ 3] * bd[10]
|
|
|
+ + (int64_t)ad[ 4] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 5]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 4]
|
|
|
+ + (int64_t)ad[10] * bd[ 3]
|
|
|
+ + (int64_t)ad[11] * bd[ 2]
|
|
|
+ + (int64_t)ad[12] * bd[ 1]
|
|
|
+ + (int64_t)ad[13] * bd[ 0];
|
|
|
+ t[14] = dd[14] + (int64_t)ad[ 0] * bd[14]
|
|
|
+ + (int64_t)ad[ 1] * bd[13]
|
|
|
+ + (int64_t)ad[ 2] * bd[12]
|
|
|
+ + (int64_t)ad[ 3] * bd[11]
|
|
|
+ + (int64_t)ad[ 4] * bd[10]
|
|
|
+ + (int64_t)ad[ 5] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 6]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 5]
|
|
|
+ + (int64_t)ad[10] * bd[ 4]
|
|
|
+ + (int64_t)ad[11] * bd[ 3]
|
|
|
+ + (int64_t)ad[12] * bd[ 2]
|
|
|
+ + (int64_t)ad[13] * bd[ 1]
|
|
|
+ + (int64_t)ad[14] * bd[ 0];
|
|
|
+ t[15] = dd[15] + (int64_t)ad[ 0] * bd[15]
|
|
|
+ + (int64_t)ad[ 1] * bd[14]
|
|
|
+ + (int64_t)ad[ 2] * bd[13]
|
|
|
+ + (int64_t)ad[ 3] * bd[12]
|
|
|
+ + (int64_t)ad[ 4] * bd[11]
|
|
|
+ + (int64_t)ad[ 5] * bd[10]
|
|
|
+ + (int64_t)ad[ 6] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 7]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 6]
|
|
|
+ + (int64_t)ad[10] * bd[ 5]
|
|
|
+ + (int64_t)ad[11] * bd[ 4]
|
|
|
+ + (int64_t)ad[12] * bd[ 3]
|
|
|
+ + (int64_t)ad[13] * bd[ 2]
|
|
|
+ + (int64_t)ad[14] * bd[ 1]
|
|
|
+ + (int64_t)ad[15] * bd[ 0];
|
|
|
+ t[16] = (int64_t)ad[ 1] * bd[15]
|
|
|
+ + (int64_t)ad[ 2] * bd[14]
|
|
|
+ + (int64_t)ad[ 3] * bd[13]
|
|
|
+ + (int64_t)ad[ 4] * bd[12]
|
|
|
+ + (int64_t)ad[ 5] * bd[11]
|
|
|
+ + (int64_t)ad[ 6] * bd[10]
|
|
|
+ + (int64_t)ad[ 7] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 8]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 7]
|
|
|
+ + (int64_t)ad[10] * bd[ 6]
|
|
|
+ + (int64_t)ad[11] * bd[ 5]
|
|
|
+ + (int64_t)ad[12] * bd[ 4]
|
|
|
+ + (int64_t)ad[13] * bd[ 3]
|
|
|
+ + (int64_t)ad[14] * bd[ 2]
|
|
|
+ + (int64_t)ad[15] * bd[ 1];
|
|
|
+ t[17] = (int64_t)ad[ 2] * bd[15]
|
|
|
+ + (int64_t)ad[ 3] * bd[14]
|
|
|
+ + (int64_t)ad[ 4] * bd[13]
|
|
|
+ + (int64_t)ad[ 5] * bd[12]
|
|
|
+ + (int64_t)ad[ 6] * bd[11]
|
|
|
+ + (int64_t)ad[ 7] * bd[10]
|
|
|
+ + (int64_t)ad[ 8] * bd[ 9]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 8]
|
|
|
+ + (int64_t)ad[10] * bd[ 7]
|
|
|
+ + (int64_t)ad[11] * bd[ 6]
|
|
|
+ + (int64_t)ad[12] * bd[ 5]
|
|
|
+ + (int64_t)ad[13] * bd[ 4]
|
|
|
+ + (int64_t)ad[14] * bd[ 3]
|
|
|
+ + (int64_t)ad[15] * bd[ 2];
|
|
|
+ t[18] = (int64_t)ad[ 3] * bd[15]
|
|
|
+ + (int64_t)ad[ 4] * bd[14]
|
|
|
+ + (int64_t)ad[ 5] * bd[13]
|
|
|
+ + (int64_t)ad[ 6] * bd[12]
|
|
|
+ + (int64_t)ad[ 7] * bd[11]
|
|
|
+ + (int64_t)ad[ 8] * bd[10]
|
|
|
+ + (int64_t)ad[ 9] * bd[ 9]
|
|
|
+ + (int64_t)ad[10] * bd[ 8]
|
|
|
+ + (int64_t)ad[11] * bd[ 7]
|
|
|
+ + (int64_t)ad[12] * bd[ 6]
|
|
|
+ + (int64_t)ad[13] * bd[ 5]
|
|
|
+ + (int64_t)ad[14] * bd[ 4]
|
|
|
+ + (int64_t)ad[15] * bd[ 3];
|
|
|
+ t[19] = (int64_t)ad[ 4] * bd[15]
|
|
|
+ + (int64_t)ad[ 5] * bd[14]
|
|
|
+ + (int64_t)ad[ 6] * bd[13]
|
|
|
+ + (int64_t)ad[ 7] * bd[12]
|
|
|
+ + (int64_t)ad[ 8] * bd[11]
|
|
|
+ + (int64_t)ad[ 9] * bd[10]
|
|
|
+ + (int64_t)ad[10] * bd[ 9]
|
|
|
+ + (int64_t)ad[11] * bd[ 8]
|
|
|
+ + (int64_t)ad[12] * bd[ 7]
|
|
|
+ + (int64_t)ad[13] * bd[ 6]
|
|
|
+ + (int64_t)ad[14] * bd[ 5]
|
|
|
+ + (int64_t)ad[15] * bd[ 4];
|
|
|
+ t[20] = (int64_t)ad[ 5] * bd[15]
|
|
|
+ + (int64_t)ad[ 6] * bd[14]
|
|
|
+ + (int64_t)ad[ 7] * bd[13]
|
|
|
+ + (int64_t)ad[ 8] * bd[12]
|
|
|
+ + (int64_t)ad[ 9] * bd[11]
|
|
|
+ + (int64_t)ad[10] * bd[10]
|
|
|
+ + (int64_t)ad[11] * bd[ 9]
|
|
|
+ + (int64_t)ad[12] * bd[ 8]
|
|
|
+ + (int64_t)ad[13] * bd[ 7]
|
|
|
+ + (int64_t)ad[14] * bd[ 6]
|
|
|
+ + (int64_t)ad[15] * bd[ 5];
|
|
|
+ t[21] = (int64_t)ad[ 6] * bd[15]
|
|
|
+ + (int64_t)ad[ 7] * bd[14]
|
|
|
+ + (int64_t)ad[ 8] * bd[13]
|
|
|
+ + (int64_t)ad[ 9] * bd[12]
|
|
|
+ + (int64_t)ad[10] * bd[11]
|
|
|
+ + (int64_t)ad[11] * bd[10]
|
|
|
+ + (int64_t)ad[12] * bd[ 9]
|
|
|
+ + (int64_t)ad[13] * bd[ 8]
|
|
|
+ + (int64_t)ad[14] * bd[ 7]
|
|
|
+ + (int64_t)ad[15] * bd[ 6];
|
|
|
+ t[22] = (int64_t)ad[ 7] * bd[15]
|
|
|
+ + (int64_t)ad[ 8] * bd[14]
|
|
|
+ + (int64_t)ad[ 9] * bd[13]
|
|
|
+ + (int64_t)ad[10] * bd[12]
|
|
|
+ + (int64_t)ad[11] * bd[11]
|
|
|
+ + (int64_t)ad[12] * bd[10]
|
|
|
+ + (int64_t)ad[13] * bd[ 9]
|
|
|
+ + (int64_t)ad[14] * bd[ 8]
|
|
|
+ + (int64_t)ad[15] * bd[ 7];
|
|
|
+ t[23] = (int64_t)ad[ 8] * bd[15]
|
|
|
+ + (int64_t)ad[ 9] * bd[14]
|
|
|
+ + (int64_t)ad[10] * bd[13]
|
|
|
+ + (int64_t)ad[11] * bd[12]
|
|
|
+ + (int64_t)ad[12] * bd[11]
|
|
|
+ + (int64_t)ad[13] * bd[10]
|
|
|
+ + (int64_t)ad[14] * bd[ 9]
|
|
|
+ + (int64_t)ad[15] * bd[ 8];
|
|
|
+ t[24] = (int64_t)ad[ 9] * bd[15]
|
|
|
+ + (int64_t)ad[10] * bd[14]
|
|
|
+ + (int64_t)ad[11] * bd[13]
|
|
|
+ + (int64_t)ad[12] * bd[12]
|
|
|
+ + (int64_t)ad[13] * bd[11]
|
|
|
+ + (int64_t)ad[14] * bd[10]
|
|
|
+ + (int64_t)ad[15] * bd[ 9];
|
|
|
+ t[25] = (int64_t)ad[10] * bd[15]
|
|
|
+ + (int64_t)ad[11] * bd[14]
|
|
|
+ + (int64_t)ad[12] * bd[13]
|
|
|
+ + (int64_t)ad[13] * bd[12]
|
|
|
+ + (int64_t)ad[14] * bd[11]
|
|
|
+ + (int64_t)ad[15] * bd[10];
|
|
|
+ t[26] = (int64_t)ad[11] * bd[15]
|
|
|
+ + (int64_t)ad[12] * bd[14]
|
|
|
+ + (int64_t)ad[13] * bd[13]
|
|
|
+ + (int64_t)ad[14] * bd[12]
|
|
|
+ + (int64_t)ad[15] * bd[11];
|
|
|
+ t[27] = (int64_t)ad[12] * bd[15]
|
|
|
+ + (int64_t)ad[13] * bd[14]
|
|
|
+ + (int64_t)ad[14] * bd[13]
|
|
|
+ + (int64_t)ad[15] * bd[12];
|
|
|
+ t[28] = (int64_t)ad[13] * bd[15]
|
|
|
+ + (int64_t)ad[14] * bd[14]
|
|
|
+ + (int64_t)ad[15] * bd[13];
|
|
|
+ t[29] = (int64_t)ad[14] * bd[15]
|
|
|
+ + (int64_t)ad[15] * bd[14];
|
|
|
+ t[30] = (int64_t)ad[15] * bd[15];
|
|
|
+ t[31] = 0;
|
|
|
+
|
|
|
+ /* Mod curve order */
|
|
|
+ /* 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d */
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 28; t[ 1] += c; t[ 0] = t[ 0] & 0xfffffff;
|
|
|
+ c = t[ 1] >> 28; t[ 2] += c; t[ 1] = t[ 1] & 0xfffffff;
|
|
|
+ c = t[ 2] >> 28; t[ 3] += c; t[ 2] = t[ 2] & 0xfffffff;
|
|
|
+ c = t[ 3] >> 28; t[ 4] += c; t[ 3] = t[ 3] & 0xfffffff;
|
|
|
+ c = t[ 4] >> 28; t[ 5] += c; t[ 4] = t[ 4] & 0xfffffff;
|
|
|
+ c = t[ 5] >> 28; t[ 6] += c; t[ 5] = t[ 5] & 0xfffffff;
|
|
|
+ c = t[ 6] >> 28; t[ 7] += c; t[ 6] = t[ 6] & 0xfffffff;
|
|
|
+ c = t[ 7] >> 28; t[ 8] += c; t[ 7] = t[ 7] & 0xfffffff;
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; t[ 8] = t[ 8] & 0xfffffff;
|
|
|
+ c = t[ 9] >> 28; t[10] += c; t[ 9] = t[ 9] & 0xfffffff;
|
|
|
+ c = t[10] >> 28; t[11] += c; t[10] = t[10] & 0xfffffff;
|
|
|
+ c = t[11] >> 28; t[12] += c; t[11] = t[11] & 0xfffffff;
|
|
|
+ c = t[12] >> 28; t[13] += c; t[12] = t[12] & 0xfffffff;
|
|
|
+ c = t[13] >> 28; t[14] += c; t[13] = t[13] & 0xfffffff;
|
|
|
+ c = t[14] >> 28; t[15] += c; t[14] = t[14] & 0xfffffff;
|
|
|
+ c = t[15] >> 28; t[16] += c; t[15] = t[15] & 0xfffffff;
|
|
|
+ c = t[16] >> 28; t[17] += c; t[16] = t[16] & 0xfffffff;
|
|
|
+ c = t[17] >> 28; t[18] += c; t[17] = t[17] & 0xfffffff;
|
|
|
+ c = t[18] >> 28; t[19] += c; t[18] = t[18] & 0xfffffff;
|
|
|
+ c = t[19] >> 28; t[20] += c; t[19] = t[19] & 0xfffffff;
|
|
|
+ c = t[20] >> 28; t[21] += c; t[20] = t[20] & 0xfffffff;
|
|
|
+ c = t[21] >> 28; t[22] += c; t[21] = t[21] & 0xfffffff;
|
|
|
+ c = t[22] >> 28; t[23] += c; t[22] = t[22] & 0xfffffff;
|
|
|
+ c = t[23] >> 28; t[24] += c; t[23] = t[23] & 0xfffffff;
|
|
|
+ c = t[24] >> 28; t[25] += c; t[24] = t[24] & 0xfffffff;
|
|
|
+ c = t[25] >> 28; t[26] += c; t[25] = t[25] & 0xfffffff;
|
|
|
+ c = t[26] >> 28; t[27] += c; t[26] = t[26] & 0xfffffff;
|
|
|
+ c = t[27] >> 28; t[28] += c; t[27] = t[27] & 0xfffffff;
|
|
|
+ c = t[28] >> 28; t[29] += c; t[28] = t[28] & 0xfffffff;
|
|
|
+ c = t[29] >> 28; t[30] += c; t[29] = t[29] & 0xfffffff;
|
|
|
+ c = t[30] >> 28; t[31] += c; t[30] = t[30] & 0xfffffff;
|
|
|
+ /* Mod top half of extra words */
|
|
|
+ t[ 8] += (int64_t)0x129eec34 * t[24];
|
|
|
+ t[ 9] += (int64_t)0x21cf5b54 * t[24];
|
|
|
+ t[10] += (int64_t)0x29c2ab70 * t[24];
|
|
|
+ t[11] += (int64_t)0x0f635c8c * t[24];
|
|
|
+ t[12] += (int64_t)0x25bf7a4c * t[24];
|
|
|
+ t[13] += (int64_t)0x2d944a70 * t[24];
|
|
|
