-/* ====================================================================
- * Copyright (c) 2016 The OpenSSL Project. All rights reserved.
+/*
+ * Copyright 2016-2019 The OpenSSL Project Authors. All Rights Reserved.
*
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in
- * the documentation and/or other materials provided with the
- * distribution.
- *
- * 3. All advertising materials mentioning features or use of this
- * software must display the following acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
- *
- * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
- * endorse or promote products derived from this software without
- * prior written permission. For written permission, please contact
- * licensing@OpenSSL.org.
- *
- * 5. Products derived from this software may not be called "OpenSSL"
- * nor may "OpenSSL" appear in their names without prior written
- * permission of the OpenSSL Project.
- *
- * 6. Redistributions of any form whatsoever must retain the following
- * acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
- *
- * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
- * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
- * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
- * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
- * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
- * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
- * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
- * OF THE POSSIBILITY OF SUCH DAMAGE.
- * ====================================================================
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
-/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
- * 20141124 (http://bench.cr.yp.to/supercop.html).
- *
- * The field functions are shared by Ed25519 and X25519 where possible. */
+/*
+ * ECDSA low level APIs are deprecated for public use, but still ok for
+ * internal use.
+ */
+#include "internal/deprecated.h"
#include <string.h>
-#include "ec_lcl.h"
+#include "crypto/ecx.h"
+#include "ec_local.h"
+#include <openssl/evp.h>
+#include <openssl/sha.h>
+
+#if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \
+ defined(_M_AMD64) || defined(_M_X64))
+
+# define BASE_2_64_IMPLEMENTED
+
+typedef uint64_t fe64[4];
+
+int x25519_fe64_eligible(void);
+
+/*
+ * Following subroutines perform corresponding operations modulo
+ * 2^256-38, i.e. double the curve modulus. However, inputs and
+ * outputs are permitted to be partially reduced, i.e. to remain
+ * in [0..2^256) range. It's all tied up in final fe64_tobytes
+ * that performs full reduction modulo 2^255-19.
+ *
+ * There are no reference C implementations for these.
+ */
+void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_sqr(fe64 h, const fe64 f);
+void x25519_fe64_mul121666(fe64 h, fe64 f);
+void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
+# define fe64_mul x25519_fe64_mul
+# define fe64_sqr x25519_fe64_sqr
+# define fe64_mul121666 x25519_fe64_mul121666
+# define fe64_add x25519_fe64_add
+# define fe64_sub x25519_fe64_sub
+# define fe64_tobytes x25519_fe64_tobytes
+
+static uint64_t load_8(const uint8_t *in)
+{
+ uint64_t result;
+
+ result = in[0];
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ result |= ((uint64_t)in[3]) << 24;
+ result |= ((uint64_t)in[4]) << 32;
+ result |= ((uint64_t)in[5]) << 40;
+ result |= ((uint64_t)in[6]) << 48;
+ result |= ((uint64_t)in[7]) << 56;
+
+ return result;
+}
+
+static void fe64_frombytes(fe64 h, const uint8_t *s)
+{
+ h[0] = load_8(s);
+ h[1] = load_8(s + 8);
+ h[2] = load_8(s + 16);
+ h[3] = load_8(s + 24) & 0x7fffffffffffffff;
+}
+
+static void fe64_0(fe64 h)
+{
+ h[0] = 0;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+}
+
+static void fe64_1(fe64 h)
+{
+ h[0] = 1;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+}
+
+static void fe64_copy(fe64 h, const fe64 f)
+{
+ h[0] = f[0];
+ h[1] = f[1];
+ h[2] = f[2];
+ h[3] = f[3];
+}
+
+static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
+{
+ int i;
+ uint64_t mask = 0 - (uint64_t)b;
+
+ for (i = 0; i < 4; i++) {
+ uint64_t x = f[i] ^ g[i];
+ x &= mask;
+ f[i] ^= x;
+ g[i] ^= x;
+ }
+}
+
+static void fe64_invert(fe64 out, const fe64 z)
+{
+ fe64 t0;
+ fe64 t1;
+ fe64 t2;
+ fe64 t3;
+ int i;
+
+ /*
+ * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+ * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+ */
+
+ /* t0 = z ** 2 */
+ fe64_sqr(t0, z);
+
+ /* t1 = t0 ** (2 ** 2) = z ** 8 */
+ fe64_sqr(t1, t0);
+ fe64_sqr(t1, t1);
+
+ /* t1 = z * t1 = z ** 9 */
+ fe64_mul(t1, z, t1);
+ /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+ fe64_mul(t0, t0, t1);
+
+ /* t2 = t0 ** 2 = z ** 22 */
+ fe64_sqr(t2, t0);
+
+ /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+ fe64_mul(t1, t1, t2);
+
+ /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+ fe64_sqr(t2, t1);
+ for (i = 1; i < 5; ++i)
+ fe64_sqr(t2, t2);
+
+ /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
+ fe64_mul(t1, t2, t1);
+
+ /* Continuing similarly... */
+
+ /* t2 = z ** (2 ** 20 - 1) */
+ fe64_sqr(t2, t1);
+ for (i = 1; i < 10; ++i)
+ fe64_sqr(t2, t2);
+
+ fe64_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 40 - 1) */
+ fe64_sqr(t3, t2);
+ for (i = 1; i < 20; ++i)
+ fe64_sqr(t3, t3);
+
+ fe64_mul(t2, t3, t2);
+
+ /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+ for (i = 0; i < 10; ++i)
+ fe64_sqr(t2, t2);
+
+ /* t1 = z ** (2 ** 50 - 1) */
+ fe64_mul(t1, t2, t1);
+
+ /* t2 = z ** (2 ** 100 - 1) */
+ fe64_sqr(t2, t1);
+ for (i = 1; i < 50; ++i)
+ fe64_sqr(t2, t2);
+
+ fe64_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 200 - 1) */
+ fe64_sqr(t3, t2);
+ for (i = 1; i < 100; ++i)
+ fe64_sqr(t3, t3);
+
+ fe64_mul(t2, t3, t2);
+
+ /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
+ for (i = 0; i < 50; ++i)
+ fe64_sqr(t2, t2);
+
+ /* t1 = z ** (2 ** 250 - 1) */
+ fe64_mul(t1, t2, t1);
+
+ /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
+ for (i = 0; i < 5; ++i)
+ fe64_sqr(t1, t1);
+
+ /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+ fe64_mul(out, t1, t0);
+}
+
+/*
+ * Duplicate of original x25519_scalar_mult_generic, but using
+ * fe64_* subroutines.
+ */
+static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32])
+{
+ fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
+ uint8_t e[32];
+ unsigned swap = 0;
+ int pos;
+
+ memcpy(e, scalar, 32);
+ e[0] &= 0xf8;
+ e[31] &= 0x7f;
+ e[31] |= 0x40;
+ fe64_frombytes(x1, point);
+ fe64_1(x2);
+ fe64_0(z2);
+ fe64_copy(x3, x1);
+ fe64_1(z3);
+
+ for (pos = 254; pos >= 0; --pos) {
+ unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
+
+ swap ^= b;
+ fe64_cswap(x2, x3, swap);
+ fe64_cswap(z2, z3, swap);
+ swap = b;
+ fe64_sub(tmp0, x3, z3);
+ fe64_sub(tmp1, x2, z2);
+ fe64_add(x2, x2, z2);
+ fe64_add(z2, x3, z3);
+ fe64_mul(z3, x2, tmp0);
+ fe64_mul(z2, z2, tmp1);
+ fe64_sqr(tmp0, tmp1);
+ fe64_sqr(tmp1, x2);
+ fe64_add(x3, z3, z2);
+ fe64_sub(z2, z3, z2);
+ fe64_mul(x2, tmp1, tmp0);
+ fe64_sub(tmp1, tmp1, tmp0);
+ fe64_sqr(z2, z2);
+ fe64_mul121666(z3, tmp1);
+ fe64_sqr(x3, x3);
+ fe64_add(tmp0, tmp0, z3);
+ fe64_mul(z3, x1, z2);
+ fe64_mul(z2, tmp1, tmp0);
+ }
+
+ fe64_invert(z2, z2);
+ fe64_mul(x2, x2, z2);
+ fe64_tobytes(out, x2);
+
+ OPENSSL_cleanse(e, sizeof(e));
+}
+#endif
+
+#if defined(X25519_ASM) \
+ || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \
+ && !defined(__sparc__) \
+ && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \
+ && !(defined(__ANDROID__) && !defined(__clang__)) )
+/*
+ * Base 2^51 implementation. It's virtually no different from reference
+ * base 2^25.5 implementation in respect to lax boundary conditions for
+ * intermediate values and even individual limbs. So that whatever you
+ * know about the reference, applies even here...
+ */
+# define BASE_2_51_IMPLEMENTED
+
+typedef uint64_t fe51[5];
+
+static const uint64_t MASK51 = 0x7ffffffffffff;
+
+static uint64_t load_7(const uint8_t *in)
+{
+ uint64_t result;
+
+ result = in[0];
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ result |= ((uint64_t)in[3]) << 24;
+ result |= ((uint64_t)in[4]) << 32;
+ result |= ((uint64_t)in[5]) << 40;
+ result |= ((uint64_t)in[6]) << 48;
+
+ return result;
+}
+
+static uint64_t load_6(const uint8_t *in)
+{
+ uint64_t result;
+
+ result = in[0];
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ result |= ((uint64_t)in[3]) << 24;
+ result |= ((uint64_t)in[4]) << 32;
+ result |= ((uint64_t)in[5]) << 40;
+
+ return result;
+}
+
+static void fe51_frombytes(fe51 h, const uint8_t *s)
+{
+ uint64_t h0 = load_7(s); /* 56 bits */
+ uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
+ uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
+ uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
+ uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
+
+ h1 |= h0 >> 51; h0 &= MASK51;
+ h2 |= h1 >> 51; h1 &= MASK51;
+ h3 |= h2 >> 51; h2 &= MASK51;
+ h4 |= h3 >> 51; h3 &= MASK51;
+
+ h[0] = h0;
+ h[1] = h1;
+ h[2] = h2;
+ h[3] = h3;
+ h[4] = h4;
+}
+
+static void fe51_tobytes(uint8_t *s, const fe51 h)
+{
+ uint64_t h0 = h[0];
+ uint64_t h1 = h[1];
+ uint64_t h2 = h[2];
+ uint64_t h3 = h[3];
+ uint64_t h4 = h[4];
+ uint64_t q;
+
+ /* compare to modulus */
+ q = (h0 + 19) >> 51;
+ q = (h1 + q) >> 51;
+ q = (h2 + q) >> 51;
+ q = (h3 + q) >> 51;
+ q = (h4 + q) >> 51;
+
+ /* full reduce */
+ h0 += 19 * q;
+ h1 += h0 >> 51; h0 &= MASK51;
+ h2 += h1 >> 51; h1 &= MASK51;
+ h3 += h2 >> 51; h2 &= MASK51;
+ h4 += h3 >> 51; h3 &= MASK51;
+ h4 &= MASK51;
+
+ /* smash */
+ s[0] = (uint8_t)(h0 >> 0);
+ s[1] = (uint8_t)(h0 >> 8);
+ s[2] = (uint8_t)(h0 >> 16);
+ s[3] = (uint8_t)(h0 >> 24);
+ s[4] = (uint8_t)(h0 >> 32);
+ s[5] = (uint8_t)(h0 >> 40);
+ s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3));
+ s[7] = (uint8_t)(h1 >> 5);
+ s[8] = (uint8_t)(h1 >> 13);
+ s[9] = (uint8_t)(h1 >> 21);
+ s[10] = (uint8_t)(h1 >> 29);
+ s[11] = (uint8_t)(h1 >> 37);
+ s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6));
+ s[13] = (uint8_t)(h2 >> 2);
+ s[14] = (uint8_t)(h2 >> 10);
+ s[15] = (uint8_t)(h2 >> 18);
+ s[16] = (uint8_t)(h2 >> 26);
+ s[17] = (uint8_t)(h2 >> 34);
+ s[18] = (uint8_t)(h2 >> 42);
+ s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1));
+ s[20] = (uint8_t)(h3 >> 7);
+ s[21] = (uint8_t)(h3 >> 15);
+ s[22] = (uint8_t)(h3 >> 23);
+ s[23] = (uint8_t)(h3 >> 31);
+ s[24] = (uint8_t)(h3 >> 39);
+ s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4));
+ s[26] = (uint8_t)(h4 >> 4);
+ s[27] = (uint8_t)(h4 >> 12);
+ s[28] = (uint8_t)(h4 >> 20);
+ s[29] = (uint8_t)(h4 >> 28);
+ s[30] = (uint8_t)(h4 >> 36);
+ s[31] = (uint8_t)(h4 >> 44);
+}
+
+# if defined(X25519_ASM)
+void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
+void x25519_fe51_sqr(fe51 h, const fe51 f);