+ t[14] += (int64_t)0x18eec490 * t[24];
|
|
|
+ t[15] += (int64_t)0x20cd7704 * t[24];
|
|
|
+ t[ 9] += (int64_t)0x129eec34 * t[25];
|
|
|
+ t[10] += (int64_t)0x21cf5b54 * t[25];
|
|
|
+ t[11] += (int64_t)0x29c2ab70 * t[25];
|
|
|
+ t[12] += (int64_t)0x0f635c8c * t[25];
|
|
|
+ t[13] += (int64_t)0x25bf7a4c * t[25];
|
|
|
+ t[14] += (int64_t)0x2d944a70 * t[25];
|
|
|
+ t[15] += (int64_t)0x18eec490 * t[25];
|
|
|
+ t[16] += (int64_t)0x20cd7704 * t[25];
|
|
|
+ t[10] += (int64_t)0x129eec34 * t[26];
|
|
|
+ t[11] += (int64_t)0x21cf5b54 * t[26];
|
|
|
+ t[12] += (int64_t)0x29c2ab70 * t[26];
|
|
|
+ t[13] += (int64_t)0x0f635c8c * t[26];
|
|
|
+ t[14] += (int64_t)0x25bf7a4c * t[26];
|
|
|
+ t[15] += (int64_t)0x2d944a70 * t[26];
|
|
|
+ t[16] += (int64_t)0x18eec490 * t[26];
|
|
|
+ t[17] += (int64_t)0x20cd7704 * t[26];
|
|
|
+ t[11] += (int64_t)0x129eec34 * t[27];
|
|
|
+ t[12] += (int64_t)0x21cf5b54 * t[27];
|
|
|
+ t[13] += (int64_t)0x29c2ab70 * t[27];
|
|
|
+ t[14] += (int64_t)0x0f635c8c * t[27];
|
|
|
+ t[15] += (int64_t)0x25bf7a4c * t[27];
|
|
|
+ t[16] += (int64_t)0x2d944a70 * t[27];
|
|
|
+ t[17] += (int64_t)0x18eec490 * t[27];
|
|
|
+ t[18] += (int64_t)0x20cd7704 * t[27];
|
|
|
+ t[12] += (int64_t)0x129eec34 * t[28];
|
|
|
+ t[13] += (int64_t)0x21cf5b54 * t[28];
|
|
|
+ t[14] += (int64_t)0x29c2ab70 * t[28];
|
|
|
+ t[15] += (int64_t)0x0f635c8c * t[28];
|
|
|
+ t[16] += (int64_t)0x25bf7a4c * t[28];
|
|
|
+ t[17] += (int64_t)0x2d944a70 * t[28];
|
|
|
+ t[18] += (int64_t)0x18eec490 * t[28];
|
|
|
+ t[19] += (int64_t)0x20cd7704 * t[28];
|
|
|
+ t[13] += (int64_t)0x129eec34 * t[29];
|
|
|
+ t[14] += (int64_t)0x21cf5b54 * t[29];
|
|
|
+ t[15] += (int64_t)0x29c2ab70 * t[29];
|
|
|
+ t[16] += (int64_t)0x0f635c8c * t[29];
|
|
|
+ t[17] += (int64_t)0x25bf7a4c * t[29];
|
|
|
+ t[18] += (int64_t)0x2d944a70 * t[29];
|
|
|
+ t[19] += (int64_t)0x18eec490 * t[29];
|
|
|
+ t[20] += (int64_t)0x20cd7704 * t[29];
|
|
|
+ t[14] += (int64_t)0x129eec34 * t[30];
|
|
|
+ t[15] += (int64_t)0x21cf5b54 * t[30];
|
|
|
+ t[16] += (int64_t)0x29c2ab70 * t[30];
|
|
|
+ t[17] += (int64_t)0x0f635c8c * t[30];
|
|
|
+ t[18] += (int64_t)0x25bf7a4c * t[30];
|
|
|
+ t[19] += (int64_t)0x2d944a70 * t[30];
|
|
|
+ t[20] += (int64_t)0x18eec490 * t[30];
|
|
|
+ t[21] += (int64_t)0x20cd7704 * t[30];
|
|
|
+ t[15] += (int64_t)0x129eec34 * t[31];
|
|
|
+ t[16] += (int64_t)0x21cf5b54 * t[31];
|
|
|
+ t[17] += (int64_t)0x29c2ab70 * t[31];
|
|
|
+ t[18] += (int64_t)0x0f635c8c * t[31];
|
|
|
+ t[19] += (int64_t)0x25bf7a4c * t[31];
|
|
|
+ t[20] += (int64_t)0x2d944a70 * t[31];
|
|
|
+ t[21] += (int64_t)0x18eec490 * t[31];
|
|
|
+ t[22] += (int64_t)0x20cd7704 * t[31];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; t[ 8] = t[ 8] & 0xfffffff;
|
|
|
+ c = t[ 9] >> 28; t[10] += c; t[ 9] = t[ 9] & 0xfffffff;
|
|
|
+ c = t[10] >> 28; t[11] += c; t[10] = t[10] & 0xfffffff;
|
|
|
+ c = t[11] >> 28; t[12] += c; t[11] = t[11] & 0xfffffff;
|
|
|
+ c = t[12] >> 28; t[13] += c; t[12] = t[12] & 0xfffffff;
|
|
|
+ c = t[13] >> 28; t[14] += c; t[13] = t[13] & 0xfffffff;
|
|
|
+ c = t[14] >> 28; t[15] += c; t[14] = t[14] & 0xfffffff;
|
|
|
+ c = t[15] >> 28; t[16] += c; t[15] = t[15] & 0xfffffff;
|
|
|
+ c = t[16] >> 28; t[17] += c; t[16] = t[16] & 0xfffffff;
|
|
|
+ c = t[17] >> 28; t[18] += c; t[17] = t[17] & 0xfffffff;
|
|
|
+ c = t[18] >> 28; t[19] += c; t[18] = t[18] & 0xfffffff;
|
|
|
+ c = t[19] >> 28; t[20] += c; t[19] = t[19] & 0xfffffff;
|
|
|
+ c = t[20] >> 28; t[21] += c; t[20] = t[20] & 0xfffffff;
|
|
|
+ c = t[21] >> 28; t[22] += c; t[21] = t[21] & 0xfffffff;
|
|
|
+ c = t[22] >> 28; t[23] += c; t[22] = t[22] & 0xfffffff;
|
|
|
+ /* Mod bottom half of extra words */
|
|
|
+ t[ 0] += (int64_t)0x129eec34 * t[16];
|
|
|
+ t[ 1] += (int64_t)0x21cf5b54 * t[16];
|
|
|
+ t[ 2] += (int64_t)0x29c2ab70 * t[16];
|
|
|
+ t[ 3] += (int64_t)0x0f635c8c * t[16];
|
|
|
+ t[ 4] += (int64_t)0x25bf7a4c * t[16];
|
|
|
+ t[ 5] += (int64_t)0x2d944a70 * t[16];
|
|
|
+ t[ 6] += (int64_t)0x18eec490 * t[16];
|
|
|
+ t[ 7] += (int64_t)0x20cd7704 * t[16];
|
|
|
+ t[ 1] += (int64_t)0x129eec34 * t[17];
|
|
|
+ t[ 2] += (int64_t)0x21cf5b54 * t[17];
|
|
|
+ t[ 3] += (int64_t)0x29c2ab70 * t[17];
|
|
|
+ t[ 4] += (int64_t)0x0f635c8c * t[17];
|
|
|
+ t[ 5] += (int64_t)0x25bf7a4c * t[17];
|
|
|
+ t[ 6] += (int64_t)0x2d944a70 * t[17];
|
|
|
+ t[ 7] += (int64_t)0x18eec490 * t[17];
|
|
|
+ t[ 8] += (int64_t)0x20cd7704 * t[17];
|
|
|
+ t[ 2] += (int64_t)0x129eec34 * t[18];
|
|
|
+ t[ 3] += (int64_t)0x21cf5b54 * t[18];
|
|
|
+ t[ 4] += (int64_t)0x29c2ab70 * t[18];
|
|
|
+ t[ 5] += (int64_t)0x0f635c8c * t[18];
|
|
|
+ t[ 6] += (int64_t)0x25bf7a4c * t[18];
|
|
|
+ t[ 7] += (int64_t)0x2d944a70 * t[18];
|
|
|
+ t[ 8] += (int64_t)0x18eec490 * t[18];
|
|
|
+ t[ 9] += (int64_t)0x20cd7704 * t[18];
|
|
|
+ t[ 3] += (int64_t)0x129eec34 * t[19];
|
|
|
+ t[ 4] += (int64_t)0x21cf5b54 * t[19];
|
|
|
+ t[ 5] += (int64_t)0x29c2ab70 * t[19];
|
|
|
+ t[ 6] += (int64_t)0x0f635c8c * t[19];
|
|
|
+ t[ 7] += (int64_t)0x25bf7a4c * t[19];
|
|
|
+ t[ 8] += (int64_t)0x2d944a70 * t[19];
|
|
|
+ t[ 9] += (int64_t)0x18eec490 * t[19];
|
|
|
+ t[10] += (int64_t)0x20cd7704 * t[19];
|
|
|
+ t[ 4] += (int64_t)0x129eec34 * t[20];
|
|
|
+ t[ 5] += (int64_t)0x21cf5b54 * t[20];
|
|
|
+ t[ 6] += (int64_t)0x29c2ab70 * t[20];
|
|
|
+ t[ 7] += (int64_t)0x0f635c8c * t[20];
|
|
|
+ t[ 8] += (int64_t)0x25bf7a4c * t[20];
|
|
|
+ t[ 9] += (int64_t)0x2d944a70 * t[20];
|
|
|
+ t[10] += (int64_t)0x18eec490 * t[20];
|
|
|
+ t[11] += (int64_t)0x20cd7704 * t[20];
|
|
|
+ t[ 5] += (int64_t)0x129eec34 * t[21];
|
|
|
+ t[ 6] += (int64_t)0x21cf5b54 * t[21];
|
|
|
+ t[ 7] += (int64_t)0x29c2ab70 * t[21];
|
|
|
+ t[ 8] += (int64_t)0x0f635c8c * t[21];
|
|
|
+ t[ 9] += (int64_t)0x25bf7a4c * t[21];
|
|
|
+ t[10] += (int64_t)0x2d944a70 * t[21];
|
|
|
+ t[11] += (int64_t)0x18eec490 * t[21];
|
|
|
+ t[12] += (int64_t)0x20cd7704 * t[21];
|
|
|
+ t[ 6] += (int64_t)0x129eec34 * t[22];
|
|
|
+ t[ 7] += (int64_t)0x21cf5b54 * t[22];
|
|
|
+ t[ 8] += (int64_t)0x29c2ab70 * t[22];
|
|
|
+ t[ 9] += (int64_t)0x0f635c8c * t[22];
|
|
|
+ t[10] += (int64_t)0x25bf7a4c * t[22];
|
|
|
+ t[11] += (int64_t)0x2d944a70 * t[22];
|
|
|
+ t[12] += (int64_t)0x18eec490 * t[22];
|
|
|
+ t[13] += (int64_t)0x20cd7704 * t[22];
|
|
|
+ t[ 7] += (int64_t)0x129eec34 * t[23];
|
|
|
+ t[ 8] += (int64_t)0x21cf5b54 * t[23];
|
|
|
+ t[ 9] += (int64_t)0x29c2ab70 * t[23];
|
|
|
+ t[10] += (int64_t)0x0f635c8c * t[23];
|
|
|
+ t[11] += (int64_t)0x25bf7a4c * t[23];
|
|
|
+ t[12] += (int64_t)0x2d944a70 * t[23];
|
|
|
+ t[13] += (int64_t)0x18eec490 * t[23];
|
|
|
+ t[14] += (int64_t)0x20cd7704 * t[23];
|
|
|
+ /* Propagate carries */
|
|
|
+ c = t[ 0] >> 28; t[ 1] += c; rd[ 0] = (int32_t)(t[ 0] & 0xfffffff);
|
|
|
+ c = t[ 1] >> 28; t[ 2] += c; rd[ 1] = (int32_t)(t[ 1] & 0xfffffff);
|
|
|
+ c = t[ 2] >> 28; t[ 3] += c; rd[ 2] = (int32_t)(t[ 2] & 0xfffffff);
|
|
|
+ c = t[ 3] >> 28; t[ 4] += c; rd[ 3] = (int32_t)(t[ 3] & 0xfffffff);
|
|
|
+ c = t[ 4] >> 28; t[ 5] += c; rd[ 4] = (int32_t)(t[ 4] & 0xfffffff);
|
|
|
+ c = t[ 5] >> 28; t[ 6] += c; rd[ 5] = (int32_t)(t[ 5] & 0xfffffff);
|
|
|
+ c = t[ 6] >> 28; t[ 7] += c; rd[ 6] = (int32_t)(t[ 6] & 0xfffffff);
|
|
|
+ c = t[ 7] >> 28; t[ 8] += c; rd[ 7] = (int32_t)(t[ 7] & 0xfffffff);
|
|
|
+ c = t[ 8] >> 28; t[ 9] += c; rd[ 8] = (int32_t)(t[ 8] & 0xfffffff);
|
|
|
+ c = t[ 9] >> 28; t[10] += c; rd[ 9] = (int32_t)(t[ 9] & 0xfffffff);
|
|
|
+ c = t[10] >> 28; t[11] += c; rd[10] = (int32_t)(t[10] & 0xfffffff);
|
|
|
+ c = t[11] >> 28; t[12] += c; rd[11] = (int32_t)(t[11] & 0xfffffff);
|
|
|
+ c = t[12] >> 28; t[13] += c; rd[12] = (int32_t)(t[12] & 0xfffffff);
|
|
|
+ c = t[13] >> 28; t[14] += c; rd[13] = (int32_t)(t[13] & 0xfffffff);
|
|
|
+ c = t[14] >> 28; t[15] += c; rd[14] = (int32_t)(t[14] & 0xfffffff);
|
|
|
+ rd[15] = t[15];
|
|
|
+ /* Mod bits over 28 in last word */
|
|
|
+ o = rd[15] >> 26; rd[15] &= 0x3ffffff;
|
|
|
+ rd[ 0] += 0x4a7bb0d * o;
|
|
|
+ rd[ 1] += 0x873d6d5 * o;
|
|
|
+ rd[ 2] += 0xa70aadc * o;
|
|
|
+ rd[ 3] += 0x3d8d723 * o;
|
|
|
+ rd[ 4] += 0x96fde93 * o;
|
|
|
+ rd[ 5] += 0xb65129c * o;
|
|
|
+ rd[ 6] += 0x63bb124 * o;
|
|
|
+ rd[ 7] += 0x8335dc1 * o;
|
|
|
+ /* Propagate carries */
|
|
|
+ o = rd[ 0] >> 28; rd[ 1] += o; rd[ 0] = rd[ 0] & 0xfffffff;
|
|
|
+ o = rd[ 1] >> 28; rd[ 2] += o; rd[ 1] = rd[ 1] & 0xfffffff;
|
|
|
+ o = rd[ 2] >> 28; rd[ 3] += o; rd[ 2] = rd[ 2] & 0xfffffff;
|
|
|
+ o = rd[ 3] >> 28; rd[ 4] += o; rd[ 3] = rd[ 3] & 0xfffffff;
|
|
|
+ o = rd[ 4] >> 28; rd[ 5] += o; rd[ 4] = rd[ 4] & 0xfffffff;
|
|
|
+ o = rd[ 5] >> 28; rd[ 6] += o; rd[ 5] = rd[ 5] & 0xfffffff;
|
|
|
+ o = rd[ 6] >> 28; rd[ 7] += o; rd[ 6] = rd[ 6] & 0xfffffff;
|
|
|
+ o = rd[ 7] >> 28; rd[ 8] += o; rd[ 7] = rd[ 7] & 0xfffffff;
|
|
|
+ o = rd[ 8] >> 28; rd[ 9] += o; rd[ 8] = rd[ 8] & 0xfffffff;
|
|
|
+ o = rd[ 9] >> 28; rd[10] += o; rd[ 9] = rd[ 9] & 0xfffffff;
|
|
|
+ o = rd[10] >> 28; rd[11] += o; rd[10] = rd[10] & 0xfffffff;
|
|
|
+ o = rd[11] >> 28; rd[12] += o; rd[11] = rd[11] & 0xfffffff;
|
|
|
+ o = rd[12] >> 28; rd[13] += o; rd[12] = rd[12] & 0xfffffff;
|
|
|
+ o = rd[13] >> 28; rd[14] += o; rd[13] = rd[13] & 0xfffffff;
|
|
|
+ o = rd[14] >> 28; rd[15] += o; rd[14] = rd[14] & 0xfffffff;
|
|
|
+
|
|
|
+ /* Convert to bytes */
|
|
|
+ r[ 0] = (rd[0 ] >> 0);
|
|
|
+ r[ 1] = (rd[0 ] >> 8);
|
|
|
+ r[ 2] = (rd[0 ] >> 16);
|
|
|
+ r[ 3] = (rd[0 ] >> 24) + ((rd[1 ] >> 0) << 4);
|
|
|
+ r[ 4] = (rd[1 ] >> 4);
|
|
|
+ r[ 5] = (rd[1 ] >> 12);
|
|
|
+ r[ 6] = (rd[1 ] >> 20);
|
|
|
+ r[ 7] = (rd[2 ] >> 0);
|
|
|
+ r[ 8] = (rd[2 ] >> 8);
|
|
|
+ r[ 9] = (rd[2 ] >> 16);
|
|
|
+ r[10] = (rd[2 ] >> 24) + ((rd[3 ] >> 0) << 4);
|
|
|
+ r[11] = (rd[3 ] >> 4);
|
|
|
+ r[12] = (rd[3 ] >> 12);
|
|
|
+ r[13] = (rd[3 ] >> 20);
|
|
|
+ r[14] = (rd[4 ] >> 0);
|
|
|
+ r[15] = (rd[4 ] >> 8);
|
|
|
+ r[16] = (rd[4 ] >> 16);
|
|
|
+ r[17] = (rd[4 ] >> 24) + ((rd[5 ] >> 0) << 4);
|
|
|
+ r[18] = (rd[5 ] >> 4);
|
|
|
+ r[19] = (rd[5 ] >> 12);
|
|
|
+ r[20] = (rd[5 ] >> 20);
|
|
|
+ r[21] = (rd[6 ] >> 0);
|
|
|
+ r[22] = (rd[6 ] >> 8);
|
|
|
+ r[23] = (rd[6 ] >> 16);
|
|
|
+ r[24] = (rd[6 ] >> 24) + ((rd[7 ] >> 0) << 4);
|
|
|
+ r[25] = (rd[7 ] >> 4);
|
|
|
+ r[26] = (rd[7 ] >> 12);
|
|
|
+ r[27] = (rd[7 ] >> 20);
|
|
|
+ r[28] = (rd[8 ] >> 0);
|
|
|
+ r[29] = (rd[8 ] >> 8);
|
|
|
+ r[30] = (rd[8 ] >> 16);
|
|
|
+ r[31] = (rd[8 ] >> 24) + ((rd[9 ] >> 0) << 4);
|
|
|
+ r[32] = (rd[9 ] >> 4);
|
|
|
+ r[33] = (rd[9 ] >> 12);
|
|
|
+ r[34] = (rd[9 ] >> 20);
|
|
|
+ r[35] = (rd[10] >> 0);
|
|
|
+ r[36] = (rd[10] >> 8);
|
|
|
+ r[37] = (rd[10] >> 16);
|
|
|
+ r[38] = (rd[10] >> 24) + ((rd[11] >> 0) << 4);
|
|
|
+ r[39] = (rd[11] >> 4);
|
|
|
+ r[40] = (rd[11] >> 12);
|
|
|
+ r[41] = (rd[11] >> 20);
|
|
|
+ r[42] = (rd[12] >> 0);
|
|
|
+ r[43] = (rd[12] >> 8);
|
|
|
+ r[44] = (rd[12] >> 16);
|
|
|
+ r[45] = (rd[12] >> 24) + ((rd[13] >> 0) << 4);
|
|
|
+ r[46] = (rd[13] >> 4);
|
|
|
+ r[47] = (rd[13] >> 12);
|
|
|
+ r[48] = (rd[13] >> 20);
|
|
|
+ r[49] = (rd[14] >> 0);
|
|
|
+ r[50] = (rd[14] >> 8);
|
|
|
+ r[51] = (rd[14] >> 16);
|
|
|
+ r[52] = (rd[14] >> 24) + ((rd[15] >> 0) << 4);
|
|
|
+ r[53] = (rd[15] >> 4);
|
|
|
+ r[54] = (rd[15] >> 12);
|
|
|
+ r[55] = (rd[15] >> 20);
|
|
|
+ r[56] = 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Precomputed multiples of the base point. */
|
|
|
+static const ge448_precomp base[58][8] = {
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x70cc05e, 0x26a82bc, 0x0938e26, 0x80e18b0, 0x511433b, 0xf72ab66,
|
|
|
+ 0x412ae1a, 0xa3d3a46, 0xa6de324, 0x0f1767e, 0x4657047, 0x36da9e1,
|
|
|
+ 0x5a622bf, 0xed221d1, 0x66bed0d, 0x4f1970c },
|
|
|
+ { 0x230fa14, 0x08795bf, 0x7c8ad98, 0x132c4ed, 0x9c4fdbd, 0x1ce67c3,
|
|
|
+ 0x73ad3ff, 0x05a0c2d, 0x7789c1e, 0xa398408, 0xa73736c, 0xc7624be,
|
|
|
+ 0x03756c9, 0x2488762, 0x16eb6bc, 0x693f467 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x5555555, 0x5555555, 0x5555555, 0x5555555, 0x5555555, 0x5555555,
|
|
|
+ 0x5555555, 0x5555555, 0xaaaaaa9, 0xaaaaaaa, 0xaaaaaaa, 0xaaaaaaa,
|
|
|
+ 0xaaaaaaa, 0xaaaaaaa, 0xaaaaaaa, 0xaaaaaaa },
|
|
|
+ { 0xa9386ed, 0xeafbcde, 0xda06bda, 0xb2bed1c, 0x098bbbc, 0x833a2a3,
|
|
|
+ 0x80d6565, 0x8ad8c4b, 0x7e36d72, 0x884dd7b, 0xed7a035, 0xc2b0036,
|
|
|
+ 0x6205086, 0x8db359d, 0x34ad704, 0xae05e96 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x6ff2f8f, 0x2817328, 0xda85757, 0xb769465, 0xfd6e862, 0xf7f6271,
|
|
|
+ 0x8daa9cb, 0x4a3fcfe, 0x2ba077a, 0xda82c7e, 0x41b8b8c, 0x9433322,
|
|
|
+ 0x4316cb6, 0x6455bd6, 0xb9108af, 0x0865886 },
|
|
|
+ { 0x88ed6fc, 0x22ac135, 0x02dafb8, 0x9a68fed, 0x7f0bffa, 0x1bdb676,
|
|
|
+ 0x8bb3a33, 0xec4e1d5, 0xce43c82, 0x56c3b9f, 0xa8d9523, 0xa6449a4,
|
|
|
+ 0xa7ad43a, 0xf706cbd, 0xbd5125c, 0xe005a8d }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x8ba7f30, 0xce42ac4, 0x9e120e2, 0xe179894, 0x8ba21ae, 0xf1515dd,
|
|
|
+ 0x301b7bd, 0x70c74cc, 0x3fda4be, 0x0891c69, 0xa09cf4e, 0x29ea255,
|
|
|
+ 0x17226f9, 0x2c1419a, 0xc6c0cce, 0x49dcbc5 },
|
|
|
+ { 0xde51839, 0xe236f86, 0xd4f5b32, 0x44285d0, 0x472b5d4, 0x7ea1ca9,
|
|
|
+ 0x1c0d8f9, 0x7b8a5bc, 0x90dc322, 0x57d845c, 0x7c02f04, 0x1b979cb,
|
|
|
+ 0x3a5de02, 0x27164b3, 0x4accde5, 0xd49077e }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x2030034, 0xa99d109, 0x6f950d0, 0x2d8cefc, 0xc96f07b, 0x7a920c3,
|
|
|
+ 0x08bc0d5, 0x9588128, 0x6d761e8, 0x62ada75, 0xbcf7285, 0x0def80c,
|
|
|
+ 0x01eedb5, 0x0e2ba76, 0x5a48dcb, 0x7a9f933 },
|
|
|
+ { 0x2f435eb, 0xb473147, 0xf225443, 0x5512881, 0x33c5840, 0xee59d2b,
|
|
|
+ 0x127d7a4, 0xb698017, 0x86551f7, 0xb18fced, 0xca1823a, 0x0ade260,
|
|
|
+ 0xce4fd58, 0xd3b9109, 0xa2517ed, 0xadfd751 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xabef79c, 0x7fd7652, 0x443a878, 0x6c20a07, 0x12a7109, 0x5c1840d,
|
|
|
+ 0x876451c, 0x4a06e4a, 0xad95f65, 0x3bed0b4, 0x3fb0260, 0x25d2e67,
|
|
|
+ 0xaebd971, 0x2e00349, 0x4498b72, 0x54523e0 },
|
|
|
+ { 0x07c7bcc, 0xea5d1da, 0x38ea98c, 0xcce7769, 0x61d2b3e, 0x80284e8,
|
|
|
+ 0x6e1ff1b, 0x48de76b, 0x9c58522, 0x7b12186, 0x2765a1a, 0xbfd053a,
|
|
|
+ 0x056c667, 0x2d743ec, 0xd8ab61c, 0x3f99b9c }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xeb5eaf7, 0xdf9567c, 0x78ac7d7, 0x110a6b4, 0x4706e0b, 0x2d33501,
|
|
|
+ 0x0b5a209, 0x0df9c7b, 0x568e684, 0xba4223d, 0x8c3719b, 0xd78af2d,
|
|
|
+ 0xa5291b6, 0x77467b9, 0x5c89bef, 0x079748e },
|
|
|
+ { 0xdac377f, 0xe20d3fa, 0x72b5c09, 0x34e8669, 0xc40bbb7, 0xd8687a3,
|
|
|
+ 0xd2f84c9, 0x7b3946f, 0xa78f50e, 0xd00e40c, 0x17e7179, 0xb875944,
|
|
|
+ 0xcb23583, 0x9c7373b, 0xc90fd69, 0x7ddeda3 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x153bde0, 0x2538a67, 0x406b696, 0x223aca9, 0x1ad713e, 0xf9080dc,
|
|
|
+ 0xd816a64, 0x6c4cb47, 0x5dc8b97, 0xbc28568, 0xc08e2d7, 0xd97b037,
|
|
|
+ 0x5d0e66b, 0x5b63fb4, 0x520e8a3, 0xd1f1bc5 },
|
|
|
+ { 0xe69e09b, 0x4eb873c, 0xbc8ee45, 0x1663164, 0xba8d89f, 0x08f7003,
|
|
|
+ 0x386ad82, 0x4b98ead, 0xbd94c7b, 0xa4b93b7, 0xc6b38b3, 0x46ba408,
|
|
|
+ 0xf3574ff, 0xdae87d1, 0xe9bea9b, 0xc7564f4 }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x5bfac1c, 0x2e4fdb2, 0xf5f3bca, 0xf0d79aa, 0x20fb7cc, 0xe756b0d,
|
|
|
+ 0xb39609a, 0xe3696be, 0x5a5ab58, 0xa019fc3, 0x3b281dd, 0xa2b2485,
|
|
|
+ 0x61ac0a2, 0xe3e2be7, 0xeb56730, 0xf19c34f },
|
|
|
+ { 0xa30241e, 0x2d25ce8, 0xb73d7a1, 0xf5661ea, 0xdaac9f4, 0x4611ed0,
|
|
|
+ 0x4ced72c, 0xd544234, 0xe92e985, 0xce78f52, 0x4da4aad, 0x6fe5dd4,
|
|
|
+ 0x1d363ce, 0xfcaddc6, 0xc9111bf, 0x3beb69c }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x940ebc9, 0xd2e7660, 0xb17bbe0, 0xe032018, 0x75c0575, 0xad49391,
|
|
|
+ 0x21c7f34, 0xdd0b147, 0x3e147e0, 0x52c2ba4, 0x0ee8973, 0x7dd03c6,
|
|
|
+ 0xecf2754, 0x5472e8d, 0xd6482bb, 0x17a1cd1 },
|
|
|
+ { 0x8128b3f, 0xdd43b84, 0xea7dd25, 0xf0cae34, 0xff07df2, 0x81ca99f,
|
|
|
+ 0x92ebbdc, 0x1c89597, 0x72155e6, 0x45c7a68, 0x39ddd08, 0x907a50e,
|
|
|
+ 0xbb2d89b, 0xbe398c2, 0x1b3b536, 0x38063f9 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xf843b23, 0x149fafb, 0xac7f22a, 0x00ab582, 0xf2f4d4c, 0xa3b981b,
|
|
|
+ 0x4341a22, 0x2ce1a65, 0x7c03b63, 0x68a4074, 0x12f2cf8, 0x63206a2,
|
|
|
+ 0x5149741, 0xc9961d3, 0xbc7099e, 0xfb85430 },
|
|
|
+ { 0x90a9e59, 0x9c91072, 0x06de367, 0x734e94a, 0xdb99214, 0x5cf3cbe,
|
|
|
+ 0x45b1fb9, 0xc6bce32, 0xdd7be0d, 0x1a82abe, 0xede7d1c, 0xf74976a,
|
|
|
+ 0x21503bd, 0x7025b7c, 0x0d096ab, 0xf789491 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x555a41b, 0x6bd48bb, 0x67de206, 0xfbdd0d0, 0xdd6dfd1, 0x98bc477,
|
|
|