+void x25519_fe51_mul121666(fe51 h, fe51 f);
+# define fe51_mul x25519_fe51_mul
+# define fe51_sq x25519_fe51_sqr
+# define fe51_mul121666 x25519_fe51_mul121666
+# else
+
+typedef __uint128_t u128;
+
+static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
+{
+ u128 h0, h1, h2, h3, h4;
+ uint64_t f_i, g0, g1, g2, g3, g4;
+
+ f_i = f[0];
+ h0 = (u128)f_i * (g0 = g[0]);
+ h1 = (u128)f_i * (g1 = g[1]);
+ h2 = (u128)f_i * (g2 = g[2]);
+ h3 = (u128)f_i * (g3 = g[3]);
+ h4 = (u128)f_i * (g4 = g[4]);
+
+ f_i = f[1];
+ h0 += (u128)f_i * (g4 *= 19);
+ h1 += (u128)f_i * g0;
+ h2 += (u128)f_i * g1;
+ h3 += (u128)f_i * g2;
+ h4 += (u128)f_i * g3;
+
+ f_i = f[2];
+ h0 += (u128)f_i * (g3 *= 19);
+ h1 += (u128)f_i * g4;
+ h2 += (u128)f_i * g0;
+ h3 += (u128)f_i * g1;
+ h4 += (u128)f_i * g2;
+
+ f_i = f[3];
+ h0 += (u128)f_i * (g2 *= 19);
+ h1 += (u128)f_i * g3;
+ h2 += (u128)f_i * g4;
+ h3 += (u128)f_i * g0;
+ h4 += (u128)f_i * g1;
+
+ f_i = f[4];
+ h0 += (u128)f_i * (g1 *= 19);
+ h1 += (u128)f_i * g2;
+ h2 += (u128)f_i * g3;
+ h3 += (u128)f_i * g4;
+ h4 += (u128)f_i * g0;
+
+ /* partial [lazy] reduction */
+ h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
+ h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
+
+ h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
+ g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
+
+ g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
+ g3 += g2 >> 51; g2 &= MASK51;
+ g1 += g0 >> 51; g0 &= MASK51;
+
+ h[0] = g0;
+ h[1] = g1;
+ h[2] = g2;
+ h[3] = g3;
+ h[4] = g4;
+}
+
+static void fe51_sq(fe51 h, const fe51 f)
+{
+# if defined(OPENSSL_SMALL_FOOTPRINT)
+ fe51_mul(h, f, f);
+# else
+ /* dedicated squaring gives 16-25% overall improvement */
+ uint64_t g0 = f[0];
+ uint64_t g1 = f[1];
+ uint64_t g2 = f[2];
+ uint64_t g3 = f[3];
+ uint64_t g4 = f[4];
+ u128 h0, h1, h2, h3, h4;
+
+ h0 = (u128)g0 * g0; g0 *= 2;
+ h1 = (u128)g0 * g1;
+ h2 = (u128)g0 * g2;
+ h3 = (u128)g0 * g3;
+ h4 = (u128)g0 * g4;
+
+ g0 = g4; /* borrow g0 */
+ h3 += (u128)g0 * (g4 *= 19);
+
+ h2 += (u128)g1 * g1; g1 *= 2;
+ h3 += (u128)g1 * g2;
+ h4 += (u128)g1 * g3;
+ h0 += (u128)g1 * g4;
+
+ g0 = g3; /* borrow g0 */
+ h1 += (u128)g0 * (g3 *= 19);
+ h2 += (u128)(g0 * 2) * g4;
+
+ h4 += (u128)g2 * g2; g2 *= 2;
+ h0 += (u128)g2 * g3;
+ h1 += (u128)g2 * g4;
+
+ /* partial [lazy] reduction */
+ h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
+ h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
+
+ h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
+ g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
+
+ g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
+ g3 += g2 >> 51; g2 &= MASK51;
+ g1 += g0 >> 51; g0 &= MASK51;
+
+ h[0] = g0;
+ h[1] = g1;
+ h[2] = g2;
+ h[3] = g3;
+ h[4] = g4;
+# endif
+}
+
+static void fe51_mul121666(fe51 h, fe51 f)
+{
+ u128 h0 = f[0] * (u128)121666;
+ u128 h1 = f[1] * (u128)121666;
+ u128 h2 = f[2] * (u128)121666;
+ u128 h3 = f[3] * (u128)121666;
+ u128 h4 = f[4] * (u128)121666;
+ uint64_t g0, g1, g2, g3, g4;
+
+ h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
+ h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
+
+ h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
+ g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
+
+ g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
+ g3 += g2 >> 51; g2 &= MASK51;
+ g1 += g0 >> 51; g0 &= MASK51;
+
+ h[0] = g0;
+ h[1] = g1;
+ h[2] = g2;
+ h[3] = g3;
+ h[4] = g4;
+}
+# endif
+
+static void fe51_add(fe51 h, const fe51 f, const fe51 g)
+{
+ h[0] = f[0] + g[0];
+ h[1] = f[1] + g[1];
+ h[2] = f[2] + g[2];
+ h[3] = f[3] + g[3];
+ h[4] = f[4] + g[4];
+}
+
+static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
+{
+ /*
+ * Add 2*modulus to ensure that result remains positive
+ * even if subtrahend is partially reduced.
+ */
+ h[0] = (f[0] + 0xfffffffffffda) - g[0];
+ h[1] = (f[1] + 0xffffffffffffe) - g[1];
+ h[2] = (f[2] + 0xffffffffffffe) - g[2];
+ h[3] = (f[3] + 0xffffffffffffe) - g[3];
+ h[4] = (f[4] + 0xffffffffffffe) - g[4];
+}
+
+static void fe51_0(fe51 h)
+{
+ h[0] = 0;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+ h[4] = 0;
+}
+
+static void fe51_1(fe51 h)
+{
+ h[0] = 1;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+ h[4] = 0;
+}
+
+static void fe51_copy(fe51 h, const fe51 f)
+{
+ h[0] = f[0];
+ h[1] = f[1];
+ h[2] = f[2];
+ h[3] = f[3];
+ h[4] = f[4];
+}
+
+static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
+{
+ int i;
+ uint64_t mask = 0 - (uint64_t)b;
+
+ for (i = 0; i < 5; i++) {
+ int64_t x = f[i] ^ g[i];
+ x &= mask;
+ f[i] ^= x;
+ g[i] ^= x;
+ }
+}
+
+static void fe51_invert(fe51 out, const fe51 z)
+{
+ fe51 t0;
+ fe51 t1;
+ fe51 t2;
+ fe51 t3;
+ int i;
+
+ /*
+ * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+ * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+ */
+
+ /* t0 = z ** 2 */
+ fe51_sq(t0, z);
+
+ /* t1 = t0 ** (2 ** 2) = z ** 8 */
+ fe51_sq(t1, t0);
+ fe51_sq(t1, t1);
+
+ /* t1 = z * t1 = z ** 9 */
+ fe51_mul(t1, z, t1);
+ /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+ fe51_mul(t0, t0, t1);
+
+ /* t2 = t0 ** 2 = z ** 22 */
+ fe51_sq(t2, t0);
+
+ /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+ fe51_mul(t1, t1, t2);
+
+ /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+ fe51_sq(t2, t1);
+ for (i = 1; i < 5; ++i)
+ fe51_sq(t2, t2);
+
+ /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
+ fe51_mul(t1, t2, t1);
+
+ /* Continuing similarly... */
+
+ /* t2 = z ** (2 ** 20 - 1) */
+ fe51_sq(t2, t1);
+ for (i = 1; i < 10; ++i)
+ fe51_sq(t2, t2);
+
+ fe51_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 40 - 1) */
+ fe51_sq(t3, t2);
+ for (i = 1; i < 20; ++i)
+ fe51_sq(t3, t3);
+
+ fe51_mul(t2, t3, t2);
+
+ /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+ for (i = 0; i < 10; ++i)
+ fe51_sq(t2, t2);
+
+ /* t1 = z ** (2 ** 50 - 1) */
+ fe51_mul(t1, t2, t1);
+ /* t2 = z ** (2 ** 100 - 1) */
+ fe51_sq(t2, t1);
+ for (i = 1; i < 50; ++i)
+ fe51_sq(t2, t2);
+
+ fe51_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 200 - 1) */
+ fe51_sq(t3, t2);
+ for (i = 1; i < 100; ++i)
+ fe51_sq(t3, t3);
+
+ fe51_mul(t2, t3, t2);
+
+ /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
+ for (i = 0; i < 50; ++i)
+ fe51_sq(t2, t2);
+
+ /* t1 = z ** (2 ** 250 - 1) */
+ fe51_mul(t1, t2, t1);
+
+ /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
+ for (i = 0; i < 5; ++i)
+ fe51_sq(t1, t1);
+
+ /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+ fe51_mul(out, t1, t0);
+}
+
+/*
+ * Duplicate of original x25519_scalar_mult_generic, but using
+ * fe51_* subroutines.
+ */
+static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32])
+{
+ fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
+ uint8_t e[32];
+ unsigned swap = 0;
+ int pos;
+
+# ifdef BASE_2_64_IMPLEMENTED
+ if (x25519_fe64_eligible()) {
+ x25519_scalar_mulx(out, scalar, point);
+ return;
+ }
+# endif
+
+ memcpy(e, scalar, 32);
+ e[0] &= 0xf8;
+ e[31] &= 0x7f;
+ e[31] |= 0x40;
+ fe51_frombytes(x1, point);
+ fe51_1(x2);
+ fe51_0(z2);
+ fe51_copy(x3, x1);
+ fe51_1(z3);
+
+ for (pos = 254; pos >= 0; --pos) {
+ unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
+
+ swap ^= b;
+ fe51_cswap(x2, x3, swap);
+ fe51_cswap(z2, z3, swap);
+ swap = b;
+ fe51_sub(tmp0, x3, z3);
+ fe51_sub(tmp1, x2, z2);
+ fe51_add(x2, x2, z2);
+ fe51_add(z2, x3, z3);
+ fe51_mul(z3, tmp0, x2);
+ fe51_mul(z2, z2, tmp1);
+ fe51_sq(tmp0, tmp1);
+ fe51_sq(tmp1, x2);
+ fe51_add(x3, z3, z2);
+ fe51_sub(z2, z3, z2);
+ fe51_mul(x2, tmp1, tmp0);
+ fe51_sub(tmp1, tmp1, tmp0);
+ fe51_sq(z2, z2);
+ fe51_mul121666(z3, tmp1);
+ fe51_sq(x3, x3);
+ fe51_add(tmp0, tmp0, z3);
+ fe51_mul(z3, x1, z2);
+ fe51_mul(z2, tmp1, tmp0);
+ }
+
+ fe51_invert(z2, z2);
+ fe51_mul(x2, x2, z2);
+ fe51_tobytes(out, x2);
+
+ OPENSSL_cleanse(e, sizeof(e));
+}
+#endif
+
+/*
+ * Reference base 2^25.5 implementation.
+ *
+ * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
+ * 20141124 (http://bench.cr.yp.to/supercop.html).
+ *
+ * The field functions are shared by Ed25519 and X25519 where possible.
+ */
-/* fe means field element. Here the field is \Z/(2^255-19). An element t,
+/*
+ * fe means field element. Here the field is \Z/(2^255-19). An element t,
* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
- * context. */
+ * context.
+ */
typedef int32_t fe[10];
-static uint64_t load_3(const uint8_t *in) {
- uint64_t result;
- result = (uint64_t)in[0];
- result |= ((uint64_t)in[1]) << 8;
- result |= ((uint64_t)in[2]) << 16;
- return result;
+static const int64_t kBottom21Bits = 0x1fffffLL;
+static const int64_t kBottom25Bits = 0x1ffffffLL;
+static const int64_t kBottom26Bits = 0x3ffffffLL;
+static const int64_t kTop39Bits = 0xfffffffffe000000LL;
+static const int64_t kTop38Bits = 0xfffffffffc000000LL;
+
+static uint64_t load_3(const uint8_t *in)
+{
+ uint64_t result;
+
+ result = ((uint64_t)in[0]);
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ return result;
}
-static uint64_t load_4(const uint8_t *in) {
- uint64_t result;
- result = (uint64_t)in[0];
- result |= ((uint64_t)in[1]) << 8;
- result |= ((uint64_t)in[2]) << 16;
- result |= ((uint64_t)in[3]) << 24;
- return result;
+static uint64_t load_4(const uint8_t *in)
+{
+ uint64_t result;
+
+ result = ((uint64_t)in[0]);
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ result |= ((uint64_t)in[3]) << 24;
+ return result;
}
-static void fe_frombytes(fe h, const uint8_t *s) {
- /* Ignores top bit of h. */
- int64_t h0 = load_4(s);
- int64_t h1 = load_3(s + 4) << 6;
- int64_t h2 = load_3(s + 7) << 5;
- int64_t h3 = load_3(s + 10) << 3;
- int64_t h4 = load_3(s + 13) << 2;
- int64_t h5 = load_4(s + 16);
- int64_t h6 = load_3(s + 20) << 7;
- int64_t h7 = load_3(s + 23) << 5;
- int64_t h8 = load_3(s + 26) << 4;
- int64_t h9 = (load_3(s + 29) & 8388607) << 2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
+static void fe_frombytes(fe h, const uint8_t *s)
+{
+ /* Ignores top bit of h. */
+ int64_t h0 = load_4(s);
+ int64_t h1 = load_3(s + 4) << 6;
+ int64_t h2 = load_3(s + 7) << 5;
+ int64_t h3 = load_3(s + 10) << 3;
+ int64_t h4 = load_3(s + 13) << 2;
+ int64_t h5 = load_4(s + 16);
+ int64_t h6 = load_3(s + 20) << 7;
+ int64_t h7 = load_3(s + 23) << 5;
+ int64_t h8 = load_3(s + 26) << 4;
+ int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+ h[0] = (int32_t)h0;
+ h[1] = (int32_t)h1;
+ h[2] = (int32_t)h2;
+ h[3] = (int32_t)h3;
+ h[4] = (int32_t)h4;
+ h[5] = (int32_t)h5;
+ h[6] = (int32_t)h6;
+ h[7] = (int32_t)h7;
+ h[8] = (int32_t)h8;
+ h[9] = (int32_t)h9;
}
-/* Preconditions:
- * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+/*
+ * Preconditions:
+ * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Write p=2^255-19; q=floor(h/p).
* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
*
* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
- * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
-static void fe_tobytes(uint8_t *s, const fe h) {
- int32_t h0 = h[0];
- int32_t h1 = h[1];
- int32_t h2 = h[2];
- int32_t h3 = h[3];
- int32_t h4 = h[4];
- int32_t h5 = h[5];
- int32_t h6 = h[6];
- int32_t h7 = h[7];
- int32_t h8 = h[8];
- int32_t h9 = h[9];
- int32_t q;
- int32_t carry0;
- int32_t carry1;
- int32_t carry2;
- int32_t carry3;
- int32_t carry4;
- int32_t carry5;
- int32_t carry6;
- int32_t carry7;
- int32_t carry8;
- int32_t carry9;
-
- q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
- q = (h0 + q) >> 26;
- q = (h1 + q) >> 25;
- q = (h2 + q) >> 26;
- q = (h3 + q) >> 25;
- q = (h4 + q) >> 26;
- q = (h5 + q) >> 25;
- q = (h6 + q) >> 26;
- q = (h7 + q) >> 25;
- q = (h8 + q) >> 26;
- q = (h9 + q) >> 25;
-
- /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
- h0 += 19 * q;
- /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
-
- carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
- carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
- carry9 = h9 >> 25; h9 -= carry9 << 25;
- /* h10 = carry9 */
-
- /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- * Have h0+...+2^230 h9 between 0 and 2^255-1;
- * evidently 2^255 h10-2^255 q = 0.
- * Goal: Output h0+...+2^230 h9. */
-
- s[0] = h0 >> 0;
- s[1] = h0 >> 8;
- s[2] = h0 >> 16;
- s[3] = (h0 >> 24) | (h1 << 2);
- s[4] = h1 >> 6;
- s[5] = h1 >> 14;
- s[6] = (h1 >> 22) | (h2 << 3);
- s[7] = h2 >> 5;
- s[8] = h2 >> 13;
- s[9] = (h2 >> 21) | (h3 << 5);
- s[10] = h3 >> 3;
- s[11] = h3 >> 11;
- s[12] = (h3 >> 19) | (h4 << 6);
- s[13] = h4 >> 2;
- s[14] = h4 >> 10;
- s[15] = h4 >> 18;
- s[16] = h5 >> 0;
- s[17] = h5 >> 8;
- s[18] = h5 >> 16;
- s[19] = (h5 >> 24) | (h6 << 1);
- s[20] = h6 >> 7;
- s[21] = h6 >> 15;
- s[22] = (h6 >> 23) | (h7 << 3);
- s[23] = h7 >> 5;
- s[24] = h7 >> 13;
- s[25] = (h7 >> 21) | (h8 << 4);
- s[26] = h8 >> 4;
- s[27] = h8 >> 12;
- s[28] = (h8 >> 20) | (h9 << 6);
- s[29] = h9 >> 2;
- s[30] = h9 >> 10;
- s[31] = h9 >> 18;
+ * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+ */
+static void fe_tobytes(uint8_t *s, const fe h)
+{
+ int32_t h0 = h[0];
+ int32_t h1 = h[1];
+ int32_t h2 = h[2];
+ int32_t h3 = h[3];
+ int32_t h4 = h[4];
+ int32_t h5 = h[5];
+ int32_t h6 = h[6];
+ int32_t h7 = h[7];
+ int32_t h8 = h[8];
+ int32_t h9 = h[9];
+ int32_t q;
+
+ q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+ q = (h0 + q) >> 26;
+ q = (h1 + q) >> 25;
+ q = (h2 + q) >> 26;
+ q = (h3 + q) >> 25;
+ q = (h4 + q) >> 26;
+ q = (h5 + q) >> 25;
+ q = (h6 + q) >> 26;
+ q = (h7 + q) >> 25;
+ q = (h8 + q) >> 26;
+ q = (h9 + q) >> 25;
+
+ /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+ h0 += 19 * q;
+ /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+ h1 += h0 >> 26; h0 &= kBottom26Bits;
+ h2 += h1 >> 25; h1 &= kBottom25Bits;
+ h3 += h2 >> 26; h2 &= kBottom26Bits;
+ h4 += h3 >> 25; h3 &= kBottom25Bits;
+ h5 += h4 >> 26; h4 &= kBottom26Bits;
+ h6 += h5 >> 25; h5 &= kBottom25Bits;
+ h7 += h6 >> 26; h6 &= kBottom26Bits;
+ h8 += h7 >> 25; h7 &= kBottom25Bits;
+ h9 += h8 >> 26; h8 &= kBottom26Bits;
+ h9 &= kBottom25Bits;
+ /* h10 = carry9 */
+
+ /*
+ * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+ * Have h0+...+2^230 h9 between 0 and 2^255-1;
+ * evidently 2^255 h10-2^255 q = 0.
+ * Goal: Output h0+...+2^230 h9.
+ */
+ s[ 0] = (uint8_t) (h0 >> 0);
+ s[ 1] = (uint8_t) (h0 >> 8);
+ s[ 2] = (uint8_t) (h0 >> 16);
+ s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
+ s[ 4] = (uint8_t) (h1 >> 6);
+ s[ 5] = (uint8_t) (h1 >> 14);
+ s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
+ s[ 7] = (uint8_t) (h2 >> 5);
+ s[ 8] = (uint8_t) (h2 >> 13);
+ s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
+ s[10] = (uint8_t) (h3 >> 3);
+ s[11] = (uint8_t) (h3 >> 11);
+ s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
+ s[13] = (uint8_t) (h4 >> 2);
+ s[14] = (uint8_t) (h4 >> 10);
+ s[15] = (uint8_t) (h4 >> 18);
+ s[16] = (uint8_t) (h5 >> 0);
+ s[17] = (uint8_t) (h5 >> 8);
+ s[18] = (uint8_t) (h5 >> 16);
+ s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
+ s[20] = (uint8_t) (h6 >> 7);
+ s[21] = (uint8_t) (h6 >> 15);
+ s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
+ s[23] = (uint8_t) (h7 >> 5);
+ s[24] = (uint8_t) (h7 >> 13);
+ s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
+ s[26] = (uint8_t) (h8 >> 4);
+ s[27] = (uint8_t) (h8 >> 12);
+ s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
+ s[29] = (uint8_t) (h9 >> 2);
+ s[30] = (uint8_t) (h9 >> 10);
+ s[31] = (uint8_t) (h9 >> 18);
}
/* h = f */
-static void fe_copy(fe h, const fe f) {
- memmove(h, f, sizeof(int32_t) * 10);
+static void fe_copy(fe h, const fe f)
+{
+ memmove(h, f, sizeof(int32_t) * 10);
}
/* h = 0 */
-static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
+static void fe_0(fe h)
+{
+ memset(h, 0, sizeof(int32_t) * 10);
+}
/* h = 1 */
-static void fe_1(fe h) {
- memset(h, 0, sizeof(int32_t) * 10);
- h[0] = 1;
+static void fe_1(fe h)
+{
+ memset(h, 0, sizeof(int32_t) * 10);
+ h[0] = 1;
}
-/* h = f + g
+/*
+ * h = f + g
+ *
* Can overlap h with f or g.
*
* Preconditions:
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
- * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static void fe_add(fe h, const fe f, const fe g) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = f[i] + g[i];
- }
+ * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static void fe_add(fe h, const fe f, const fe g)
+{
+ unsigned i;
+
+ for (i = 0; i < 10; i++) {
+ h[i] = f[i] + g[i];
+ }
}
-/* h = f - g
+/*
+ * h = f - g
+ *
* Can overlap h with f or g.
*
* Preconditions:
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
- * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static void fe_sub(fe h, const fe f, const fe g) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = f[i] - g[i];
- }
+ * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static void fe_sub(fe h, const fe f, const fe g)
+{
+ unsigned i;
+
+ for (i = 0; i < 10; i++) {
+ h[i] = f[i] - g[i];
+ }
}
-/* h = f * g
+/*
+ * h = f * g
+ *
* Can overlap h with f or g.
*
* Preconditions:
* 10 of them are 2-way parallelizable and vectorizable.
* Can get away with 11 carries, but then data flow is much deeper.