+ 0x3e40b8a, 0x1d0693b, 0xda32ae4, 0x6e15563, 0xfcebaa2, 0x0194a20,
|
|
|
+ 0x0980a93, 0xda11615, 0x0109cec, 0x8e11920 },
|
|
|
+ { 0xffb9726, 0x8ea0552, 0x047e44b, 0xeba50a4, 0x60ddf76, 0xc050d24,
|
|
|
+ 0xac690e0, 0xe009204, 0x9b18edc, 0x47b8639, 0xc77f23f, 0x2f5b76a,
|
|
|
+ 0x0792905, 0x4296c24, 0x06f6dc7, 0x73f6b4a }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x3b10cad, 0xb6ef9ea, 0xf7c8fce, 0x312843d, 0x8bedf86, 0x5bdcd52,
|
|
|
+ 0xf6dd823, 0x2889059, 0x08bfde0, 0x04578e9, 0x123e2e5, 0x3245df3,
|
|
|
+ 0x7ee9e3a, 0xbf461d5, 0x6f94ceb, 0xddec2d4 },
|
|
|
+ { 0x145768f, 0x21b43b9, 0xdae962a, 0xe79a8f9, 0xcbb043f, 0xff1972b,
|
|
|
+ 0x239649b, 0xe3dcf6d, 0xc533b85, 0xed592bd, 0xdbe22d0, 0x14ff94f,
|
|
|
+ 0xf1d8e22, 0x6c4eb87, 0xd18cf6d, 0xd8d4c71 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x8d96345, 0xcda666c, 0x836cd21, 0x9ecaa25, 0x984606e, 0x6e885bd,
|
|
|
+ 0x804f054, 0x1dd5fef, 0x6959ae4, 0x9dfff6b, 0xc9b55cc, 0x99b9cf8,
|
|
|
+ 0x62b9b80, 0xb4716b0, 0x554b128, 0x13ec87c },
|
|
|
+ { 0x75aacc2, 0xe696d1f, 0x87fc5ff, 0xf78c993, 0x3809d42, 0x76c0947,
|
|
|
+ 0xb618fa8, 0x99ce62d, 0x2f53341, 0x35e3e02, 0x0db6c5e, 0x62fc1ac,
|
|
|
+ 0x00d8b47, 0xa1fb8e6, 0x58f0d1e, 0x0bc1070 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x16da513, 0x1f45269, 0xf5cf341, 0x1f2fc04, 0x64d23e0, 0xae92086,
|
|
|
+ 0xda8a113, 0x4e33082, 0x1cfc085, 0x2688ec6, 0x6e5327f, 0x6f2e8de,
|
|
|
+ 0xb4e48a8, 0x2070db3, 0x3240ade, 0xd662697 },
|
|
|
+ { 0xfbd997b, 0xa6b317f, 0x49e26bd, 0x9fa1b56, 0x8cba0f3, 0xcbf0d25,
|
|
|
+ 0x17b4745, 0x4a7791b, 0x5c9e190, 0x25f555b, 0x923ec4c, 0x7cd3940,
|
|
|
+ 0xe98f1b6, 0x16f4c6a, 0xbcd4e0f, 0x7962116 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x02491e3, 0x8d58fa3, 0x7ab3898, 0x7cf76c6, 0x647ebc7, 0xbc2f657,
|
|
|
+ 0xd25f5a3, 0x5f4bfe0, 0xd69505d, 0x503f478, 0x3fb6645, 0x4a889fc,
|
|
|
+ 0xfa86b18, 0x33e1bc1, 0x5508dd8, 0xabb234f },
|
|
|
+ { 0x9a05b48, 0x5348e1b, 0x64dc858, 0x57ac5f1, 0xec8a2d3, 0x21f4d38,
|
|
|
+ 0xa3a3e9d, 0x5ec6d3c, 0x560a0b8, 0xcd4062e, 0x3433f59, 0x49b74f7,
|
|
|
+ 0xcab14e3, 0xefd9d87, 0xeb964f5, 0x858ce7f }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0xeb731b4, 0x7577254, 0x4e2397e, 0x9fff1fb, 0xc821715, 0x749b145,
|
|
|
+ 0x2e65e67, 0x40619fe, 0x2e618d8, 0x57b8281, 0x707b83e, 0x063186c,
|
|
|
+ 0x31b24a2, 0xcfc80cb, 0xac75169, 0xcca6185 },
|
|
|
+ { 0xb255818, 0x6539f44, 0x0368bce, 0x5895da0, 0x17c7482, 0x841a309,
|
|
|
+ 0xb1a9c9e, 0x85469e1, 0xe4f7d9d, 0x05664c0, 0x7b35cc0, 0x8a06318,
|
|
|
+ 0xa0e9b0a, 0x214763a, 0x4b26ac2, 0x1bd872c }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xa93762b, 0x3578f97, 0x72d52bc, 0x434f69a, 0x22cb565, 0xddcca40,
|
|
|
+ 0xff20544, 0xa7d1e41, 0x8a66588, 0x823475d, 0x99d7baf, 0x9fc97c7,
|
|
|
+ 0x660e421, 0x15542f1, 0x843faf6, 0xa7d1f60 },
|
|
|
+ { 0x4063ccc, 0xbbfaab5, 0xa49855a, 0x3ad9bad, 0x5bddbfe, 0xffd5f1c,
|
|
|
+ 0xae87e59, 0x0e419c2, 0xf89956b, 0xdce6ed6, 0xccd8951, 0xf047c21,
|
|
|
+ 0xa83c991, 0x6ed4a1b, 0x2d28e0a, 0x85af86e }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x9ed48a8, 0x04433c4, 0x0bc375d, 0xeffa858, 0xfa6e3b5, 0xfb0e1b2,
|
|
|
+ 0xa1aadda, 0x51483a2, 0xf8b2ea8, 0x733448d, 0xf639f0c, 0xaa0513c,
|
|
|
+ 0xa23bf84, 0x6bc61a3, 0xdc2430d, 0x3e64f68 },
|
|
|
+ { 0xc5876b1, 0x51bf502, 0x1c0dd2a, 0x6b83375, 0x342914f, 0xe597be1,
|
|
|
+ 0xf8e632c, 0x43d5ab0, 0xd62587b, 0x2696715, 0xed34f24, 0xe87d20a,
|
|
|
+ 0xe18baf7, 0x25b7e14, 0xe22e084, 0xf5eb753 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x24d8295, 0x51da717, 0x18d1340, 0xd478e43, 0x2cf7f66, 0xacf94f4,
|
|
|
+ 0x3760711, 0x230d7d1, 0x5abc626, 0x078a66a, 0x6b5f6da, 0xd78b0bd,
|
|
|
+ 0x96d1d0b, 0x23a9713, 0x4bd960f, 0x87623d6 },
|
|
|
+ { 0x77db53f, 0x0841a99, 0xf4d03ee, 0x23c1a53, 0x1f95df1, 0x2f62c2e,
|
|
|
+ 0x116f4e7, 0xd1e2ec1, 0x34811a9, 0x896d2fe, 0xec8096e, 0xad65e2b,
|
|
|
+ 0xb1744a6, 0x09d36f9, 0xff5ddf7, 0x564bac7 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xc3f77cb, 0x48b41e2, 0x0968938, 0x5227673, 0xfd9b452, 0xff1b899,
|
|
|
+ 0x2e03908, 0x67cf3bf, 0x248a6fb, 0x3731d90, 0x256598f, 0xd800a05,
|
|
|
+ 0xbdc8530, 0x347d2f2, 0x7ad08a1, 0xc72a300 },
|
|
|
+ { 0x1d65f73, 0x5e5be74, 0x4206ead, 0x183d4ae, 0xade4013, 0xcb50c1c,
|
|
|
+ 0x3102483, 0x39db43d, 0x70d6325, 0x0eb49fa, 0xc1f02b9, 0xa18f6a2,
|
|
|
+ 0xdbf5e66, 0x3e6fe30, 0x3a82aa5, 0xac4eeb9 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x3613d47, 0x295affd, 0xb56f343, 0x7b7e68a, 0x92b173b, 0x9806296,
|
|
|
+ 0xbad35fb, 0x937061e, 0x5c21eea, 0x2501978, 0x787a746, 0xe92721b,
|
|
|
+ 0x3651631, 0x463c46c, 0xc6f2d5a, 0x6da4b5d },
|
|
|
+ { 0x6e6d18c, 0xcb67cc1, 0x0010588, 0x1b30d52, 0xdb1d1e8, 0x1bb6ea6,
|
|
|
+ 0xad11474, 0x9c6308a, 0x3d19b1c, 0xc316741, 0xbe4fb79, 0xf2e84d7,
|
|
|
+ 0xe050f77, 0xeccb873, 0xcc2bf86, 0xf7c8d80 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x7ab20e5, 0x16fe2e1, 0xecf3a92, 0x274dead, 0x0972f67, 0x9f43487,
|
|
|
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|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x1ae05e9, 0x1dae3bf, 0x1f21fef, 0x6a02996, 0x7aec3c6, 0x95df2b9,
|
|
|
+ 0xd83189b, 0x9abbc5a, 0x2d13140, 0xaf994af, 0x86aa406, 0xc3f8846,
|
|
|
+ 0x75284c5, 0xcd77e50, 0x2a9a4d7, 0x1c1e13d },
|
|
|
+ { 0x744b89d, 0x7f8815d, 0x2ba673e, 0xb189133, 0xd594570, 0x55ea93c,
|
|
|
+ 0xd61b041, 0x19c8a18, 0x8d2c580, 0x938ebaa, 0x05ba078, 0x9b4344d,
|
|
|
+ 0x8eaf9b7, 0x622da43, 0x9fea368, 0x809b807 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xc33b7a2, 0x3780e51, 0x387b1c8, 0xd7a205c, 0x4be60e4, 0x79515f8,
|
|
|
+ 0x1e18277, 0xde02a8b, 0xf0d9150, 0x4645c96, 0xe0b3fd1, 0x45f8acb,
|
|
|
+ 0x9b53ac3, 0x5d532ba, 0xb0557c9, 0x7984dcd },
|
|
|
+ { 0x8a92f01, 0x5ae5ca6, 0x9d569ca, 0xd2fbb3c, 0x0c297c1, 0x668cc57,
|
|
|
+ 0x6295e89, 0xa482943, 0xa33ad40, 0xf646bc1, 0xc3f425d, 0x066aaa4,
|
|
|
+ 0xd005de2, 0x23434cd, 0xdb35af4, 0x5aca9e9 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x6877c56, 0x2bca35c, 0xf0ddd7d, 0xab864b4, 0x404f46c, 0x5f6aa74,
|
|
|
+ 0x539c279, 0x72be164, 0xe0283cf, 0x1b1d73e, 0xad583d9, 0xe550f46,
|
|
|
+ 0xe739ad1, 0x4ac6518, 0x8d42100, 0x6b6def7 },
|
|
|
+ { 0xfa8468d, 0x4d36b8c, 0x5a3d7b8, 0x2cb3773, 0x5016281, 0x577f86f,
|
|
|
+ 0x9124733, 0xdb6fe5f, 0xe29e039, 0xacb6d2a, 0x580b8a1, 0x2ab8330,
|
|
|
+ 0x643b2d0, 0x130a4ac, 0x5e6884e, 0xa7996e3 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x60a0aa8, 0x6fb6277, 0xcbe04f0, 0xe046843, 0xe6ad443, 0xc01d120,
|
|
|
+ 0xabef2fc, 0xa42a05c, 0x12ff09c, 0x6b793f1, 0xa3e5854, 0x5734ea8,
|
|
|
+ 0x775f0ad, 0xe482b36, 0xf864a34, 0x2f4f60d },
|
|
|
+ { 0x84f2449, 0xf521c58, 0x9186a71, 0x58734a9, 0xac5eacc, 0x157f5d5,
|
|
|
+ 0x248ee61, 0x858d9a4, 0x48149c3, 0x0727e6d, 0xac9ec50, 0xd5c3eaa,
|
|
|
+ 0x20ee9b5, 0xa63a64a, 0x87be9de, 0x3f0dfc4 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xb13e3f4, 0x836349d, 0x3e9316d, 0xebdd026, 0x324fd6c, 0x3fd61e8,
|
|
|
+ 0x0964f41, 0x85dddfa, 0x52add1b, 0x06e72de, 0x8c4a9e2, 0xb752cff,
|
|
|
+ 0xfdf09f7, 0x53b0894, 0x0bc24fd, 0xd5220ab },
|
|
|
+ { 0xfb1981a, 0x8442b35, 0x3edd701, 0xa733a37, 0xd0ef089, 0x42b60c3,
|
|
|
+ 0x46e7bca, 0xa1b16ec, 0xa09aaf4, 0xc0df179, 0x638f3a1, 0xcd4f187,
|
|
|
+ 0x9eab1c2, 0x9af64f7, 0xd1d78e3, 0x86fed79 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xfe29980, 0x42c8d86, 0x6575660, 0x6657b81, 0x80f92ca, 0x82d52c6,
|
|
|
+ 0x02d42be, 0x8587af1, 0x6e8bdf0, 0xb515131, 0xc333495, 0x706e2d9,
|
|
|
+ 0x9673064, 0xd53601a, 0x8219099, 0x27b1fbb },
|
|
|
+ { 0x705f7c8, 0x3f0929d, 0xf3d6e6f, 0xff40b10, 0x026af5c, 0x673c703,
|
|
|
+ 0xe25a422, 0x2c1dce4, 0x3dad8b6, 0x5348bd7, 0xbe2c329, 0xc39b6b6,
|
|
|
+ 0xb921084, 0x47854ff, 0xb391f20, 0xb347b8b }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xeb9b774, 0x79fc841, 0xb4b6c1d, 0xf32da25, 0xfe492cb, 0xcbba76b,
|
|
|
+ 0xd623903, 0x76c51fc, 0xcf0705a, 0x114cf6f, 0x7815daf, 0x6b72049,
|
|
|
+ 0x473382e, 0x630b362, 0x9704db5, 0xbf40c3a },
|
|
|
+ { 0xc5456eb, 0xa8a9ddc, 0x72f2dc1, 0x2b4472a, 0xd6d6ef3, 0x9874444,
|
|
|
+ 0xa0ba5ed, 0x27e8d85, 0x194849f, 0x5d225b4, 0xebaa40d, 0xe852cd6,
|
|
|
+ 0x8d4bf3f, 0xb669c24, 0x2343991, 0xa8601eb }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x59502d3, 0x8a04854, 0xe269a7b, 0xcab27ee, 0x4875ada, 0x4179307,
|
|
|