*
- * With tighter constraints on inputs can squeeze carries into int32. */
-static void fe_mul(fe h, const fe f, const fe g) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
- int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
- int32_t g3_19 = 19 * g3;
- int32_t g4_19 = 19 * g4;
- int32_t g5_19 = 19 * g5;
- int32_t g6_19 = 19 * g6;
- int32_t g7_19 = 19 * g7;
- int32_t g8_19 = 19 * g8;
- int32_t g9_19 = 19 * g9;
- int32_t f1_2 = 2 * f1;
- int32_t f3_2 = 2 * f3;
- int32_t f5_2 = 2 * f5;
- int32_t f7_2 = 2 * f7;
- int32_t f9_2 = 2 * f9;
- int64_t f0g0 = f0 * (int64_t) g0;
- int64_t f0g1 = f0 * (int64_t) g1;
- int64_t f0g2 = f0 * (int64_t) g2;
- int64_t f0g3 = f0 * (int64_t) g3;
- int64_t f0g4 = f0 * (int64_t) g4;
- int64_t f0g5 = f0 * (int64_t) g5;
- int64_t f0g6 = f0 * (int64_t) g6;
- int64_t f0g7 = f0 * (int64_t) g7;
- int64_t f0g8 = f0 * (int64_t) g8;
- int64_t f0g9 = f0 * (int64_t) g9;
- int64_t f1g0 = f1 * (int64_t) g0;
- int64_t f1g1_2 = f1_2 * (int64_t) g1;
- int64_t f1g2 = f1 * (int64_t) g2;
- int64_t f1g3_2 = f1_2 * (int64_t) g3;
- int64_t f1g4 = f1 * (int64_t) g4;
- int64_t f1g5_2 = f1_2 * (int64_t) g5;
- int64_t f1g6 = f1 * (int64_t) g6;
- int64_t f1g7_2 = f1_2 * (int64_t) g7;
- int64_t f1g8 = f1 * (int64_t) g8;
- int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
- int64_t f2g0 = f2 * (int64_t) g0;
- int64_t f2g1 = f2 * (int64_t) g1;
- int64_t f2g2 = f2 * (int64_t) g2;
- int64_t f2g3 = f2 * (int64_t) g3;
- int64_t f2g4 = f2 * (int64_t) g4;
- int64_t f2g5 = f2 * (int64_t) g5;
- int64_t f2g6 = f2 * (int64_t) g6;
- int64_t f2g7 = f2 * (int64_t) g7;
- int64_t f2g8_19 = f2 * (int64_t) g8_19;
- int64_t f2g9_19 = f2 * (int64_t) g9_19;
- int64_t f3g0 = f3 * (int64_t) g0;
- int64_t f3g1_2 = f3_2 * (int64_t) g1;
- int64_t f3g2 = f3 * (int64_t) g2;
- int64_t f3g3_2 = f3_2 * (int64_t) g3;
- int64_t f3g4 = f3 * (int64_t) g4;
- int64_t f3g5_2 = f3_2 * (int64_t) g5;
- int64_t f3g6 = f3 * (int64_t) g6;
- int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
- int64_t f3g8_19 = f3 * (int64_t) g8_19;
- int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
- int64_t f4g0 = f4 * (int64_t) g0;
- int64_t f4g1 = f4 * (int64_t) g1;
- int64_t f4g2 = f4 * (int64_t) g2;
- int64_t f4g3 = f4 * (int64_t) g3;
- int64_t f4g4 = f4 * (int64_t) g4;
- int64_t f4g5 = f4 * (int64_t) g5;
- int64_t f4g6_19 = f4 * (int64_t) g6_19;
- int64_t f4g7_19 = f4 * (int64_t) g7_19;
- int64_t f4g8_19 = f4 * (int64_t) g8_19;
- int64_t f4g9_19 = f4 * (int64_t) g9_19;
- int64_t f5g0 = f5 * (int64_t) g0;
- int64_t f5g1_2 = f5_2 * (int64_t) g1;
- int64_t f5g2 = f5 * (int64_t) g2;
- int64_t f5g3_2 = f5_2 * (int64_t) g3;
- int64_t f5g4 = f5 * (int64_t) g4;
- int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
- int64_t f5g6_19 = f5 * (int64_t) g6_19;
- int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
- int64_t f5g8_19 = f5 * (int64_t) g8_19;
- int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
- int64_t f6g0 = f6 * (int64_t) g0;
- int64_t f6g1 = f6 * (int64_t) g1;
- int64_t f6g2 = f6 * (int64_t) g2;
- int64_t f6g3 = f6 * (int64_t) g3;
- int64_t f6g4_19 = f6 * (int64_t) g4_19;
- int64_t f6g5_19 = f6 * (int64_t) g5_19;
- int64_t f6g6_19 = f6 * (int64_t) g6_19;
- int64_t f6g7_19 = f6 * (int64_t) g7_19;
- int64_t f6g8_19 = f6 * (int64_t) g8_19;
- int64_t f6g9_19 = f6 * (int64_t) g9_19;
- int64_t f7g0 = f7 * (int64_t) g0;
- int64_t f7g1_2 = f7_2 * (int64_t) g1;
- int64_t f7g2 = f7 * (int64_t) g2;
- int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
- int64_t f7g4_19 = f7 * (int64_t) g4_19;
- int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
- int64_t f7g6_19 = f7 * (int64_t) g6_19;
- int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
- int64_t f7g8_19 = f7 * (int64_t) g8_19;
- int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
- int64_t f8g0 = f8 * (int64_t) g0;
- int64_t f8g1 = f8 * (int64_t) g1;
- int64_t f8g2_19 = f8 * (int64_t) g2_19;
- int64_t f8g3_19 = f8 * (int64_t) g3_19;
- int64_t f8g4_19 = f8 * (int64_t) g4_19;
- int64_t f8g5_19 = f8 * (int64_t) g5_19;
- int64_t f8g6_19 = f8 * (int64_t) g6_19;
- int64_t f8g7_19 = f8 * (int64_t) g7_19;
- int64_t f8g8_19 = f8 * (int64_t) g8_19;
- int64_t f8g9_19 = f8 * (int64_t) g9_19;
- int64_t f9g0 = f9 * (int64_t) g0;
- int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
- int64_t f9g2_19 = f9 * (int64_t) g2_19;
- int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
- int64_t f9g4_19 = f9 * (int64_t) g4_19;
- int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
- int64_t f9g6_19 = f9 * (int64_t) g6_19;
- int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
- int64_t f9g8_19 = f9 * (int64_t) g8_19;
- int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
- int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
- int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
- int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
- int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
- int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
- int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
- int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
- int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
- int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
- int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
- * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
- * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
- * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- /* |h0| <= 2^25 */
- /* |h4| <= 2^25 */
- /* |h1| <= 1.71*2^59 */
- /* |h5| <= 1.71*2^59 */
-
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
- /* |h1| <= 2^24; from now on fits into int32 */
- /* |h5| <= 2^24; from now on fits into int32 */
- /* |h2| <= 1.41*2^60 */
- /* |h6| <= 1.41*2^60 */
-
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
- /* |h2| <= 2^25; from now on fits into int32 unchanged */
- /* |h6| <= 2^25; from now on fits into int32 unchanged */
- /* |h3| <= 1.71*2^59 */
- /* |h7| <= 1.71*2^59 */
-
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
- /* |h3| <= 2^24; from now on fits into int32 unchanged */
- /* |h7| <= 2^24; from now on fits into int32 unchanged */
- /* |h4| <= 1.72*2^34 */
- /* |h8| <= 1.41*2^60 */
-
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
- /* |h4| <= 2^25; from now on fits into int32 unchanged */
- /* |h8| <= 2^25; from now on fits into int32 unchanged */
- /* |h5| <= 1.01*2^24 */
- /* |h9| <= 1.71*2^59 */
-
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
- /* |h9| <= 2^24; from now on fits into int32 unchanged */
- /* |h0| <= 1.1*2^39 */
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- /* |h0| <= 2^25; from now on fits into int32 unchanged */
- /* |h1| <= 1.01*2^24 */
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
+ * With tighter constraints on inputs can squeeze carries into int32.
+ */
+static void fe_mul(fe h, const fe f, const fe g)
+{
+ int32_t f0 = f[0];
+ int32_t f1 = f[1];
+ int32_t f2 = f[2];
+ int32_t f3 = f[3];
+ int32_t f4 = f[4];
+ int32_t f5 = f[5];
+ int32_t f6 = f[6];
+ int32_t f7 = f[7];
+ int32_t f8 = f[8];
+ int32_t f9 = f[9];
+ int32_t g0 = g[0];
+ int32_t g1 = g[1];
+ int32_t g2 = g[2];
+ int32_t g3 = g[3];
+ int32_t g4 = g[4];
+ int32_t g5 = g[5];
+ int32_t g6 = g[6];
+ int32_t g7 = g[7];
+ int32_t g8 = g[8];
+ int32_t g9 = g[9];
+ int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+ int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+ int32_t g3_19 = 19 * g3;
+ int32_t g4_19 = 19 * g4;
+ int32_t g5_19 = 19 * g5;
+ int32_t g6_19 = 19 * g6;
+ int32_t g7_19 = 19 * g7;
+ int32_t g8_19 = 19 * g8;
+ int32_t g9_19 = 19 * g9;
+ int32_t f1_2 = 2 * f1;
+ int32_t f3_2 = 2 * f3;
+ int32_t f5_2 = 2 * f5;
+ int32_t f7_2 = 2 * f7;
+ int32_t f9_2 = 2 * f9;
+ int64_t f0g0 = f0 * (int64_t) g0;
+ int64_t f0g1 = f0 * (int64_t) g1;
+ int64_t f0g2 = f0 * (int64_t) g2;
+ int64_t f0g3 = f0 * (int64_t) g3;
+ int64_t f0g4 = f0 * (int64_t) g4;
+ int64_t f0g5 = f0 * (int64_t) g5;
+ int64_t f0g6 = f0 * (int64_t) g6;
+ int64_t f0g7 = f0 * (int64_t) g7;
+ int64_t f0g8 = f0 * (int64_t) g8;
+ int64_t f0g9 = f0 * (int64_t) g9;
+ int64_t f1g0 = f1 * (int64_t) g0;
+ int64_t f1g1_2 = f1_2 * (int64_t) g1;
+ int64_t f1g2 = f1 * (int64_t) g2;
+ int64_t f1g3_2 = f1_2 * (int64_t) g3;
+ int64_t f1g4 = f1 * (int64_t) g4;
+ int64_t f1g5_2 = f1_2 * (int64_t) g5;
+ int64_t f1g6 = f1 * (int64_t) g6;
+ int64_t f1g7_2 = f1_2 * (int64_t) g7;
+ int64_t f1g8 = f1 * (int64_t) g8;
+ int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+ int64_t f2g0 = f2 * (int64_t) g0;
+ int64_t f2g1 = f2 * (int64_t) g1;
+ int64_t f2g2 = f2 * (int64_t) g2;
+ int64_t f2g3 = f2 * (int64_t) g3;
+ int64_t f2g4 = f2 * (int64_t) g4;
+ int64_t f2g5 = f2 * (int64_t) g5;
+ int64_t f2g6 = f2 * (int64_t) g6;
+ int64_t f2g7 = f2 * (int64_t) g7;
+ int64_t f2g8_19 = f2 * (int64_t) g8_19;
+ int64_t f2g9_19 = f2 * (int64_t) g9_19;
+ int64_t f3g0 = f3 * (int64_t) g0;
+ int64_t f3g1_2 = f3_2 * (int64_t) g1;
+ int64_t f3g2 = f3 * (int64_t) g2;
+ int64_t f3g3_2 = f3_2 * (int64_t) g3;
+ int64_t f3g4 = f3 * (int64_t) g4;
+ int64_t f3g5_2 = f3_2 * (int64_t) g5;
+ int64_t f3g6 = f3 * (int64_t) g6;
+ int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+ int64_t f3g8_19 = f3 * (int64_t) g8_19;
+ int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+ int64_t f4g0 = f4 * (int64_t) g0;
+ int64_t f4g1 = f4 * (int64_t) g1;
+ int64_t f4g2 = f4 * (int64_t) g2;
+ int64_t f4g3 = f4 * (int64_t) g3;
+ int64_t f4g4 = f4 * (int64_t) g4;
+ int64_t f4g5 = f4 * (int64_t) g5;
+ int64_t f4g6_19 = f4 * (int64_t) g6_19;
+ int64_t f4g7_19 = f4 * (int64_t) g7_19;
+ int64_t f4g8_19 = f4 * (int64_t) g8_19;
+ int64_t f4g9_19 = f4 * (int64_t) g9_19;
+ int64_t f5g0 = f5 * (int64_t) g0;
+ int64_t f5g1_2 = f5_2 * (int64_t) g1;
+ int64_t f5g2 = f5 * (int64_t) g2;
+ int64_t f5g3_2 = f5_2 * (int64_t) g3;
+ int64_t f5g4 = f5 * (int64_t) g4;
+ int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+ int64_t f5g6_19 = f5 * (int64_t) g6_19;
+ int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+ int64_t f5g8_19 = f5 * (int64_t) g8_19;
+ int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+ int64_t f6g0 = f6 * (int64_t) g0;
+ int64_t f6g1 = f6 * (int64_t) g1;
+ int64_t f6g2 = f6 * (int64_t) g2;
+ int64_t f6g3 = f6 * (int64_t) g3;
+ int64_t f6g4_19 = f6 * (int64_t) g4_19;
+ int64_t f6g5_19 = f6 * (int64_t) g5_19;
+ int64_t f6g6_19 = f6 * (int64_t) g6_19;
+ int64_t f6g7_19 = f6 * (int64_t) g7_19;
+ int64_t f6g8_19 = f6 * (int64_t) g8_19;
+ int64_t f6g9_19 = f6 * (int64_t) g9_19;
+ int64_t f7g0 = f7 * (int64_t) g0;
+ int64_t f7g1_2 = f7_2 * (int64_t) g1;
+ int64_t f7g2 = f7 * (int64_t) g2;
+ int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+ int64_t f7g4_19 = f7 * (int64_t) g4_19;
+ int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+ int64_t f7g6_19 = f7 * (int64_t) g6_19;
+ int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+ int64_t f7g8_19 = f7 * (int64_t) g8_19;
+ int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+ int64_t f8g0 = f8 * (int64_t) g0;
+ int64_t f8g1 = f8 * (int64_t) g1;
+ int64_t f8g2_19 = f8 * (int64_t) g2_19;
+ int64_t f8g3_19 = f8 * (int64_t) g3_19;
+ int64_t f8g4_19 = f8 * (int64_t) g4_19;
+ int64_t f8g5_19 = f8 * (int64_t) g5_19;
+ int64_t f8g6_19 = f8 * (int64_t) g6_19;
+ int64_t f8g7_19 = f8 * (int64_t) g7_19;
+ int64_t f8g8_19 = f8 * (int64_t) g8_19;
+ int64_t f8g9_19 = f8 * (int64_t) g9_19;
+ int64_t f9g0 = f9 * (int64_t) g0;
+ int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+ int64_t f9g2_19 = f9 * (int64_t) g2_19;
+ int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+ int64_t f9g4_19 = f9 * (int64_t) g4_19;
+ int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+ int64_t f9g6_19 = f9 * (int64_t) g6_19;
+ int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+ int64_t f9g8_19 = f9 * (int64_t) g8_19;
+ int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+ int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+ int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+ int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+ int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+ int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+ int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+ int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
+ int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
+ int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
+ int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+
+ /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+ * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+ * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+ * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ /* |h0| <= 2^25 */
+ /* |h4| <= 2^25 */
+ /* |h1| <= 1.71*2^59 */
+ /* |h5| <= 1.71*2^59 */
+
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+ /* |h1| <= 2^24; from now on fits into int32 */
+ /* |h5| <= 2^24; from now on fits into int32 */
+ /* |h2| <= 1.41*2^60 */
+ /* |h6| <= 1.41*2^60 */
+
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+ /* |h2| <= 2^25; from now on fits into int32 unchanged */
+ /* |h6| <= 2^25; from now on fits into int32 unchanged */
+ /* |h3| <= 1.71*2^59 */
+ /* |h7| <= 1.71*2^59 */
+
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+ /* |h3| <= 2^24; from now on fits into int32 unchanged */
+ /* |h7| <= 2^24; from now on fits into int32 unchanged */
+ /* |h4| <= 1.72*2^34 */
+ /* |h8| <= 1.41*2^60 */
+
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+ /* |h4| <= 2^25; from now on fits into int32 unchanged */
+ /* |h8| <= 2^25; from now on fits into int32 unchanged */
+ /* |h5| <= 1.01*2^24 */
+ /* |h9| <= 1.71*2^59 */
+
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+ /* |h9| <= 2^24; from now on fits into int32 unchanged */
+ /* |h0| <= 1.1*2^39 */
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ /* |h0| <= 2^25; from now on fits into int32 unchanged */
+ /* |h1| <= 1.01*2^24 */
+
+ h[0] = (int32_t)h0;
+ h[1] = (int32_t)h1;
+ h[2] = (int32_t)h2;
+ h[3] = (int32_t)h3;
+ h[4] = (int32_t)h4;
+ h[5] = (int32_t)h5;
+ h[6] = (int32_t)h6;
+ h[7] = (int32_t)h7;
+ h[8] = (int32_t)h8;
+ h[9] = (int32_t)h9;
}
-/* h = f * f
+/*
+ * h = f * f
+ *
* Can overlap h with f.
*
* Preconditions:
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
- * See fe_mul.c for discussion of implementation strategy. */
-static void fe_sq(fe h, const fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t f0_2 = 2 * f0;
- int32_t f1_2 = 2 * f1;
- int32_t f2_2 = 2 * f2;
- int32_t f3_2 = 2 * f3;
- int32_t f4_2 = 2 * f4;
- int32_t f5_2 = 2 * f5;
- int32_t f6_2 = 2 * f6;
- int32_t f7_2 = 2 * f7;
- int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
- int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
- int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
- int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
- int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
- int64_t f0f0 = f0 * (int64_t) f0;
- int64_t f0f1_2 = f0_2 * (int64_t) f1;
- int64_t f0f2_2 = f0_2 * (int64_t) f2;
- int64_t f0f3_2 = f0_2 * (int64_t) f3;
- int64_t f0f4_2 = f0_2 * (int64_t) f4;
- int64_t f0f5_2 = f0_2 * (int64_t) f5;
- int64_t f0f6_2 = f0_2 * (int64_t) f6;
- int64_t f0f7_2 = f0_2 * (int64_t) f7;
- int64_t f0f8_2 = f0_2 * (int64_t) f8;
- int64_t f0f9_2 = f0_2 * (int64_t) f9;
- int64_t f1f1_2 = f1_2 * (int64_t) f1;
- int64_t f1f2_2 = f1_2 * (int64_t) f2;
- int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
- int64_t f1f4_2 = f1_2 * (int64_t) f4;
- int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
- int64_t f1f6_2 = f1_2 * (int64_t) f6;
- int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
- int64_t f1f8_2 = f1_2 * (int64_t) f8;
- int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
- int64_t f2f2 = f2 * (int64_t) f2;
- int64_t f2f3_2 = f2_2 * (int64_t) f3;
- int64_t f2f4_2 = f2_2 * (int64_t) f4;
- int64_t f2f5_2 = f2_2 * (int64_t) f5;
- int64_t f2f6_2 = f2_2 * (int64_t) f6;
- int64_t f2f7_2 = f2_2 * (int64_t) f7;
- int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
- int64_t f2f9_38 = f2 * (int64_t) f9_38;
- int64_t f3f3_2 = f3_2 * (int64_t) f3;
- int64_t f3f4_2 = f3_2 * (int64_t) f4;
- int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
- int64_t f3f6_2 = f3_2 * (int64_t) f6;
- int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
- int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
- int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
- int64_t f4f4 = f4 * (int64_t) f4;
- int64_t f4f5_2 = f4_2 * (int64_t) f5;
- int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
- int64_t f4f7_38 = f4 * (int64_t) f7_38;
- int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
- int64_t f4f9_38 = f4 * (int64_t) f9_38;
- int64_t f5f5_38 = f5 * (int64_t) f5_38;
- int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
- int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
- int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
- int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
- int64_t f6f6_19 = f6 * (int64_t) f6_19;
- int64_t f6f7_38 = f6 * (int64_t) f7_38;
- int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
- int64_t f6f9_38 = f6 * (int64_t) f9_38;
- int64_t f7f7_38 = f7 * (int64_t) f7_38;
- int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
- int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
- int64_t f8f8_19 = f8 * (int64_t) f8_19;
- int64_t f8f9_38 = f8 * (int64_t) f9_38;
- int64_t f9f9_38 = f9 * (int64_t) f9_38;
- int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
- int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
- int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
- int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
- int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
- int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
- int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
- int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
- int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
- int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
-
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
-
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
-
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
-
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
+ * See fe_mul.c for discussion of implementation strategy.
+ */
+static void fe_sq(fe h, const fe f)
+{
+ int32_t f0 = f[0];
+ int32_t f1 = f[1];
+ int32_t f2 = f[2];
+ int32_t f3 = f[3];
+ int32_t f4 = f[4];
+ int32_t f5 = f[5];
+ int32_t f6 = f[6];
+ int32_t f7 = f[7];
+ int32_t f8 = f[8];
+ int32_t f9 = f[9];
+ int32_t f0_2 = 2 * f0;
+ int32_t f1_2 = 2 * f1;
+ int32_t f2_2 = 2 * f2;
+ int32_t f3_2 = 2 * f3;
+ int32_t f4_2 = 2 * f4;
+ int32_t f5_2 = 2 * f5;
+ int32_t f6_2 = 2 * f6;
+ int32_t f7_2 = 2 * f7;
+ int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+ int64_t f0f0 = f0 * (int64_t) f0;
+ int64_t f0f1_2 = f0_2 * (int64_t) f1;
+ int64_t f0f2_2 = f0_2 * (int64_t) f2;
+ int64_t f0f3_2 = f0_2 * (int64_t) f3;
+ int64_t f0f4_2 = f0_2 * (int64_t) f4;
+ int64_t f0f5_2 = f0_2 * (int64_t) f5;
+ int64_t f0f6_2 = f0_2 * (int64_t) f6;
+ int64_t f0f7_2 = f0_2 * (int64_t) f7;
+ int64_t f0f8_2 = f0_2 * (int64_t) f8;
+ int64_t f0f9_2 = f0_2 * (int64_t) f9;
+ int64_t f1f1_2 = f1_2 * (int64_t) f1;
+ int64_t f1f2_2 = f1_2 * (int64_t) f2;
+ int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
+ int64_t f1f4_2 = f1_2 * (int64_t) f4;
+ int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
+ int64_t f1f6_2 = f1_2 * (int64_t) f6;
+ int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
+ int64_t f1f8_2 = f1_2 * (int64_t) f8;
+ int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+ int64_t f2f2 = f2 * (int64_t) f2;
+ int64_t f2f3_2 = f2_2 * (int64_t) f3;
+ int64_t f2f4_2 = f2_2 * (int64_t) f4;
+ int64_t f2f5_2 = f2_2 * (int64_t) f5;
+ int64_t f2f6_2 = f2_2 * (int64_t) f6;
+ int64_t f2f7_2 = f2_2 * (int64_t) f7;
+ int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+ int64_t f2f9_38 = f2 * (int64_t) f9_38;
+ int64_t f3f3_2 = f3_2 * (int64_t) f3;
+ int64_t f3f4_2 = f3_2 * (int64_t) f4;
+ int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
+ int64_t f3f6_2 = f3_2 * (int64_t) f6;
+ int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+ int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+ int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+ int64_t f4f4 = f4 * (int64_t) f4;
+ int64_t f4f5_2 = f4_2 * (int64_t) f5;
+ int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+ int64_t f4f7_38 = f4 * (int64_t) f7_38;
+ int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+ int64_t f4f9_38 = f4 * (int64_t) f9_38;
+ int64_t f5f5_38 = f5 * (int64_t) f5_38;
+ int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+ int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+ int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+ int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+ int64_t f6f6_19 = f6 * (int64_t) f6_19;
+ int64_t f6f7_38 = f6 * (int64_t) f7_38;
+ int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+ int64_t f6f9_38 = f6 * (int64_t) f9_38;
+ int64_t f7f7_38 = f7 * (int64_t) f7_38;
+ int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+ int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+ int64_t f8f8_19 = f8 * (int64_t) f8_19;
+ int64_t f8f9_38 = f8 * (int64_t) f9_38;
+ int64_t f9f9_38 = f9 * (int64_t) f9_38;
+ int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+ int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+ int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+ int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+ int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
+ int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+ int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+ int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+ int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
+ int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+ h[0] = (int32_t)h0;
+ h[1] = (int32_t)h1;
+ h[2] = (int32_t)h2;
+ h[3] = (int32_t)h3;
+ h[4] = (int32_t)h4;
+ h[5] = (int32_t)h5;
+ h[6] = (int32_t)h6;
+ h[7] = (int32_t)h7;
+ h[8] = (int32_t)h8;
+ h[9] = (int32_t)h9;
}
-static void fe_invert(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- fe t3;
- int i;
+static void fe_invert(fe out, const fe z)
+{
+ fe t0;
+ fe t1;
+ fe t2;
+ fe t3;
+ int i;
- fe_sq(t0, z);
- for (i = 1; i < 1; ++i) {
- fe_sq(t0, t0);
- }
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
+ /*
+ * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+ * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+ */
+
+ /* t0 = z ** 2 */
+ fe_sq(t0, z);
+
+ /* t1 = t0 ** (2 ** 2) = z ** 8 */
+ fe_sq(t1, t0);
fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t2, t0);
- for (i = 1; i < 1; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t1, t2);
- fe_sq(t2, t1);
- for (i = 1; i < 5; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
- for (i = 1; i < 20; ++i) {
- fe_sq(t3, t3);
- }
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
- for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
- for (i = 1; i < 50; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
- for (i = 1; i < 100; ++i) {
- fe_sq(t3, t3);
- }
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
- for (i = 1; i < 50; ++i) {
+
+ /* t1 = z * t1 = z ** 9 */
+ fe_mul(t1, z, t1);
+ /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+ fe_mul(t0, t0, t1);
+
+ /* t2 = t0 ** 2 = z ** 22 */
+ fe_sq(t2, t0);
+
+ /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+ fe_mul(t1, t1, t2);
+
+ /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+ fe_sq(t2, t1);
+ for (i = 1; i < 5; ++i) {
+ fe_sq(t2, t2);
+ }
+
+ /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
+ fe_mul(t1, t2, t1);
+
+ /* Continuing similarly... */
+
+ /* t2 = z ** (2 ** 20 - 1) */
+ fe_sq(t2, t1);
+ for (i = 1; i < 10; ++i) {
+ fe_sq(t2, t2);
+ }
+ fe_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 40 - 1) */
+ fe_sq(t3, t2);
+ for (i = 1; i < 20; ++i) {
+ fe_sq(t3, t3);
+ }
+ fe_mul(t2, t3, t2);
+
+ /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+ for (i = 0; i < 10; ++i) {
+ fe_sq(t2, t2);
+ }
+ /* t1 = z ** (2 ** 50 - 1) */
+ fe_mul(t1, t2, t1);
+
+ /* t2 = z ** (2 ** 100 - 1) */
+ fe_sq(t2, t1);
+ for (i = 1; i < 50; ++i) {
+ fe_sq(t2, t2);
+ }
+ fe_mul(t2, t2, t1);
+
+ /* t2 = z ** (2 ** 200 - 1) */
+ fe_sq(t3, t2);
+ for (i = 1; i < 100; ++i) {
+ fe_sq(t3, t3);
+ }
+ fe_mul(t2, t3, t2);
+
+ /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 5; ++i) {
+ for (i = 1; i < 50; ++i) {
+ fe_sq(t2, t2);
+ }
+
+ /* t1 = z ** (2 ** 250 - 1) */
+ fe_mul(t1, t2, t1);
+
+ /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
fe_sq(t1, t1);
- }
- fe_mul(out, t1, t0);
-}
+ for (i = 1; i < 5; ++i) {
+ fe_sq(t1, t1);
+ }
-#if 0 /* Ed25519 code: not used yet */
+ /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+ fe_mul(out, t1, t0);
+}
-/* h = -f
+/*
+ * h = -f
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
- * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
-static void fe_neg(fe h, const fe f) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = -f[i];
- }
+ * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ */
+static void fe_neg(fe h, const fe f)
+{
+ unsigned i;
+
+ for (i = 0; i < 10; i++) {
+ h[i] = -f[i];
+ }
}
-/* Replace (f,g) with (g,g) if b == 1;
+/*
+ * Replace (f,g) with (g,g) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
- * Preconditions: b in {0,1}. */
-static void fe_cmov(fe f, const fe g, unsigned b) {
- size_t i;
- b = 0-b;
- for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
- x &= b;
- f[i] ^= x;
- }
+ * Preconditions: b in {0,1}.
+ */
+static void fe_cmov(fe f, const fe g, unsigned b)
+{
+ size_t i;
+
+ b = 0-b;
+ for (i = 0; i < 10; i++) {
+ int32_t x = f[i] ^ g[i];
+ x &= b;
+ f[i] ^= x;
+ }
}
-/* return 0 if f == 0
+/*
+ * return 0 if f == 0
* return 1 if f != 0
*
* Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnonzero(const fe f) {
- uint8_t s[32];
- static const uint8_t zero[32] = {0};
+ * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static int fe_isnonzero(const fe f)
+{
+ uint8_t s[32];
+ static const uint8_t zero[32] = {0};
+
+ fe_tobytes(s, f);
- fe_tobytes(s, f);
- return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+ return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
}
-/* return 1 if f is in {1,3,5,...,q-2}
+/*
+ * return 1 if f is in {1,3,5,...,q-2}
* return 0 if f is in {0,2,4,...,q-1}
*
* Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnegative(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
- return s[0] & 1;
+ * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static int fe_isnegative(const fe f)
+{
+ uint8_t s[32];
+
+ fe_tobytes(s, f);
+ return s[0] & 1;
}
-/* h = 2 * f * f
+/*
+ * h = 2 * f * f
+ *
* Can overlap h with f.