+ 0xe2405f9, 0x179e685, 0x7b28963, 0x0d7b698, 0x422a43e, 0x80c9db8,
|
|
|
+ 0xa0f43ee, 0xf5ff318, 0x4ba7aa7, 0x7a92805 },
|
|
|
+ { 0x0c0834e, 0xa5c79fe, 0x1f849ec, 0x837ca0d, 0x628ab7b, 0xfe0d7fa,
|
|
|
+ 0x6edd19a, 0x94bcb95, 0x2226fbf, 0xa18bc93, 0xaad54a3, 0x2795379,
|
|
|
+ 0x371129e, 0xceeacf8, 0xa588be5, 0x65ca57f }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x2caa330, 0x7a578b5, 0xd8ca34a, 0x7c21944, 0x6447282, 0x6c0fbbb,
|
|
|
+ 0xf90b2e5, 0xa8a9957, 0x6586b71, 0xbbe1066, 0x49138a2, 0x716a902,
|
|
|
+ 0xe7ed66d, 0x2fa6034, 0x2b9916a, 0x56f77ed },
|
|
|
+ { 0xbddefb3, 0x69f1e26, 0x8c08420, 0xa497809, 0x09bc184, 0xc3377eb,
|
|
|
+ 0xbe6dade, 0x796ce0c, 0xd103bbb, 0x3be0625, 0x992685c, 0x01be27c,
|
|
|
+ 0x7755f9f, 0xc0e2559, 0x1c0dbfa, 0x165c40d }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x659c761, 0xc63a397, 0x630fbad, 0x10a0e5b, 0x655ac56, 0xf21e8a6,
|
|
|
+ 0xc1181e2, 0xe8580fa, 0x0a84b5c, 0xbfc2d9c, 0x7afd5d1, 0x2cdbaff,
|
|
|
+ 0xf61e85a, 0x95f1182, 0x719eaf4, 0x1173e96 },
|
|
|
+ { 0xc6de8b9, 0xc06d55e, 0xafcbcaa, 0x1b4c8eb, 0xbc2bbcd, 0x52af5cb,
|
|
|
+ 0x77bcd10, 0x564fab8, 0xae85a6e, 0xfd53a18, 0x94c712f, 0x2257859,
|
|
|
+ 0x1352121, 0x29b11d7, 0xc40491a, 0xab1cb76 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xce32eb4, 0xb4e8ca8, 0xb250b49, 0x7e484ac, 0xa3e31a2, 0x062c6f7,
|
|
|
+ 0x625d1fc, 0x497fd83, 0x362dda7, 0x98f821c, 0x6be3111, 0xcae1f8f,
|
|
|
+ 0x5d4fa42, 0x9077e95, 0xa65855a, 0xa589971 },
|
|
|
+ { 0x28832a9, 0xda6321d, 0x3936e9e, 0xf9ef5dc, 0xc9797ef, 0xa37f117,
|
|
|
+ 0xdb581be, 0x0eb3c80, 0xbaa0002, 0x207c5c4, 0xf38faa0, 0xc0401b5,
|
|
|
+ 0xd0f1e6e, 0xceee523, 0xd1f0045, 0x8d27a5f }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xcf0af29, 0x9411063, 0x89a6693, 0x3043857, 0x640145e, 0x9a9fb8f,
|
|
|
+ 0x54832eb, 0x7d82fe9, 0x898c520, 0xf2789e1, 0xf948dc0, 0x448b402,
|
|
|
+ 0x68996dd, 0xeca8fdf, 0xa149b2f, 0x22227e9 },
|
|
|
+ { 0x8e62d6a, 0x63509ff, 0x8c9c57f, 0xe98d81c, 0x1fe3bed, 0xd387407,
|
|
|
+ 0x539538f, 0xf1db013, 0x48418ce, 0xb04092e, 0xd6d9d4d, 0xbbf8e76,
|
|
|
+ 0x2cec5ae, 0x2ea9cda, 0x5078fa9, 0x8414b3e }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xd68a073, 0x5ad1cdb, 0xc18b591, 0xd4cedaf, 0x8e4c1c9, 0x7826707,
|
|
|
+ 0x9ca302a, 0x9b8d920, 0x326115b, 0x3101bd2, 0x4c2717a, 0x6f154b5,
|
|
|
+ 0x263e84b, 0x618c31b, 0xbbd6942, 0x12c4138 },
|
|
|
+ { 0x80da426, 0xf9ead25, 0x47d9680, 0xe748e99, 0x8a4210e, 0x9b396a3,
|
|
|
+ 0xf4b8f72, 0xfaf03dd, 0x66159e7, 0xbd94a52, 0x1d4c7cb, 0x5e73049,
|
|
|
+ 0x7910f38, 0x31d1f9a, 0x08d6dd1, 0x4fd10ca }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x9f2331e, 0x4f510ac, 0x7e3dcc2, 0xee872dc, 0xa0a0c73, 0x4a11a32,
|
|
|
+ 0xaa5a630, 0x27e5803, 0x7af4a8a, 0xe5ae503, 0x9fffeb0, 0x2dcdeba,
|
|
|
+ 0x719d91f, 0x8c27748, 0xb9cc61c, 0xd3b5b62 },
|
|
|
+ { 0xcca7939, 0x998ac90, 0x64514e5, 0xc22b598, 0xb35738a, 0x950aaa1,
|
|
|
+ 0xdab0264, 0x4b208bb, 0xa557d2e, 0x6677931, 0xf7c17d3, 0x2c696d8,
|
|
|
+ 0x3e15c51, 0x1672d4a, 0x3db0e82, 0x95fab66 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x6ff205e, 0x3d42734, 0x0ea9fbe, 0x7f187d9, 0x466b2af, 0xbd9367f,
|
|
|
+ 0x03daf2f, 0x188e532, 0x27b54d8, 0xefe1329, 0xef70435, 0x14faf85,
|
|
|
+ 0x1ec95c4, 0xa506128, 0xc22cba7, 0xad01705 },
|
|
|
+ { 0x6197333, 0x7d2dfa6, 0x8b4f6ed, 0xedd7f07, 0x75df105, 0xe0cb685,
|
|
|
+ 0x80f76bc, 0x47c9ddb, 0x9073c54, 0x49ab531, 0xe607f44, 0x845255a,
|
|
|
+ 0xcc74b7c, 0x0b4ed9f, 0x0f5c3a6, 0xcfb52d5 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xc278776, 0x545c7c6, 0x98c30f0, 0x92a39ae, 0xd2f4680, 0x8aa8c01,
|
|
|
+ 0x6b7f840, 0xa5409ed, 0xdcb24e7, 0x0c450ac, 0xc5770d9, 0x5da6fb2,
|
|
|
+ 0x8658333, 0x5b8e8be, 0x67ea4ad, 0xb26bf4a },
|
|
|
+ { 0xc7d91fa, 0x2e30c81, 0x0eeb69f, 0x6e50a49, 0xee4bc26, 0x9458c2b,
|
|
|
+ 0x33be250, 0x419acf2, 0x87881ab, 0x79d6f81, 0x403b1be, 0x694565d,
|
|
|
+ 0x234fe1d, 0x34b3990, 0x2132b38, 0x60997d7 }
|
|
|
+ },
|
|
|
+},
|
|
|
+{
|
|
|
+ {
|
|
|
+ { 0x26975dc, 0x00a9741, 0x6cf94e7, 0x42161c4, 0xc64ed99, 0xcc9fe4b,
|
|
|
+ 0x4680570, 0x020019a, 0x698da0d, 0x885595a, 0x77dd962, 0x008444b,
|
|
|
+ 0xa4fea0e, 0xbf3c22d, 0x2c81245, 0xc463048 },
|
|
|
+ { 0x793ab18, 0xcb248c5, 0xeb4320b, 0x4dc7a20, 0x1572b7d, 0x9a0906f,
|
|
|
+ 0xf9ac20f, 0xd5b3019, 0x34520a3, 0x79b1bf5, 0x69b5322, 0x788dfe8,
|
|
|
+ 0x455b7e2, 0x9a05298, 0x016bca9, 0x2f4aecb }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x8745618, 0x414d379, 0xb7c983c, 0x64ba22e, 0x9f9d532, 0x9a5d19f,
|
|
|
+ 0x44a80c8, 0x81a00d8, 0xcae98d6, 0xb9e24f5, 0xaca965a, 0x6c3769c,
|
|
|
+ 0xf6e4e6d, 0x50d6081, 0x54422a6, 0x0d96980 },
|
|
|
+ { 0x5cdd790, 0xbd7e792, 0x6a35219, 0xcff65da, 0x8b60ebe, 0x40dc363,
|
|
|
+ 0x92a50dc, 0x84bee74, 0x15ad65e, 0x57d4be4, 0x1a6d1d3, 0xc54256b,
|
|
|
+ 0x45717cc, 0x141c649, 0xcd1c736, 0x05eb609 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x1e3c7ec, 0xfd52eab, 0x9f24895, 0xa4a5eca, 0x79fdb83, 0xaaa2a8d,
|
|
|
+ 0x72bdfda, 0xd105e60, 0x681d97e, 0x59e6ae2, 0x8e8077f, 0xfedf8e0,
|
|
|
+ 0x629e462, 0xb06d0ad, 0x96fa863, 0x8c7c2d0 },
|
|
|
+ { 0xee8fc91, 0x5eecc4c, 0x9e61174, 0x5e83ab2, 0xb28c02d, 0x1fd8925,
|
|
|
+ 0x2072864, 0x93be538, 0x24c984e, 0xda0c886, 0xa008286, 0xdcf9f0c,
|
|
|
+ 0xa58ba75, 0x1ecb5a6, 0xc2e3c83, 0x1d9b890 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xeeee062, 0x19e866e, 0x4f7b387, 0x31c1c7f, 0x1c06652, 0x9be6018,
|
|
|
+ 0x2b68bbb, 0xc00a93a, 0x9d52b2b, 0x54c65d6, 0xe8b744a, 0x4591416,
|
|
|
+ 0x9a64ab6, 0x641bcca, 0xab08098, 0xf22bcb1 },
|
|
|
+ { 0xf1f726c, 0x3c0db8f, 0x9d2e6a6, 0x4f5739e, 0x45c9530, 0x5cb669b,
|
|
|
+ 0x7b472d0, 0x861b04e, 0x894da77, 0x3e30515, 0xc9ac39b, 0x3344685,
|
|
|
+ 0x73bdd29, 0x9e17305, 0x808dc85, 0x9cac12c }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x5e27087, 0xf152b86, 0x90a580e, 0x267bd85, 0x8baafc1, 0xba79cec,
|
|
|
+ 0x9442686, 0x6140ab1, 0x5b31693, 0xa67090c, 0x28b4117, 0x50a103a,
|
|
|
+ 0x0ddc08f, 0x7722e61, 0xe6569b2, 0x5d19d43 },
|
|
|
+ { 0x5962bf6, 0x70e0c52, 0xfb5fb02, 0x808e316, 0x5b667be, 0x3fb80da,
|
|
|
+ 0xfcfacec, 0x8aa366e, 0x134280e, 0xcb0b3e7, 0xcd7d944, 0x0bf1de4,
|
|
|
+ 0xd092df5, 0x0cd23be, 0xa153a0c, 0xc9a6a79 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x2d5a4b7, 0x1c69ad0, 0xd9e6f4a, 0x4bb28d0, 0xa984fc6, 0x815308c,
|
|
|
+ 0x9037ca5, 0x40929c7, 0x1bd0357, 0x0ea2b49, 0x42aad4e, 0xec17e5b,
|
|
|
+ 0x18e7235, 0x1f32ade, 0xa96a9d3, 0xbc60b05 },
|
|
|
+ { 0xe20f707, 0x3b0229a, 0x56bdfad, 0xd635050, 0xd8b2e1e, 0xac2d922,
|
|
|
+ 0x235c748, 0x92b2998, 0xd766f97, 0x6002c3a, 0x1a2a862, 0x9919800,
|
|
|
+ 0xb58b684, 0x2af7567, 0xaaafce5, 0xd8fe707 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x5df7a4b, 0x54487ab, 0xc57ccc2, 0x51cccde, 0x7510b53, 0x2394327,
|
|
|
+ 0xf555de3, 0x3a09f02, 0x1be484d, 0xa696aec, 0x37817a2, 0x56f459f,
|
|
|
+ 0x623dcb4, 0x8d8f61c, 0x5335656, 0xc52223c },
|
|
|
+ { 0xb49914a, 0xf634111, 0x8e4f9bb, 0xbf8e1ab, 0xf4dba02, 0x2f59578,
|
|
|
+ 0xe004319, 0x2a94199, 0x654d005, 0x87931f0, 0x6fa0814, 0x7df57d9,
|
|
|
+ 0xa154031, 0xc8da316, 0x41f658b, 0x2a44ac0 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x9e34ac6, 0xfb5f4f8, 0x97790f2, 0x0a1b10b, 0x4b8a06c, 0x58fe4e7,
|
|
|
+ 0x955f27c, 0x10c1710, 0xd5ebe19, 0x77b798a, 0x1f1c2dc, 0xaf1c35b,
|
|
|
+ 0xa1f8d69, 0xc25b8e6, 0xf76bf23, 0x49cf751 },
|
|
|
+ { 0x436f7b7, 0x15cb2db, 0x7e74d1a, 0x186d7c2, 0xc00a415, 0x60731de,
|
|
|
+ 0x15f0772, 0xea1e156, 0x714463f, 0xf02d591, 0x51adeb1, 0x26a0c64,
|
|
|
+ 0xcc5229e, 0x20174cd, 0xefd512a, 0xb817e50 }
|
|
|
+ },
|
|
|
+},
|
|
|
+};
|
|
|
+
|
|
|
+static const ge448_precomp base_i[16] = {
|
|
|
+ {
|
|
|
+ { 0x70cc05e, 0x26a82bc, 0x0938e26, 0x80e18b0, 0x511433b, 0xf72ab66,
|
|
|
+ 0x412ae1a, 0xa3d3a46, 0xa6de324, 0x0f1767e, 0x4657047, 0x36da9e1,
|
|
|
+ 0x5a622bf, 0xed221d1, 0x66bed0d, 0x4f1970c },
|
|
|
+ { 0x230fa14, 0x08795bf, 0x7c8ad98, 0x132c4ed, 0x9c4fdbd, 0x1ce67c3,
|
|
|
+ 0x73ad3ff, 0x05a0c2d, 0x7789c1e, 0xa398408, 0xa73736c, 0xc7624be,
|
|
|
+ 0x03756c9, 0x2488762, 0x16eb6bc, 0x693f467 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x6ff2f8f, 0x2817328, 0xda85757, 0xb769465, 0xfd6e862, 0xf7f6271,
|
|
|
+ 0x8daa9cb, 0x4a3fcfe, 0x2ba077a, 0xda82c7e, 0x41b8b8c, 0x9433322,
|
|
|
+ 0x4316cb6, 0x6455bd6, 0xb9108af, 0x0865886 },
|