*
* Preconditions:
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
- * See fe_mul.c for discussion of implementation strategy. */
-static void fe_sq2(fe h, const fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t f0_2 = 2 * f0;
- int32_t f1_2 = 2 * f1;
- int32_t f2_2 = 2 * f2;
- int32_t f3_2 = 2 * f3;
- int32_t f4_2 = 2 * f4;
- int32_t f5_2 = 2 * f5;
- int32_t f6_2 = 2 * f6;
- int32_t f7_2 = 2 * f7;
- int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
- int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
- int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
- int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
- int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
- int64_t f0f0 = f0 * (int64_t) f0;
- int64_t f0f1_2 = f0_2 * (int64_t) f1;
- int64_t f0f2_2 = f0_2 * (int64_t) f2;
- int64_t f0f3_2 = f0_2 * (int64_t) f3;
- int64_t f0f4_2 = f0_2 * (int64_t) f4;
- int64_t f0f5_2 = f0_2 * (int64_t) f5;
- int64_t f0f6_2 = f0_2 * (int64_t) f6;
- int64_t f0f7_2 = f0_2 * (int64_t) f7;
- int64_t f0f8_2 = f0_2 * (int64_t) f8;
- int64_t f0f9_2 = f0_2 * (int64_t) f9;
- int64_t f1f1_2 = f1_2 * (int64_t) f1;
- int64_t f1f2_2 = f1_2 * (int64_t) f2;
- int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
- int64_t f1f4_2 = f1_2 * (int64_t) f4;
- int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
- int64_t f1f6_2 = f1_2 * (int64_t) f6;
- int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
- int64_t f1f8_2 = f1_2 * (int64_t) f8;
- int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
- int64_t f2f2 = f2 * (int64_t) f2;
- int64_t f2f3_2 = f2_2 * (int64_t) f3;
- int64_t f2f4_2 = f2_2 * (int64_t) f4;
- int64_t f2f5_2 = f2_2 * (int64_t) f5;
- int64_t f2f6_2 = f2_2 * (int64_t) f6;
- int64_t f2f7_2 = f2_2 * (int64_t) f7;
- int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
- int64_t f2f9_38 = f2 * (int64_t) f9_38;
- int64_t f3f3_2 = f3_2 * (int64_t) f3;
- int64_t f3f4_2 = f3_2 * (int64_t) f4;
- int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
- int64_t f3f6_2 = f3_2 * (int64_t) f6;
- int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
- int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
- int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
- int64_t f4f4 = f4 * (int64_t) f4;
- int64_t f4f5_2 = f4_2 * (int64_t) f5;
- int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
- int64_t f4f7_38 = f4 * (int64_t) f7_38;
- int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
- int64_t f4f9_38 = f4 * (int64_t) f9_38;
- int64_t f5f5_38 = f5 * (int64_t) f5_38;
- int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
- int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
- int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
- int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
- int64_t f6f6_19 = f6 * (int64_t) f6_19;
- int64_t f6f7_38 = f6 * (int64_t) f7_38;
- int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
- int64_t f6f9_38 = f6 * (int64_t) f9_38;
- int64_t f7f7_38 = f7 * (int64_t) f7_38;
- int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
- int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
- int64_t f8f8_19 = f8 * (int64_t) f8_19;
- int64_t f8f9_38 = f8 * (int64_t) f9_38;
- int64_t f9f9_38 = f9 * (int64_t) f9_38;
- int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
- int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
- int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
- int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
- int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
- int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
- int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
- int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
- int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
- int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- h0 += h0;
- h1 += h1;
- h2 += h2;
- h3 += h3;
- h4 += h4;
- h5 += h5;
- h6 += h6;
- h7 += h7;
- h8 += h8;
- h9 += h9;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
-
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
-
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
-
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
-
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
+ * See fe_mul.c for discussion of implementation strategy.
+ */
+static void fe_sq2(fe h, const fe f)
+{
+ int32_t f0 = f[0];
+ int32_t f1 = f[1];
+ int32_t f2 = f[2];
+ int32_t f3 = f[3];
+ int32_t f4 = f[4];
+ int32_t f5 = f[5];
+ int32_t f6 = f[6];
+ int32_t f7 = f[7];
+ int32_t f8 = f[8];
+ int32_t f9 = f[9];
+ int32_t f0_2 = 2 * f0;
+ int32_t f1_2 = 2 * f1;
+ int32_t f2_2 = 2 * f2;
+ int32_t f3_2 = 2 * f3;
+ int32_t f4_2 = 2 * f4;
+ int32_t f5_2 = 2 * f5;
+ int32_t f6_2 = 2 * f6;
+ int32_t f7_2 = 2 * f7;
+ int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+ int64_t f0f0 = f0 * (int64_t) f0;
+ int64_t f0f1_2 = f0_2 * (int64_t) f1;
+ int64_t f0f2_2 = f0_2 * (int64_t) f2;
+ int64_t f0f3_2 = f0_2 * (int64_t) f3;
+ int64_t f0f4_2 = f0_2 * (int64_t) f4;
+ int64_t f0f5_2 = f0_2 * (int64_t) f5;
+ int64_t f0f6_2 = f0_2 * (int64_t) f6;
+ int64_t f0f7_2 = f0_2 * (int64_t) f7;
+ int64_t f0f8_2 = f0_2 * (int64_t) f8;
+ int64_t f0f9_2 = f0_2 * (int64_t) f9;
+ int64_t f1f1_2 = f1_2 * (int64_t) f1;
+ int64_t f1f2_2 = f1_2 * (int64_t) f2;
+ int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
+ int64_t f1f4_2 = f1_2 * (int64_t) f4;
+ int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
+ int64_t f1f6_2 = f1_2 * (int64_t) f6;
+ int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
+ int64_t f1f8_2 = f1_2 * (int64_t) f8;
+ int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+ int64_t f2f2 = f2 * (int64_t) f2;
+ int64_t f2f3_2 = f2_2 * (int64_t) f3;
+ int64_t f2f4_2 = f2_2 * (int64_t) f4;
+ int64_t f2f5_2 = f2_2 * (int64_t) f5;
+ int64_t f2f6_2 = f2_2 * (int64_t) f6;
+ int64_t f2f7_2 = f2_2 * (int64_t) f7;
+ int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+ int64_t f2f9_38 = f2 * (int64_t) f9_38;
+ int64_t f3f3_2 = f3_2 * (int64_t) f3;
+ int64_t f3f4_2 = f3_2 * (int64_t) f4;
+ int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
+ int64_t f3f6_2 = f3_2 * (int64_t) f6;
+ int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+ int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+ int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+ int64_t f4f4 = f4 * (int64_t) f4;
+ int64_t f4f5_2 = f4_2 * (int64_t) f5;
+ int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+ int64_t f4f7_38 = f4 * (int64_t) f7_38;
+ int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+ int64_t f4f9_38 = f4 * (int64_t) f9_38;
+ int64_t f5f5_38 = f5 * (int64_t) f5_38;
+ int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+ int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+ int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+ int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+ int64_t f6f6_19 = f6 * (int64_t) f6_19;
+ int64_t f6f7_38 = f6 * (int64_t) f7_38;
+ int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+ int64_t f6f9_38 = f6 * (int64_t) f9_38;
+ int64_t f7f7_38 = f7 * (int64_t) f7_38;
+ int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+ int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+ int64_t f8f8_19 = f8 * (int64_t) f8_19;
+ int64_t f8f9_38 = f8 * (int64_t) f9_38;
+ int64_t f9f9_38 = f9 * (int64_t) f9_38;
+ int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+ int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+ int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+ int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+ int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
+ int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+ int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+ int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+ int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
+ int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+
+ h0 += h0;
+ h1 += h1;
+ h2 += h2;
+ h3 += h3;
+ h4 += h4;
+ h5 += h5;
+ h6 += h6;
+ h7 += h7;
+ h8 += h8;
+ h9 += h9;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+ h[0] = (int32_t)h0;
+ h[1] = (int32_t)h1;
+ h[2] = (int32_t)h2;
+ h[3] = (int32_t)h3;
+ h[4] = (int32_t)h4;
+ h[5] = (int32_t)h5;
+ h[6] = (int32_t)h6;
+ h[7] = (int32_t)h7;
+ h[8] = (int32_t)h8;
+ h[9] = (int32_t)h9;
}
-static void fe_pow22523(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- int i;
-
- fe_sq(t0, z);
- for (i = 1; i < 1; ++i) {
- fe_sq(t0, t0);
- }
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t0, t0);
- for (i = 1; i < 1; ++i) {
+static void fe_pow22523(fe out, const fe z)
+{
+ fe t0;
+ fe t1;
+ fe t2;
+ int i;
+
+ fe_sq(t0, z);
+ fe_sq(t1, t0);
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t1, z, t1);
+ fe_mul(t0, t0, t1);
fe_sq(t0, t0);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 20; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 50; ++i) {
+ fe_mul(t0, t1, t0);
+ fe_sq(t1, t0);
+ for (i = 1; i < 5; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t0, t1, t0);
+ fe_sq(t1, t0);
+ for (i = 1; i < 10; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t1, t1, t0);
+ fe_sq(t2, t1);
+ for (i = 1; i < 20; ++i) {
+ fe_sq(t2, t2);
+ }
+ fe_mul(t1, t2, t1);
fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 100; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 50; ++i) {
+ for (i = 1; i < 10; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t0, t1, t0);
+ fe_sq(t1, t0);
+ for (i = 1; i < 50; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t1, t1, t0);
+ fe_sq(t2, t1);
+ for (i = 1; i < 100; ++i) {
+ fe_sq(t2, t2);
+ }
+ fe_mul(t1, t2, t1);
fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t0, t0);
- for (i = 1; i < 2; ++i) {
+ for (i = 1; i < 50; ++i) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t0, t1, t0);
fe_sq(t0, t0);
- }
- fe_mul(out, t0, z);
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t0, t0);
+ }
+ fe_mul(out, t0, z);
}
-/* ge means group element.
-
+/*
+ * ge means group element.
+ *
* Here the group is the set of pairs (x,y) of field elements (see fe.h)
* satisfying -x^2 + y^2 = 1 + d x^2y^2
* where d = -121665/121666.
* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
- * ge_precomp (Duif): (y+x,y-x,2dxy) */
-
+ * ge_precomp (Duif): (y+x,y-x,2dxy)
+ */
typedef struct {
- fe X;
- fe Y;
- fe Z;
+ fe X;
+ fe Y;
+ fe Z;
} ge_p2;
typedef struct {
- fe X;
- fe Y;
- fe Z;
- fe T;
+ fe X;
+ fe Y;
+ fe Z;
+ fe T;
} ge_p3;
typedef struct {
- fe X;
- fe Y;
- fe Z;
- fe T;
+ fe X;
+ fe Y;
+ fe Z;
+ fe T;
} ge_p1p1;
typedef struct {
- fe yplusx;
- fe yminusx;
- fe xy2d;
+ fe yplusx;
+ fe yminusx;
+ fe xy2d;
} ge_precomp;
typedef struct {
- fe YplusX;
- fe YminusX;
- fe Z;
- fe T2d;
+ fe YplusX;
+ fe YminusX;
+ fe Z;
+ fe T2d;
} ge_cached;
-static void ge_tobytes(uint8_t *s, const ge_p2 *h) {
- fe recip;
- fe x;
- fe y;
+static void ge_tobytes(uint8_t *s, const ge_p2 *h)
+{
+ fe recip;
+ fe x;
+ fe y;
+
+ fe_invert(recip, h->Z);
+ fe_mul(x, h->X, recip);
+ fe_mul(y, h->Y, recip);
+ fe_tobytes(s, y);
+ s[31] ^= fe_isnegative(x) << 7;
+}
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
+static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
+{
+ fe recip;
+ fe x;
+ fe y;
+
+ fe_invert(recip, h->Z);
+ fe_mul(x, h->X, recip);
+ fe_mul(y, h->Y, recip);
+ fe_tobytes(s, y);
+ s[31] ^= fe_isnegative(x) << 7;
}
-static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
- fe recip;
- fe x;
- fe y;
+static const fe d = {
+ -10913610, 13857413, -15372611, 6949391, 114729,
+ -8787816, -6275908, -3247719, -18696448, -12055116
+};
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
+static const fe sqrtm1 = {
+ -32595792, -7943725, 9377950, 3500415, 12389472,
+ -272473, -25146209, -2005654, 326686, 11406482
+};
-static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116};
-
-static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482};
-
-static int ge_frombytes_negate_vartime(ge_p3 *h, const uint8_t *s) {
- fe u;
- fe v;
- fe v3;
- fe vxx;
- fe check;
-
- fe_frombytes(h->Y, s);
- fe_1(h->Z);
- fe_sq(u, h->Y);
- fe_mul(v, u, d);
- fe_sub(u, u, h->Z); /* u = y^2-1 */
- fe_add(v, v, h->Z); /* v = dy^2+1 */
-
- fe_sq(v3, v);
- fe_mul(v3, v3, v); /* v3 = v^3 */
- fe_sq(h->X, v3);
- fe_mul(h->X, h->X, v);
- fe_mul(h->X, h->X, u); /* x = uv^7 */
-
- fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
- fe_mul(h->X, h->X, v3);
- fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
-
- fe_sq(vxx, h->X);
- fe_mul(vxx, vxx, v);
- fe_sub(check, vxx, u); /* vx^2-u */
- if (fe_isnonzero(check)) {
- fe_add(check, vxx, u); /* vx^2+u */
+static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
+{
+ fe u;
+ fe v;
+ fe v3;
+ fe vxx;
+ fe check;
+
+ fe_frombytes(h->Y, s);
+ fe_1(h->Z);
+ fe_sq(u, h->Y);
+ fe_mul(v, u, d);
+ fe_sub(u, u, h->Z); /* u = y^2-1 */
+ fe_add(v, v, h->Z); /* v = dy^2+1 */
+
+ fe_sq(v3, v);
+ fe_mul(v3, v3, v); /* v3 = v^3 */
+ fe_sq(h->X, v3);
+ fe_mul(h->X, h->X, v);
+ fe_mul(h->X, h->X, u); /* x = uv^7 */
+
+ fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+ fe_mul(h->X, h->X, v3);
+ fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
+
+ fe_sq(vxx, h->X);
+ fe_mul(vxx, vxx, v);
+ fe_sub(check, vxx, u); /* vx^2-u */
if (fe_isnonzero(check)) {
- return -1;
+ fe_add(check, vxx, u); /* vx^2+u */
+ if (fe_isnonzero(check)) {
+ return -1;
+ }
+ fe_mul(h->X, h->X, sqrtm1);
}
- fe_mul(h->X, h->X, sqrtm1);
- }
- if (fe_isnegative(h->X) == (s[31] >> 7)) {
- fe_neg(h->X, h->X);
- }
+ if (fe_isnegative(h->X) != (s[31] >> 7)) {
+ fe_neg(h->X, h->X);
+ }
- fe_mul(h->T, h->X, h->Y);
- return 0;
+ fe_mul(h->T, h->X, h->Y);
+ return 0;
}
-static void ge_p2_0(ge_p2 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
+static void ge_p2_0(ge_p2 *h)
+{
+ fe_0(h->X);
+ fe_1(h->Y);
+ fe_1(h->Z);
}
-static void ge_p3_0(ge_p3 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
- fe_0(h->T);
+static void ge_p3_0(ge_p3 *h)
+{
+ fe_0(h->X);
+ fe_1(h->Y);
+ fe_1(h->Z);
+ fe_0(h->T);
}
-static void ge_precomp_0(ge_precomp *h) {
- fe_1(h->yplusx);
- fe_1(h->yminusx);
- fe_0(h->xy2d);
+static void ge_precomp_0(ge_precomp *h)
+{
+ fe_1(h->yplusx);
+ fe_1(h->yminusx);
+ fe_0(h->xy2d);
}
/* r = p */
-static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
- fe_copy(r->X, p->X);
- fe_copy(r->Y, p->Y);
- fe_copy(r->Z, p->Z);
+static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
+{
+ fe_copy(r->X, p->X);
+ fe_copy(r->Y, p->Y);
+ fe_copy(r->Z, p->Z);
}
-static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199};
+static const fe d2 = {
+ -21827239, -5839606, -30745221, 13898782, 229458,
+ 15978800, -12551817, -6495438, 29715968, 9444199
+};
/* r = p */
-static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
- fe_add(r->YplusX, p->Y, p->X);
- fe_sub(r->YminusX, p->Y, p->X);
- fe_copy(r->Z, p->Z);
- fe_mul(r->T2d, p->T, d2);
+static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
+{
+ fe_add(r->YplusX, p->Y, p->X);
+ fe_sub(r->YminusX, p->Y, p->X);
+ fe_copy(r->Z, p->Z);
+ fe_mul(r->T2d, p->T, d2);
}
/* r = p */
-static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
+static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
+{
+ fe_mul(r->X, p->X, p->T);
+ fe_mul(r->Y, p->Y, p->Z);
+ fe_mul(r->Z, p->Z, p->T);
}
/* r = p */
-static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
- fe_mul(r->T, p->X, p->Y);
+static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
+{
+ fe_mul(r->X, p->X, p->T);
+ fe_mul(r->Y, p->Y, p->Z);
+ fe_mul(r->Z, p->Z, p->T);
+ fe_mul(r->T, p->X, p->Y);
}
/* r = 2 * p */
-static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
- fe t0;
-
- fe_sq(r->X, p->X);
- fe_sq(r->Z, p->Y);
- fe_sq2(r->T, p->Z);
- fe_add(r->Y, p->X, p->Y);
- fe_sq(t0, r->Y);
- fe_add(r->Y, r->Z, r->X);
- fe_sub(r->Z, r->Z, r->X);
- fe_sub(r->X, t0, r->Y);
- fe_sub(r->T, r->T, r->Z);
+static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
+{
+ fe t0;
+
+ fe_sq(r->X, p->X);
+ fe_sq(r->Z, p->Y);
+ fe_sq2(r->T, p->Z);
+ fe_add(r->Y, p->X, p->Y);
+ fe_sq(t0, r->Y);
+ fe_add(r->Y, r->Z, r->X);
+ fe_sub(r->Z, r->Z, r->X);
+ fe_sub(r->X, t0, r->Y);
+ fe_sub(r->T, r->T, r->Z);
}
/* r = 2 * p */
-static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
- ge_p2 q;
- ge_p3_to_p2(&q, p);
- ge_p2_dbl(r, &q);
+static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
+{
+ ge_p2 q;
+ ge_p3_to_p2(&q, p);
+ ge_p2_dbl(r, &q);
}
/* r = p + q */
-static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yplusx);
- fe_mul(r->Y, r->Y, q->yminusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
+static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
+{
+ fe t0;
+
+ fe_add(r->X, p->Y, p->X);
+ fe_sub(r->Y, p->Y, p->X);
+ fe_mul(r->Z, r->X, q->yplusx);
+ fe_mul(r->Y, r->Y, q->yminusx);
+ fe_mul(r->T, q->xy2d, p->T);
+ fe_add(t0, p->Z, p->Z);
+ fe_sub(r->X, r->Z, r->Y);
+ fe_add(r->Y, r->Z, r->Y);
+ fe_add(r->Z, t0, r->T);
+ fe_sub(r->T, t0, r->T);
}
/* r = p - q */
-static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yminusx);
- fe_mul(r->Y, r->Y, q->yplusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
+static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
+{
+ fe t0;
+
+ fe_add(r->X, p->Y, p->X);
+ fe_sub(r->Y, p->Y, p->X);
+ fe_mul(r->Z, r->X, q->yminusx);
+ fe_mul(r->Y, r->Y, q->yplusx);
+ fe_mul(r->T, q->xy2d, p->T);
+ fe_add(t0, p->Z, p->Z);
+ fe_sub(r->X, r->Z, r->Y);
+ fe_add(r->Y, r->Z, r->Y);
+ fe_sub(r->Z, t0, r->T);
+ fe_add(r->T, t0, r->T);
}
/* r = p + q */
-static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YplusX);
- fe_mul(r->Y, r->Y, q->YminusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
+static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
+{
+ fe t0;
+
+ fe_add(r->X, p->Y, p->X);
+ fe_sub(r->Y, p->Y, p->X);
+ fe_mul(r->Z, r->X, q->YplusX);
+ fe_mul(r->Y, r->Y, q->YminusX);
+ fe_mul(r->T, q->T2d, p->T);
+ fe_mul(r->X, p->Z, q->Z);
+ fe_add(t0, r->X, r->X);
+ fe_sub(r->X, r->Z, r->Y);
+ fe_add(r->Y, r->Z, r->Y);
+ fe_add(r->Z, t0, r->T);
+ fe_sub(r->T, t0, r->T);
}
/* r = p - q */
-static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YminusX);
- fe_mul(r->Y, r->Y, q->YplusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
+static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
+{
+ fe t0;
+
+ fe_add(r->X, p->Y, p->X);
+ fe_sub(r->Y, p->Y, p->X);
+ fe_mul(r->Z, r->X, q->YminusX);
+ fe_mul(r->Y, r->Y, q->YplusX);
+ fe_mul(r->T, q->T2d, p->T);
+ fe_mul(r->X, p->Z, q->Z);
+ fe_add(t0, r->X, r->X);
+ fe_sub(r->X, r->Z, r->Y);
+ fe_add(r->Y, r->Z, r->Y);
+ fe_sub(r->Z, t0, r->T);
+ fe_add(r->T, t0, r->T);
}
-static uint8_t equal(signed char b, signed char c) {
- uint8_t ub = b;
- uint8_t uc = c;
- uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
- uint32_t y = x; /* 0: yes; 1..255: no */
- y -= 1; /* 4294967295: yes; 0..254: no */
- y >>= 31; /* 1: yes; 0: no */
- return y;
+static uint8_t equal(signed char b, signed char c)
+{
+ uint8_t ub = b;
+ uint8_t uc = c;
+ uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
+ uint32_t y = x; /* 0: yes; 1..255: no */
+ y -= 1; /* 4294967295: yes; 0..254: no */
+ y >>= 31; /* 1: yes; 0: no */
+ return y;
}
-static void cmov(ge_precomp *t, ge_precomp *u, uint8_t b) {
- fe_cmov(t->yplusx, u->yplusx, b);
- fe_cmov(t->yminusx, u->yminusx, b);
- fe_cmov(t->xy2d, u->xy2d, b);
+static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
+{
+ fe_cmov(t->yplusx, u->yplusx, b);
+ fe_cmov(t->yminusx, u->yminusx, b);
+ fe_cmov(t->xy2d, u->xy2d, b);
}
-#if defined(OPENSSL_SMALL)
-
-/* This block of code replaces the standard base-point table with a much smaller
- * one. The standard table is 30,720 bytes while this one is just 960.
- *
- * This table contains 15 pairs of group elements, (x, y), where each field
- * element is serialised with |fe_tobytes|. If |i| is the index of the group
- * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
- * is the most significant bit). The value of the group element is then:
- * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */
-static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
- 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
- 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
- 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
- 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
- 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
- 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
- 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
- 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
- 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
- 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
- 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
- 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
- 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
- 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
- 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
- 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
- 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
- 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
- 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
- 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
- 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
- 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
- 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
- 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
- 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
- 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
- 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
- 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
- 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
- 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
- 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
- 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
- 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
- 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
- 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
- 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
- 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
- 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
- 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
- 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
- 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
- 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
- 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
- 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
- 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
- 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
- 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
- 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
- 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
- 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
- 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
- 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
- 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
- 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
- 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
- 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
- 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
- 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
- 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
- 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
- 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
- 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
- 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
- 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
- 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
- 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
- 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
- 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
- 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
- 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
- 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
- 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
- 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
- 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
- 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
- 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
- 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
-};
-
-static void ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
- /* k25519SmallPrecomp is first expanded into matching |ge_precomp|
- * elements. */
- ge_precomp multiples[15];
-
- unsigned i;
- for (i = 0; i < 15; i++) {
- const uint8_t *bytes = &k25519SmallPrecomp[i*(2 * 32)];
- fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
-
- ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
- }
-
- /* See the comment above |k25519SmallPrecomp| about the structure of the
- * precomputed elements. This loop does 64 additions and 64 doublings to
- * calculate the result. */
- ge_p3_0(h);
-
- for (i = 63; i < 64; i--) {
- unsigned j;
- signed char index = 0;
-
- for (j = 0; j < 4; j++) {
- const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
- index |= (bit << j);
- }
-
- ge_precomp e;
- ge_precomp_0(&e);
-
- for (j = 1; j < 16; j++) {
- cmov(&e, &multiples[j-1], equal(index, j));
- }
-
- ge_cached cached;
- ge_p1p1 r;
- ge_p3_to_cached(&cached, h);
- ge_add(&r, h, &cached);
- ge_p1p1_to_p3(h, &r);
-
- ge_madd(&r, h, &e);
- ge_p1p1_to_p3(h, &r);
- }
-}
-
-#else
-
/* k25519Precomp[i][j] = (j+1)*256^i*B */
-static ge_precomp k25519Precomp[32][8] = {
+static const ge_precomp k25519Precomp[32][8] = {
{
{
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
},
};
-static uint8_t negative(signed char b) {
- uint32_t x = b;
- x >>= 31; /* 1: yes; 0: no */
- return x;
+static uint8_t negative(signed char b)
+{
+ uint32_t x = b;
+
+ x >>= 31; /* 1: yes; 0: no */
+ return x;
}
-static void table_select(ge_precomp *t, int pos, signed char b) {
- ge_precomp minust;
- uint8_t bnegative = negative(b);
- uint8_t babs = b - (((-bnegative) & b) << 1);
-
- ge_precomp_0(t);
- cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
- cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
- cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
- cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
- cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
- cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
- cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
- cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
- fe_copy(minust.yplusx, t->yminusx);
- fe_copy(minust.yminusx, t->yplusx);
- fe_neg(minust.xy2d, t->xy2d);
- cmov(t, &minust, bnegative);
+static void table_select(ge_precomp *t, int pos, signed char b)
+{
+ ge_precomp minust;
+ uint8_t bnegative = negative(b);
+ uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
+
+ ge_precomp_0(t);
+ cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
+ cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
+ cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
+ cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
+ cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
+ cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
+ cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
+ cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
+ fe_copy(minust.yplusx, t->yminusx);
+ fe_copy(minust.yminusx, t->yplusx);
+ fe_neg(minust.xy2d, t->xy2d);
+ cmov(t, &minust, bnegative);
}
-/* h = a * B
+/*
+ * h = a * B
+ *
* where a = a[0]+256*a[1]+...+256^31 a[31]
* B is the Ed25519 base point (x,4/5) with x positive.