|
|
+ { 0x88ed6fc, 0x22ac135, 0x02dafb8, 0x9a68fed, 0x7f0bffa, 0x1bdb676,
|
|
|
+ 0x8bb3a33, 0xec4e1d5, 0xce43c82, 0x56c3b9f, 0xa8d9523, 0xa6449a4,
|
|
|
+ 0xa7ad43a, 0xf706cbd, 0xbd5125c, 0xe005a8d }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x2030034, 0xa99d109, 0x6f950d0, 0x2d8cefc, 0xc96f07b, 0x7a920c3,
|
|
|
+ 0x08bc0d5, 0x9588128, 0x6d761e8, 0x62ada75, 0xbcf7285, 0x0def80c,
|
|
|
+ 0x01eedb5, 0x0e2ba76, 0x5a48dcb, 0x7a9f933 },
|
|
|
+ { 0x2f435eb, 0xb473147, 0xf225443, 0x5512881, 0x33c5840, 0xee59d2b,
|
|
|
+ 0x127d7a4, 0xb698017, 0x86551f7, 0xb18fced, 0xca1823a, 0x0ade260,
|
|
|
+ 0xce4fd58, 0xd3b9109, 0xa2517ed, 0xadfd751 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xeb5eaf7, 0xdf9567c, 0x78ac7d7, 0x110a6b4, 0x4706e0b, 0x2d33501,
|
|
|
+ 0x0b5a209, 0x0df9c7b, 0x568e684, 0xba4223d, 0x8c3719b, 0xd78af2d,
|
|
|
+ 0xa5291b6, 0x77467b9, 0x5c89bef, 0x079748e },
|
|
|
+ { 0xdac377f, 0xe20d3fa, 0x72b5c09, 0x34e8669, 0xc40bbb7, 0xd8687a3,
|
|
|
+ 0xd2f84c9, 0x7b3946f, 0xa78f50e, 0xd00e40c, 0x17e7179, 0xb875944,
|
|
|
+ 0xcb23583, 0x9c7373b, 0xc90fd69, 0x7ddeda3 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x6ab686b, 0x3d0def7, 0x49f7c79, 0x1a467ec, 0xc8989ed, 0x3e53f4f,
|
|
|
+ 0x430a0d9, 0x101e344, 0x8ad44ee, 0xa3ae731, 0xae1d134, 0xaefa6cd,
|
|
|
+ 0x824ad4d, 0xaa8cd7d, 0xed584fc, 0xef1650c },
|
|
|
+ { 0x4f4754f, 0xa74df67, 0xef3fb8b, 0xf52cea8, 0x2971140, 0x47c32d4,
|
|
|
+ 0xa256fbb, 0x391c15d, 0xa605671, 0xc165fab, 0x87993b9, 0xf2518c6,
|
|
|
+ 0xbd5a84d, 0x2daf7ac, 0x98f12ae, 0x1560b62 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x54dc10a, 0xef4da02, 0x5940db8, 0x6311865, 0x82f2948, 0xe20b149,
|
|
|
+ 0x5581dba, 0x67b9377, 0x04f5029, 0x422ee71, 0x5122d34, 0x5d440db,
|
|
|
+ 0x1a4c640, 0xb1e56d7, 0xc2408ee, 0xbf12abb },
|
|
|
+ { 0x016af01, 0x0cc9f86, 0xf3d8cab, 0x88366ab, 0xa2efe12, 0x85dda13,
|
|
|
+ 0x5d00674, 0x390df60, 0x6d187f7, 0xf18f580, 0xf0c5d20, 0x28c900f,
|
|
|
+ 0x3e01733, 0xad30812, 0x54bf2fd, 0x42d35b5 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x2ffb1f1, 0x009135f, 0x8f9c605, 0x099fc7e, 0x26bfa5a, 0xcc67da6,
|
|
|
+ 0x344552b, 0xc186d12, 0x1b339e1, 0xb523250, 0xc9708c5, 0x70a544f,
|
|
|
+ 0x1e928e7, 0x06baaec, 0xef0f50f, 0x0baedd2 },
|
|
|
+ { 0xbf479e5, 0x535d6d8, 0xe4ec3e9, 0x156e536, 0xddb9be2, 0x3165741,
|
|
|
+ 0x59fd736, 0x988af71, 0x2e33ddd, 0x13d8a78, 0x4e69002, 0x5460421,
|
|
|
+ 0x804a268, 0x34d56e0, 0x0e52a4c, 0xc59b84f }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x24729d9, 0x525d45f, 0x8712327, 0x5768aba, 0x43035db, 0xa25e43b,
|
|
|
+ 0x927ef21, 0x15a1ee8, 0x6056112, 0xa785d21, 0xd508af9, 0x45e2fbf,
|
|
|
+ 0x37ba969, 0xb6f721a, 0x216d8d3, 0x30d6d8c },
|
|
|
+ { 0x52074c3, 0x3065e08, 0x2a0684e, 0xfa40b4a, 0x763f955, 0x851325a,
|
|
|
+ 0x9f25900, 0xd4ef19c, 0xf665756, 0x799c869, 0x3312990, 0x7b05222,
|
|
|
+ 0x28db802, 0xc986c2b, 0x28ade0a, 0xf48fb8f }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x1649b68, 0x1e46173, 0x5beb9dc, 0xa96e5d6, 0x481935d, 0x765ddff,
|
|
|
+ 0x9f3bf2a, 0x6cf132c, 0x7c35658, 0x9f6c5c9, 0x4696e60, 0x99cd139,
|
|
|
+ 0x9c0d5e4, 0x99fa924, 0x8845a95, 0x1acd063 },
|
|
|
+ { 0x3636087, 0x0b06541, 0xea17b7f, 0xea20e78, 0x6161967, 0x20afc5f,
|
|
|
+ 0xdc81028, 0xfd6c8a2, 0xe32c8fd, 0x4ef1357, 0x00e4a88, 0x8aa4004,
|
|
|
+ 0x48cb82f, 0xd6fcaef, 0xb3cd4fa, 0x7ba7c6d }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xd19c7ab, 0xf843473, 0xc655c4d, 0x968e76d, 0xc4b9c2f, 0x52c87d9,
|
|
|
+ 0xe4aa082, 0x65f641a, 0x33c3603, 0x491a397, 0x5810098, 0xa606ffe,
|
|
|
+ 0x8bf8ad4, 0x09920e6, 0x6db7882, 0x691a0c8 },
|
|
|
+ { 0xa4d3ef5, 0x5205883, 0xacf2efe, 0xee839b7, 0xc00ca66, 0x4b78e2a,
|
|
|
+ 0xf9fcb91, 0xbe3f071, 0xbf6943a, 0x61e66c9, 0x061b79d, 0xe9b4e57,
|
|
|
+ 0x56c06bd, 0x8d1b01b, 0xdf76ae5, 0x0dfa315 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xf1fd093, 0x803df65, 0x489b77e, 0x1cd6523, 0xc20e295, 0x2cd2e15,
|
|
|
+ 0x9b912d1, 0xcd490be, 0x2e886d2, 0xdd9a2ff, 0xfe9d72a, 0xa3c836d,
|
|
|
+ 0x298e0c1, 0xfcad5f2, 0x4bcf067, 0xed126e2 },
|
|
|
+ { 0x3dc81bc, 0x1e33953, 0xece6a08, 0xbea4d76, 0x991b252, 0x1d15de3,
|
|
|
+ 0xe6daf97, 0x74cc5cf, 0x0826493, 0x5ad343f, 0x1064049, 0x2d38a47,
|
|
|
+ 0xffcfa4d, 0xf7f47b9, 0x418066c, 0xef14490 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x9bb55ab, 0x4e7f86b, 0x3f496a3, 0x310d785, 0x0dec42c, 0xbd682fc,
|
|
|
+ 0x411d32a, 0xbde047a, 0xc5a5ea2, 0xea639b4, 0xba08fa1, 0x5052078,
|
|
|
+ 0x07729f2, 0xc968b23, 0x23d3e28, 0x567b5a6 },
|
|
|
+ { 0x977fbf7, 0x171e825, 0xbe990aa, 0x0319c70, 0xe12cd69, 0x8f65023,
|
|
|
+ 0xf5015e6, 0x1fb9b19, 0x3568a7c, 0x0083f60, 0x1f3c5ac, 0xba3d30b,
|
|
|
+ 0x3d7a988, 0xe7b509d, 0xcd0f6b6, 0x2318b99 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x93ab2cf, 0x54d3b87, 0xd2d8306, 0x366abea, 0xd7a4977, 0x66e8eb6,
|
|
|
+ 0xae0072e, 0xa61888c, 0xdbc3315, 0x9eeeef5, 0x163e7f5, 0x93f09db,
|
|
|
+ 0x59ade9a, 0xee90959, 0xce59be0, 0xaf7f578 },
|
|
|
+ { 0x5ece59e, 0x24bfd8d, 0x3689523, 0x8aa698b, 0x2de92cf, 0xa9a65de,
|
|
|
+ 0xa6ad300, 0xec11dbc, 0x09f88ca, 0x217f3fa, 0xb4d6af7, 0xf6c33e3,
|
|
|
+ 0x1d86d2d, 0xcd3bfa2, 0x5f13f25, 0x1497f83 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0xcd03d1d, 0xa579568, 0xe158af6, 0xd717cda, 0x389a19f, 0x59eda97,
|
|
|
+ 0x099e99c, 0xb32c370, 0xdabb591, 0xa2dba91, 0x77c2c97, 0x6d697d5,
|
|
|
+ 0xd43fa6d, 0x5423fc2, 0x0b382bf, 0x56ea8a5 },
|
|
|
+ { 0xd80c11a, 0x4a987ba, 0x7d590a5, 0xe4cde21, 0xf97e559, 0x3dd8860,
|
|
|
+ 0x43b593c, 0xff45e25, 0x5343cb5, 0x00eb453, 0x7bbfbdd, 0x06b9b99,
|
|
|
+ 0x16aea24, 0x4da36b7, 0x57a624e, 0x2476517 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x3474e0d, 0x32207d0, 0xb41cc73, 0x3ffbf04, 0x319eb39, 0x5c4dc45,
|
|
|
+ 0x758b463, 0xfee29be, 0xc30c7a7, 0xcc8a381, 0x9fe0e53, 0x147f4e4,
|
|
|
+ 0xe35a2de, 0x05b2e26, 0x92f3666, 0x4362f02 },
|
|
|
+ { 0x8474b85, 0x0476d0c, 0xccaf108, 0x9d8c65f, 0x1d54b6a, 0xf58d404,
|
|
|
+ 0xf38e4b0, 0x3ee6862, 0x3b44f54, 0x7c7c9d5, 0x0fb0db5, 0x36a3fd8,
|
|
|
+ 0x18a8ac8, 0xfcd94ba, 0x8f35c05, 0xc1b1d56 }
|
|
|
+ },
|
|
|
+ {
|
|
|
+ { 0x1bdd30d, 0x16539fc, 0x8df4afb, 0x1356e53, 0x5a1aedb, 0xc0545d8,
|
|
|
+ 0x489396b, 0xeb2037a, 0x5660894, 0x897fcbd, 0xb7d104a, 0x02a58a9,
|
|
|
+ 0xc96b980, 0x57fa24c, 0x5bd8946, 0xf6448e3 },
|
|
|
+ { 0x8805c83, 0xee72741, 0x992cfc6, 0x10fa274, 0x9e66b21, 0x9514193,
|
|
|
+ 0xbd08009, 0xe0ffa44, 0x20da22b, 0x1743322, 0x59e6831, 0x4891ff3,
|
|
|
+ 0xa7d687b, 0x407ed73, 0x51d99cf, 0x2fb4e07 }
|
|
|
+ },
|
|
|
+};
|
|
|
+#endif
|
|
|
+
|
|
|
+/* Set the 0 point.
|
|
|
+ *
|
|
|
+ * p [in] Point to set to 0.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_0(ge448_p2 *p)
|
|
|
+{
|
|
|
+ fe448_0(p->X);
|
|
|
+ fe448_1(p->Y);
|
|
|
+ fe448_1(p->Z);
|
|
|
+}
|
|
|
+
|
|
|
+/* Set the precompute point to 0.
|
|
|
+ *
|
|
|
+ * p [in] Precompute point to set.
|
|
|
+ */
|
|
|
+static void ge448_precomp_0(ge448_precomp *p)
|
|
|
+{
|
|
|
+ fe448_0(p->x);
|
|
|
+ fe448_1(p->y);
|
|
|
+}
|
|
|
+
|
|
|
+/* Double the point on the Twisted Edwards curve. r = 2.p
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * p [in] Point to double.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_dbl(ge448_p2 *r,const ge448_p2 *p)
|
|
|
+{
|
|
|
+ ge448 t0[GE448_WORDS];
|
|
|
+ ge448 t1[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_add(t0, p->X, p->Y); /* t0 = B1 = X1+Y1 */
|
|
|
+ fe448_reduce(t0);
|
|
|
+ fe448_sqr(t0, t0); /* t0 = B = (X1+Y1)^2 */
|
|
|
+ fe448_sqr(r->X, p->X); /* r->X = C = X1^2 */
|
|
|
+ fe448_sqr(r->Y, p->Y); /* r->Y = D = Y1^2 */
|
|
|
+ fe448_add(t1, r->X, r->Y); /* t1 = E = C+D */
|
|
|
+ fe448_reduce(t1);
|
|
|
+ fe448_sub(r->Y, r->X, r->Y); /* r->Y = Y31 = C-D */
|
|
|
+ fe448_sqr(r->Z, p->Z); /* r->Z = H = Z1^2 */
|
|
|
+ fe448_add(r->Z, r->Z, r->Z); /* r->Z = J1 = 2*H */
|
|
|
+ fe448_sub(r->Z, t1, r->Z); /* r->Z = J = E-2*H */
|
|
|
+ fe448_reduce(r->Z);
|
|
|
+ fe448_sub(r->X, t0, t1); /* r->X = X31 = B-E */
|
|
|
+ fe448_mul(r->X, r->X, r->Z); /* r->X = X3 = (B-E)*J */
|
|
|
+ fe448_mul(r->Y, r->Y, t1); /* r->Y = Y3 = E*(C-D) */
|
|
|
+ fe448_mul(r->Z, t1, r->Z); /* r->Z = Z3 = E*J */
|
|
|
+}
|
|
|
+
|
|
|
+/* Add two point on the Twisted Edwards curve. r = p + q
|
|
|
+ * Second point has z-ordinate of 1.
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * p [in] Point to add.
|
|
|
+ * q [in] Point to add.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_madd(ge448_p2 *r, const ge448_p2 *p,
|
|
|
+ const ge448_precomp *q)
|
|
|
+{
|
|
|
+ ge448 t0[GE448_WORDS];
|
|
|
+ ge448 t1[GE448_WORDS];
|
|
|
+ ge448 t2[GE448_WORDS];
|
|
|
+ ge448 t3[GE448_WORDS];
|
|
|
+ ge448 t4[GE448_WORDS];
|
|
|
+
|
|
|
+ /* p->Z = A */
|
|
|
+ fe448_mul(t1, p->X, q->x); /* t1 = C = X1*X2 */
|
|
|
+ fe448_mul(t2, p->Y, q->y); /* t2 = D = Y1*Y2 */
|
|
|
+ fe448_mul(t3, t1, t2); /* t3 = E1 = C*D */
|
|
|
+ fe448_mul39081(t3, t3); /* t3 = E = d*C*D */
|
|
|
+ fe448_sqr(t0, p->Z); /* t0 = B = A^2 */
|
|
|
+ fe448_add(t4, t0, t3); /* t4 = F = B-(-E) */
|
|
|
+ fe448_sub(t0, t0, t3); /* t0 = G = B+(-E) */
|
|
|
+ fe448_reduce(t0);
|
|
|
+ fe448_add(r->X, p->X, p->Y); /* r->X = H1 = X1+Y1 */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_add(r->Y, q->x, q->y); /* r->Y = H2 = X2+Y2 */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->X, r->X, r->Y); /* r->X = H = (X1+Y1)*(X2+Y2) */
|
|
|
+ fe448_sub(r->X, r->X, t1); /* r->X = X31 = H-C */
|
|
|
+ fe448_sub(r->X, r->X, t2); /* r->X = X32 = H-C-D */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_mul(r->X, r->X, t4); /* r->X = X33 = F*(H-C-D) */
|
|
|
+ fe448_mul(r->X, r->X, p->Z); /* r->X = X3 = A*F*(H-C-D) */
|
|
|
+ fe448_sub(r->Y, t2, t1); /* r->Y = Y31 = D-C */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->Y, r->Y, t0); /* r->Y = Y32 = G*(D-C) */
|
|
|
+ fe448_mul(r->Y, r->Y, p->Z); /* r->Y = Y3 = A*F*(D-C) */
|
|
|
+ fe448_mul(r->Z, t4, t0); /* r->Z = Z3 = F*G */
|
|
|
+}
|
|
|
+
|
|
|
+/* Subtract one point from another on the Twisted Edwards curve. r = p - q
|
|
|
+ * Second point has z-ordinate of 1.
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * p [in] Point to subtract from.
|
|
|
+ * q [in] Point to subtract.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_msub(ge448_p2 *r, const ge448_p2 *p,
|
|
|
+ const ge448_precomp *q)
|
|
|
+{
|
|
|
+ ge448 t0[GE448_WORDS];
|
|
|
+ ge448 t1[GE448_WORDS];
|
|
|
+ ge448 t2[GE448_WORDS];
|
|
|
+ ge448 t3[GE448_WORDS];
|
|
|
+ ge448 t4[GE448_WORDS];
|
|
|
+
|
|
|
+ /* p->Z = A */
|
|
|
+ fe448_sqr(t0, p->Z); /* t0 = B = A^2 */
|
|
|
+ fe448_mul(t1, p->X, q->x); /* t1 = C = X1*X2 */
|
|
|
+ fe448_mul(t2, p->Y, q->y); /* t2 = D = Y1*Y2 */
|
|
|
+ fe448_mul(t3, t1, t2); /* t3 = E1 = C*D */
|
|
|
+ fe448_mul39081(t3, t3); /* t3 = E = d*C*D */
|
|
|
+ fe448_sub(t4, t0, t3); /* t4 = F = B-(--E) */
|
|
|
+ fe448_add(t0, t0, t3); /* t0 = G = B+(--E) */
|
|
|
+ fe448_reduce(t0);
|
|
|
+ fe448_add(r->X, p->X, p->Y); /* r->X = H1 = X1+Y1 */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_sub(r->Y, q->y, q->x); /* r->Y = H2 = Y2+(-X2) */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->X, r->X, r->Y); /* r->X = H = (X1+Y1)*(X2+Y2) */
|
|
|
+ fe448_add(r->X, r->X, t1); /* r->X = X31 = H-(-C) */
|
|
|
+ fe448_sub(r->X, r->X, t2); /* r->X = X32 = H-(-C)-D */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_mul(r->X, r->X, t4); /* r->X = X33 = F*(H-C-D) */
|
|
|
+ fe448_mul(r->X, r->X, p->Z); /* r->X = X3 = A*F*(H-C-D) */
|
|
|
+ fe448_add(r->Y, t2, t1); /* r->Y = Y31 = D-C */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->Y, r->Y, t0); /* r->Y = Y32 = G*(D-C) */
|
|
|
+ fe448_mul(r->Y, r->Y, p->Z); /* r->Y = Y3 = A*F*(D-C) */
|
|
|
+ fe448_mul(r->Z, t4, t0); /* r->Z = Z3 = F*G */
|
|
|
+}
|
|
|
+
|
|
|
+/* Add two point on the Twisted Edwards curve. r = p + q
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * p [in] Point to add.
|
|
|
+ * q [in] Point to add.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_add(ge448_p2* r, const ge448_p2* p,
|
|
|
+ const ge448_p2* q)
|
|
|
+{
|
|
|
+ ge448 t0[GE448_WORDS];
|
|
|
+ ge448 t1[GE448_WORDS];
|
|
|
+ ge448 t2[GE448_WORDS];
|
|
|
+ ge448 t3[GE448_WORDS];
|
|
|
+ ge448 t4[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_mul(t1, p->X, q->X); /* t1 = C = X1*X2 */
|
|
|
+ fe448_mul(t2, p->Y, q->Y); /* t2 = D = Y1*Y2 */
|
|
|
+ fe448_mul(t3, t1, t2); /* t3 = E1 = C*D */
|
|
|
+ fe448_mul39081(t3, t3); /* t3 = E = d*C*D */
|
|
|
+ fe448_mul(r->Z, p->Z, q->Z); /* r->Z = A = Z1*Z2 */
|
|
|
+ fe448_sqr(t0, r->Z); /* t0 = B = A^2 */
|
|
|
+ fe448_add(t4, t0, t3); /* t4 = F = B-(-E) */
|
|
|
+ fe448_sub(t0, t0, t3); /* t0 = G = B+(-E) */
|
|
|
+ fe448_reduce(t0);
|
|
|
+ fe448_add(r->X, p->X, p->Y); /* r->X = H1 = X1+Y1 */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_add(r->Y, q->X, q->Y); /* r->Y = H2 = X2+Y2 */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->X, r->X, r->Y); /* r->X = H = (X1+Y1)*(X2+Y2) */
|
|
|
+ fe448_sub(r->X, r->X, t1); /* r->X = X31 = H-C */
|
|
|
+ fe448_sub(r->X, r->X, t2); /* r->X = X32 = H-C-D */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_mul(r->X, r->X, t4); /* r->X = X33 = F*(H-C-D) */
|
|
|
+ fe448_mul(r->X, r->X, r->Z); /* r->X = X3 = A*F*(H-C-D) */
|
|
|
+ fe448_sub(r->Y, t2, t1); /* r->Y = Y31 = D-C */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->Y, r->Y, t0); /* r->Y = Y32 = G*(D-C) */
|
|
|
+ fe448_mul(r->Y, r->Y, r->Z); /* r->Y = Y3 = A*F*(D-C) */
|
|
|
+ fe448_mul(r->Z, t4, t0); /* r->Z = Z3 = F*G */
|
|
|
+}
|
|
|
+
|
|
|
+/* Subtract one point from another on the Twisted Edwards curve. r = p - q
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * p [in] Point to subtract from.
|
|
|
+ * q [in] Point to subtract.
|
|
|
+ */
|
|
|
+static WC_INLINE void ge448_sub(ge448_p2 *r, const ge448_p2 *p,
|
|
|
+ const ge448_p2 *q)
|
|
|
+{
|
|
|
+ ge448 t0[GE448_WORDS];
|
|
|
+ ge448 t1[GE448_WORDS];
|
|
|
+ ge448 t2[GE448_WORDS];
|
|
|
+ ge448 t3[GE448_WORDS];
|
|
|
+ ge448 t4[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_mul(t1, p->X, q->X); /* t1 = C = X1*X2 */
|
|
|
+ fe448_mul(t2, p->Y, q->Y); /* t2 = D = Y1*Y2 */
|
|
|
+ fe448_mul(t3, t1, t2); /* t3 = E1 = C*D */
|
|
|
+ fe448_mul39081(t3, t3); /* t3 = E = d*C*D */
|
|
|
+ fe448_mul(r->Z, p->Z, q->Z); /* r->Z = A = Z1*Z2 */
|
|
|
+ fe448_sqr(t0, p->Z); /* t0 = B = A^2 */
|
|
|
+ fe448_sub(t4, t0, t3); /* t4 = F = B-(--E) */
|
|
|
+ fe448_add(t0, t0, t3); /* t0 = G = B+(--E) */
|
|
|
+ fe448_reduce(t0);
|
|
|
+ fe448_add(r->X, p->X, p->Y); /* r->X = H1 = X1+Y1 */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_sub(r->Y, q->Y, q->X); /* r->Y = H2 = Y2+(-X2) */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->X, r->X, r->Y); /* r->X = H = (X1+Y1)*(X2+Y2) */
|
|
|
+ fe448_add(r->X, r->X, t1); /* r->X = X31 = H-(-C) */
|
|
|
+ fe448_sub(r->X, r->X, t2); /* r->X = X32 = H-(-C)-D */
|
|
|
+ fe448_reduce(r->X);
|
|
|
+ fe448_mul(r->X, r->X, t4); /* r->X = X33 = F*(H-C-D) */
|
|
|
+ fe448_mul(r->X, r->X, r->Z); /* r->X = X3 = A*F*(H-C-D) */
|
|
|
+ fe448_add(r->Y, t2, t1); /* r->Y = Y31 = D-C */
|
|
|
+ fe448_reduce(r->Y);
|
|
|
+ fe448_mul(r->Y, r->Y, t0); /* r->Y = Y32 = G*(D-C) */
|
|
|
+ fe448_mul(r->Y, r->Y, r->Z); /* r->Y = Y3 = A*F*(D-C) */
|
|
|
+ fe448_mul(r->Z, t4, t0); /* r->Z = Z3 = F*G */
|
|
|
+}
|
|
|
+
|
|
|
+/* Convert point to byte array assuming projective ordinates.
|
|
|
+ *
|
|
|
+ * b [in] Array of bytes to hold compressed point.
|
|
|
+ * p [in] Point to convert.
|
|
|
+ */
|
|
|
+void ge448_to_bytes(uint8_t *b, const ge448_p2 *p)
|
|
|
+{
|
|
|
+ ge448 recip[GE448_WORDS];
|
|
|
+ ge448 x[GE448_WORDS];
|
|
|
+ ge448 y[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_invert(recip, p->Z);
|
|
|
+ fe448_mul(x, p->X, recip);
|
|
|
+ fe448_mul(y, p->Y, recip);
|
|
|
+ fe448_to_bytes(b, y);
|
|
|
+ b[56] = fe448_isnegative(x) << 7;
|
|
|
+}
|
|
|
+
|
|
|
+/* Convert point to byte array assuming z is 1.
|
|
|
+ *
|
|
|
+ * b [in] Array of bytes to hold compressed point.
|
|
|
+ * p [in] Point to convert.
|
|
|
+ */
|
|
|
+static void ge448_p2z1_to_bytes(uint8_t *b, const ge448_p2 *p)
|
|
|
+{
|
|
|
+ fe448_to_bytes(b, p->Y);
|
|
|
+ b[56] = fe448_isnegative(p->X) << 7;
|
|
|
+}
|
|
|
+
|
|
|
+/* Compress the point to y-ordinate and negative bit.
|
|
|
+ *
|
|
|
+ * out [in] Array of bytes to hold compressed key.
|
|
|
+ * xIn [in] The x-ordinate.
|
|
|
+ * yIn [in] The y-ordinate.
|
|
|
+ */
|
|
|
+int ge448_compress_key(uint8_t* out, const uint8_t* xIn, const uint8_t* yIn)
|
|
|
+{
|
|
|
+ ge448_p2 g;
|
|
|
+ uint8_t bArray[ED448_KEY_SIZE];
|
|
|
+ uint32_t i;
|
|
|
+
|
|
|
+ fe448_from_bytes(g.X, xIn);
|
|
|
+ fe448_from_bytes(g.Y, yIn);
|
|
|
+ fe448_1(g.Z);
|
|
|
+
|
|
|
+ ge448_p2z1_to_bytes(bArray, &g);
|
|
|
+
|
|
|
+ for (i = 0; i < 57; i++) {
|
|
|
+ out[57 - 1 - i] = bArray[i];
|
|
|
+ }
|
|
|
+
|
|
|
+ return 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Determine whether the value is negative.
|
|
|
+ *
|
|
|
+ * b [in] An 8-bit signed value.
|
|
|
+ * returns 1 when negative and 0 otherwise.
|
|
|
+ */
|
|
|
+static uint8_t negative(int8_t b)
|
|
|
+{
|
|
|
+ return ((uint8_t)b) >> 7;
|
|
|
+}
|
|
|
+
|
|
|
+/* Determine whether two values are equal. a == b
|
|
|
+ * Constant time implementation.
|
|
|
+ *
|
|
|
+ * a [in] An 8-bit unsigned value.
|
|
|
+ * b [in] An 8-bit unsigned value.
|
|
|
+ * returns 1 when equal and 0 otherwise.
|
|
|
+ */
|
|
|
+static uint8_t equal(uint8_t a, uint8_t b)
|
|
|
+{
|
|
|
+ return (uint8_t)(((uint32_t)(a ^ b) - 1) >> 31);
|
|
|
+}
|
|
|
+
|
|
|
+/* Conditional move the point into result point if two values are equal.
|
|
|
+ * Constant time implementation.
|
|
|
+ *
|
|
|
+ * f [in] Point to conditionally overwrite.
|
|
|
+ * p [in] Point to conditionally copy.
|
|
|
+ * b [in] An 8-bit unsigned value.
|
|
|
+ * n [in] An 8-bit unsigned value.
|
|
|
+ */
|
|
|
+static WC_INLINE void cmov(ge448_precomp* r, const ge448_precomp* p, uint8_t b,
|
|
|
+ uint8_t n)
|
|
|
+{
|
|
|
+ b = equal(b, n);
|
|
|
+ fe448_cmov(r->x, p->x, b);
|
|
|
+ fe448_cmov(r->y, p->y, b);
|
|
|
+}
|
|
|
+
|
|
|
+/* Select one of the entries from the precomputed table and negate if required.
|
|
|
+ * Constant time implementation.
|
|
|
+ *
|
|
|
+ * r [in] Point to hold chosen point.
|
|
|
+ * pos [in] Position of array of entries to choose from.
|
|
|
+ * b [in] Index of point to select. -ve value means negate the point.
|
|
|
+ */
|
|
|
+static void ge448_select(ge448_precomp* r, int pos, int8_t b)
|
|
|
+{
|
|
|
+ ge448 minusx[16];
|
|
|
+ uint8_t bnegative = negative(b);
|
|
|
+ uint8_t babs = b - (((-bnegative) & b) << 1);
|
|
|
+
|
|
|
+ ge448_precomp_0(r);
|
|
|
+ cmov(r, &base[pos][0], babs, 1);
|
|
|
+ cmov(r, &base[pos][1], babs, 2);
|
|
|
+ cmov(r, &base[pos][2], babs, 3);
|
|
|
+ cmov(r, &base[pos][3], babs, 4);
|
|
|
+ cmov(r, &base[pos][4], babs, 5);
|
|
|
+ cmov(r, &base[pos][5], babs, 6);
|
|
|
+ cmov(r, &base[pos][6], babs, 7);
|
|
|
+ cmov(r, &base[pos][7], babs, 8);
|
|
|
+ fe448_neg(minusx, r->x);
|
|
|
+ fe448_cmov(r->x, minusx, bnegative);
|
|
|
+}
|
|
|
+
|
|
|
+/* Perform a scalar multiplication of the base point. r = a * base
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * a [in] Scalar to multiply by.
|
|
|
+ */
|
|
|
+void ge448_scalarmult_base(ge448_p2* r, const uint8_t* a)
|
|
|
+{
|
|
|
+ int8_t carry;
|
|
|
+ ge448_precomp t;
|
|
|
+ int i;
|
|
|
+ int8_t e[113];
|
|
|
+
|
|
|
+ carry = 0;
|
|
|
+ for (i = 0; i < 56; ++i) {
|
|
|
+ e[2 * i + 0] = ((a[i] >> 0) & 0xf) + carry;
|
|
|
+ carry = e[2 * i + 0] + 8;
|
|
|
+ carry >>= 4;
|
|
|
+ e[2 * i + 0] -= carry << 4;
|
|
|
+
|
|
|
+ e[2 * i + 1] = ((a[i] >> 4) & 0xf) + carry;
|
|
|
+ carry = e[2 * i + 1] + 8;
|
|
|
+ carry >>= 4;
|
|
|
+ e[2 * i + 1] -= carry << 4;
|
|
|
+ }
|
|
|
+ e[112] = carry;
|
|
|
+ /* each e[i] is between -8 and 8 */
|
|
|
+
|
|
|
+ /* Odd indeces first - sum based on even index so multiply by 16 */
|
|
|
+ ge448_select(&t, 0, e[1]);
|
|
|
+ fe448_copy(r->X, t.x);
|
|
|
+ fe448_copy(r->Y, t.y);
|
|
|
+ fe448_1(r->Z);
|
|
|
+ for (i = 3; i < 112; i += 2) {
|
|
|
+ ge448_select(&t, i / 2, e[i]);
|
|
|
+ ge448_madd(r, r, &t);
|
|
|
+ }
|
|
|
+
|
|
|
+ ge448_dbl(r, r);
|
|
|
+ ge448_dbl(r, r);
|
|
|
+ ge448_dbl(r, r);
|
|
|
+ ge448_dbl(r, r);
|
|
|
+
|
|
|
+ /* Add even indeces */
|
|
|
+ for (i = 0; i <= 112; i += 2) {
|
|
|
+ ge448_select(&t, i / 2, e[i]);
|
|
|
+ ge448_madd(r, r, &t);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+/* Create to a sliding window for the scalar multiplicaton.
|
|
|
+ *
|
|
|
+ * r [in] Array of indeces.
|
|
|
+ * a [in] Scalar to break up.
|
|
|
+ */
|
|
|
+static void slide(int8_t *r, const uint8_t *a)
|
|
|
+{
|
|
|
+ int i;
|
|
|
+ int b;
|
|
|
+ int k;
|
|
|
+
|
|
|
+ for (i = 0; i < 448; ++i) {
|
|
|
+ r[i] = (a[i >> 3] >> (i & 7)) & 1;
|
|
|
+ }
|
|
|
+
|
|
|
+ for (i = 0; i < 448; ++i) {
|
|
|
+ if (r[i] == 0) {
|
|
|
+ continue;
|
|
|
+ }
|
|
|
+
|
|
|
+ for (b = 1; b <= 7 && i + b < 448; ++b) {
|
|
|
+ if (r[i + b] == 0) {
|
|
|
+ continue;
|
|
|
+ }
|
|
|
+
|
|
|
+ if (r[i] + (r[i + b] << b) <= 31) {
|
|
|
+ r[i] += r[i + b] << b; r[i + b] = 0;
|
|
|
+ }
|
|
|
+ else if (r[i] - (r[i + b] << b) >= -31) {
|
|
|
+ r[i] -= r[i + b] << b;
|
|
|
+ for (k = i + b; k < 448; ++k) {
|
|
|
+ if (!r[k]) {
|
|
|
+ r[k] = 1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ r[k] = 0;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+/* Perform a scalar multplication of the base point and public point.
|
|
|
+ * r = a * p + b * base
|
|
|
+ * Uses a sliding window of 5 bits.
|
|
|
+ * Not constant time.
|
|
|
+ *
|
|
|
+ * r [in] Point to hold result.
|
|
|
+ * a [in] Scalar to multiply by.
|
|
|
+ */
|
|
|
+int ge448_double_scalarmult_vartime(ge448_p2 *r, const uint8_t *a,
|
|
|
+ const ge448_p2 *p, const uint8_t *b)
|
|
|
+{
|
|
|
+ int8_t aslide[448];
|
|
|
+ int8_t bslide[448];
|
|
|
+ ge448_p2 pi[16]; /* p,3p,..,31p */
|
|
|
+ ge448_p2 p2;
|
|
|
+ int i;
|
|
|
+
|
|
|
+ slide(aslide, a);
|
|
|
+ slide(bslide, b);
|
|
|
+
|
|
|
+ fe448_copy(pi[0].X, p->X);
|
|
|
+ fe448_copy(pi[0].Y, p->Y);
|
|
|
+ fe448_copy(pi[0].Z, p->Z);
|
|
|
+ ge448_dbl(&p2, p);
|
|
|
+ ge448_add(&pi[1], &p2, &pi[0]);
|
|
|
+ ge448_add(&pi[2], &p2, &pi[1]);
|
|
|
+ ge448_add(&pi[3], &p2, &pi[2]);
|
|
|
+ ge448_add(&pi[4], &p2, &pi[3]);
|
|
|
+ ge448_add(&pi[5], &p2, &pi[4]);
|
|
|
+ ge448_add(&pi[6], &p2, &pi[5]);
|
|
|
+ ge448_add(&pi[7], &p2, &pi[6]);
|
|
|
+ ge448_add(&pi[8], &p2, &pi[7]);
|
|
|
+ ge448_add(&pi[9], &p2, &pi[8]);
|
|
|
+ ge448_add(&pi[10], &p2, &pi[9]);
|
|
|
+ ge448_add(&pi[11], &p2, &pi[10]);
|
|
|
+ ge448_add(&pi[12], &p2, &pi[11]);
|
|
|
+ ge448_add(&pi[13], &p2, &pi[12]);
|
|
|
+ ge448_add(&pi[14], &p2, &pi[13]);
|
|
|
+ ge448_add(&pi[15], &p2, &pi[14]);
|
|
|
+
|
|
|
+ ge448_0(r);
|
|
|
+
|
|
|
+ /* Find first index that is not 0. */
|
|
|
+ for (i = 447; i >= 0; --i) {
|
|
|
+ if (aslide[i] || bslide[i]) {
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ for (; i >= 0; --i) {
|
|
|
+ ge448_dbl(r, r);
|
|
|
+
|
|
|
+ if (aslide[i] > 0)
|
|
|
+ ge448_add(r, r, &pi[aslide[i]/2]);
|
|
|
+ else if (aslide[i] < 0)
|
|
|
+ ge448_sub(r, r ,&pi[(-aslide[i])/2]);
|
|
|
+
|
|
|
+ if (bslide[i] > 0)
|
|
|
+ ge448_madd(r, r, &base_i[bslide[i]/2]);
|
|
|
+ else if (bslide[i] < 0)
|
|
|
+ ge448_msub(r, r, &base_i[(-bslide[i])/2]);
|
|
|
+ }
|
|
|
+
|
|
|
+ return 0;
|
|
|
+}
|
|
|
+
|
|
|
+/* Convert compressed point to negative of affine point.
|
|
|
+ * Calculates x from the y and the negative bit.
|
|
|
+ * Not constant time.
|
|
|
+ *
|
|
|
+ * r [in] Uncompressed point.
|
|
|
+ * b [in] Array of bytes representing point.
|
|
|
+ * returns 0 on success and -1 on failure.
|
|
|
+ */
|
|
|
+int ge448_from_bytes_negate_vartime(ge448_p2 *r, const uint8_t *b)
|
|
|
+{
|
|
|
+ int ret = 0;
|
|
|
+ ge448 u[GE448_WORDS];
|
|
|
+ ge448 v[GE448_WORDS];
|
|
|
+ ge448 u3[GE448_WORDS];
|
|
|
+ ge448 vxx[GE448_WORDS];
|
|
|
+ ge448 check[GE448_WORDS];
|
|
|
+
|
|
|
+ fe448_from_bytes(r->Y, b);
|
|
|
+ fe448_1(r->Z);
|
|
|
+ fe448_sqr(u, r->Y); /* u = y^2 */
|
|
|
+ fe448_mul39081(v, u); /* v = 39081.y^2 */
|
|
|
+ fe448_sub(u, u, r->Z); /* u = y^2-1 */
|
|
|
+ fe448_reduce(u);
|
|
|
+ fe448_add(v, v, r->Z); /* v = 39081.y^2-1 */
|
|
|
+ fe448_reduce(v);
|
|
|
+ fe448_neg(v, v); /* v = -39081.y^2-1 = d.y^2-1 */
|
|
|
+
|
|
|
+ fe448_sqr(r->X, v); /* x = v^2 */
|
|
|
+ fe448_mul(r->X, r->X, v); /* x = v^3 */
|
|
|
+ fe448_sqr(u3, u); /* x = u^2.v^3 */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^2.v^3 */
|
|
|
+ fe448_mul(u3, u3, u); /* u3 = u^3 */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^5.v^3 */
|
|
|
+
|
|
|
+ fe448_pow_2_446_222_1(r->X, r->X); /* x = (u^5.v^3)^((q-3)/4) */
|
|
|
+ fe448_mul(r->X, r->X, u3); /* x = u^3(u^5.v^3)^((q-3)/4) */
|
|
|
+ fe448_mul(r->X, r->X, v); /* x = u^3.v(u^5.v^3)^((q-3)/4) */
|
|
|
+
|
|
|
+ fe448_sqr(vxx, r->X);
|
|
|
+ fe448_mul(vxx, vxx, v);
|
|
|
+ fe448_sub(check, vxx, u); /* check = v.x^2-u */
|
|
|
+ fe448_reduce(check);
|
|
|
+ /* Note; vx^2+u is NOT correct. */
|
|
|
+ if (fe448_isnonzero(check)) {
|
|
|
+ ret = -1;
|
|
|
+ }
|
|
|
+
|
|
|
+ /* Calculating negative of point in bytes - negate only if X is correct. */
|
|
|
+ if (fe448_isnegative(r->X) == (b[56] >> 7)) {
|
|
|
+ fe448_neg(r->X, r->X);
|
|
|
+ }
|
|
|
+
|
|
|
+ return ret;
|
|
|
+}
|
|
|
+
|
|
|
+#endif /* ED448_SMALL */
|
|
|
+#endif /* HAVE_CURVE448 || HAVE_ED448 */
|
Sean Parkinson