*
* Preconditions:
- * a[31] <= 127 */
-static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
- signed char e[64];
- signed char carry;
- ge_p1p1 r;
- ge_p2 s;
- ge_precomp t;
- int i;
-
- for (i = 0; i < 32; ++i) {
- e[2 * i + 0] = (a[i] >> 0) & 15;
- e[2 * i + 1] = (a[i] >> 4) & 15;
- }
- /* each e[i] is between 0 and 15 */
- /* e[63] is between 0 and 7 */
-
- carry = 0;
- for (i = 0; i < 63; ++i) {
- e[i] += carry;
- carry = e[i] + 8;
- carry >>= 4;
- e[i] -= carry << 4;
- }
- e[63] += carry;
- /* each e[i] is between -8 and 8 */
-
- ge_p3_0(h);
- for (i = 1; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
- ge_p1p1_to_p3(h, &r);
- }
-
- ge_p3_dbl(&r, h);
- ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- ge_p1p1_to_p3(h, &r);
-
- for (i = 0; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
+ * a[31] <= 127
+ */
+static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
+{
+ signed char e[64];
+ signed char carry;
+ ge_p1p1 r;
+ ge_p2 s;
+ ge_precomp t;
+ int i;
+
+ for (i = 0; i < 32; ++i) {
+ e[2 * i + 0] = (a[i] >> 0) & 15;
+ e[2 * i + 1] = (a[i] >> 4) & 15;
+ }
+ /* each e[i] is between 0 and 15 */
+ /* e[63] is between 0 and 7 */
+
+ carry = 0;
+ for (i = 0; i < 63; ++i) {
+ e[i] += carry;
+ carry = e[i] + 8;
+ carry >>= 4;
+ e[i] -= carry << 4;
+ }
+ e[63] += carry;
+ /* each e[i] is between -8 and 8 */
+
+ ge_p3_0(h);
+ for (i = 1; i < 64; i += 2) {
+ table_select(&t, i / 2, e[i]);
+ ge_madd(&r, h, &t);
+ ge_p1p1_to_p3(h, &r);
+ }
+
+ ge_p3_dbl(&r, h);
+ ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
+ ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
+ ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
ge_p1p1_to_p3(h, &r);
- }
+
+ for (i = 0; i < 64; i += 2) {
+ table_select(&t, i / 2, e[i]);
+ ge_madd(&r, h, &t);
+ ge_p1p1_to_p3(h, &r);
+ }
+
+ OPENSSL_cleanse(e, sizeof(e));
+}
+
+#if !defined(BASE_2_51_IMPLEMENTED)
+/*
+ * Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
+ *
+ * Preconditions: b in {0,1}.
+ */
+static void fe_cswap(fe f, fe g, unsigned int b)
+{
+ size_t i;
+
+ b = 0-b;
+ for (i = 0; i < 10; i++) {
+ int32_t x = f[i] ^ g[i];
+ x &= b;
+ f[i] ^= x;
+ g[i] ^= x;
+ }
}
+/*
+ * h = f * 121666
+ *
+ * Can overlap h with f.
+ *
+ * Preconditions:
+ * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ *
+ * Postconditions:
+ * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ */
+static void fe_mul121666(fe h, fe f)
+{
+ int32_t f0 = f[0];
+ int32_t f1 = f[1];
+ int32_t f2 = f[2];
+ int32_t f3 = f[3];
+ int32_t f4 = f[4];
+ int32_t f5 = f[5];
+ int32_t f6 = f[6];
+ int32_t f7 = f[7];
+ int32_t f8 = f[8];
+ int32_t f9 = f[9];
+ int64_t h0 = f0 * (int64_t) 121666;
+ int64_t h1 = f1 * (int64_t) 121666;
+ int64_t h2 = f2 * (int64_t) 121666;
+ int64_t h3 = f3 * (int64_t) 121666;
+ int64_t h4 = f4 * (int64_t) 121666;
+ int64_t h5 = f5 * (int64_t) 121666;
+ int64_t h6 = f6 * (int64_t) 121666;
+ int64_t h7 = f7 * (int64_t) 121666;
+ int64_t h8 = f8 * (int64_t) 121666;
+ int64_t h9 = f9 * (int64_t) 121666;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+ h[0] = (int32_t)h0;
+ h[1] = (int32_t)h1;
+ h[2] = (int32_t)h2;
+ h[3] = (int32_t)h3;
+ h[4] = (int32_t)h4;
+ h[5] = (int32_t)h5;
+ h[6] = (int32_t)h6;
+ h[7] = (int32_t)h7;
+ h[8] = (int32_t)h8;
+ h[9] = (int32_t)h9;
+}
+
+static void x25519_scalar_mult_generic(uint8_t out[32],
+ const uint8_t scalar[32],
+ const uint8_t point[32]) {
+ fe x1, x2, z2, x3, z3, tmp0, tmp1;
+ uint8_t e[32];
+ unsigned swap = 0;
+ int pos;
+
+ memcpy(e, scalar, 32);
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+ fe_frombytes(x1, point);
+ fe_1(x2);
+ fe_0(z2);
+ fe_copy(x3, x1);
+ fe_1(z3);
+
+ for (pos = 254; pos >= 0; --pos) {
+ unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+ swap ^= b;
+ fe_cswap(x2, x3, swap);
+ fe_cswap(z2, z3, swap);
+ swap = b;
+ fe_sub(tmp0, x3, z3);
+ fe_sub(tmp1, x2, z2);
+ fe_add(x2, x2, z2);
+ fe_add(z2, x3, z3);
+ fe_mul(z3, tmp0, x2);
+ fe_mul(z2, z2, tmp1);
+ fe_sq(tmp0, tmp1);
+ fe_sq(tmp1, x2);
+ fe_add(x3, z3, z2);
+ fe_sub(z2, z3, z2);
+ fe_mul(x2, tmp1, tmp0);
+ fe_sub(tmp1, tmp1, tmp0);
+ fe_sq(z2, z2);
+ fe_mul121666(z3, tmp1);
+ fe_sq(x3, x3);
+ fe_add(tmp0, tmp0, z3);
+ fe_mul(z3, x1, z2);
+ fe_mul(z2, tmp1, tmp0);
+ }
+
+ fe_invert(z2, z2);
+ fe_mul(x2, x2, z2);
+ fe_tobytes(out, x2);
+
+ OPENSSL_cleanse(e, sizeof(e));
+}
+
+static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32]) {
+ x25519_scalar_mult_generic(out, scalar, point);
+}
#endif
-static void slide(signed char *r, const uint8_t *a) {
- int i;
- int b;
- int k;
-
- for (i = 0; i < 256; ++i) {
- r[i] = 1 & (a[i >> 3] >> (i & 7));
- }
-
- for (i = 0; i < 256; ++i) {
- if (r[i]) {
- for (b = 1; b <= 6 && i + b < 256; ++b) {
- if (r[i + b]) {
- if (r[i] + (r[i + b] << b) <= 15) {
- r[i] += r[i + b] << b;
- r[i + b] = 0;
- } else if (r[i] - (r[i + b] << b) >= -15) {
- r[i] -= r[i + b] << b;
- for (k = i + b; k < 256; ++k) {
- if (!r[k]) {
- r[k] = 1;
- break;
- }
- r[k] = 0;
+static void slide(signed char *r, const uint8_t *a)
+{
+ int i;
+ int b;
+ int k;
+
+ for (i = 0; i < 256; ++i) {
+ r[i] = 1 & (a[i >> 3] >> (i & 7));
+ }
+
+ for (i = 0; i < 256; ++i) {
+ if (r[i]) {
+ for (b = 1; b <= 6 && i + b < 256; ++b) {
+ if (r[i + b]) {
+ if (r[i] + (r[i + b] << b) <= 15) {
+ r[i] += r[i + b] << b;
+ r[i + b] = 0;
+ } else if (r[i] - (r[i + b] << b) >= -15) {
+ r[i] -= r[i + b] << b;
+ for (k = i + b; k < 256; ++k) {
+ if (!r[k]) {
+ r[k] = 1;
+ break;
+ }
+ r[k] = 0;
+ }
+ } else {
+ break;
+ }
+ }
}
- } else {
- break;
- }
}
- }
}
- }
}
-static ge_precomp Bi[8] = {
+static const ge_precomp Bi[8] = {
{
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
-11754271, -6079156, 2047605},
},
};
-/* r = a * A + b * B
+/*
+ * r = a * A + b * B
+ *
* where a = a[0]+256*a[1]+...+256^31 a[31].
* and b = b[0]+256*b[1]+...+256^31 b[31].
- * B is the Ed25519 base point (x,4/5) with x positive. */
-void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
- const ge_p3 *A, const uint8_t *b) {
- signed char aslide[256];
- signed char bslide[256];
- ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
- ge_p1p1 t;
- ge_p3 u;
- ge_p3 A2;
- int i;
-
- slide(aslide, a);
- slide(bslide, b);
-
- ge_p3_to_cached(&Ai[0], A);
- ge_p3_dbl(&t, A);
- ge_p1p1_to_p3(&A2, &t);
- ge_add(&t, &A2, &Ai[0]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[1], &u);
- ge_add(&t, &A2, &Ai[1]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[2], &u);
- ge_add(&t, &A2, &Ai[2]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[3], &u);
- ge_add(&t, &A2, &Ai[3]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[4], &u);
- ge_add(&t, &A2, &Ai[4]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[5], &u);
- ge_add(&t, &A2, &Ai[5]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[6], &u);
- ge_add(&t, &A2, &Ai[6]);
- ge_p1p1_to_p3(&u, &t);
- ge_p3_to_cached(&Ai[7], &u);
-
- ge_p2_0(r);
-
- for (i = 255; i >= 0; --i) {
- if (aslide[i] || bslide[i]) {
- break;
+ * B is the Ed25519 base point (x,4/5) with x positive.
+ */
+static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
+ const ge_p3 *A, const uint8_t *b)
+{
+ signed char aslide[256];
+ signed char bslide[256];
+ ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+ ge_p1p1 t;
+ ge_p3 u;
+ ge_p3 A2;
+ int i;
+
+ slide(aslide, a);
+ slide(bslide, b);
+
+ ge_p3_to_cached(&Ai[0], A);
+ ge_p3_dbl(&t, A);
+ ge_p1p1_to_p3(&A2, &t);
+ ge_add(&t, &A2, &Ai[0]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[1], &u);
+ ge_add(&t, &A2, &Ai[1]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[2], &u);
+ ge_add(&t, &A2, &Ai[2]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[3], &u);
+ ge_add(&t, &A2, &Ai[3]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[4], &u);
+ ge_add(&t, &A2, &Ai[4]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[5], &u);
+ ge_add(&t, &A2, &Ai[5]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[6], &u);
+ ge_add(&t, &A2, &Ai[6]);
+ ge_p1p1_to_p3(&u, &t);
+ ge_p3_to_cached(&Ai[7], &u);
+
+ ge_p2_0(r);
+
+ for (i = 255; i >= 0; --i) {
+ if (aslide[i] || bslide[i]) {
+ break;
+ }
}
- }
- for (; i >= 0; --i) {
- ge_p2_dbl(&t, r);
+ for (; i >= 0; --i) {
+ ge_p2_dbl(&t, r);
- if (aslide[i] > 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_add(&t, &u, &Ai[aslide[i] / 2]);
- } else if (aslide[i] < 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
- }
+ if (aslide[i] > 0) {
+ ge_p1p1_to_p3(&u, &t);
+ ge_add(&t, &u, &Ai[aslide[i] / 2]);
+ } else if (aslide[i] < 0) {
+ ge_p1p1_to_p3(&u, &t);
+ ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+ }
- if (bslide[i] > 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_madd(&t, &u, &Bi[bslide[i] / 2]);
- } else if (bslide[i] < 0) {
- ge_p1p1_to_p3(&u, &t);
- ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
- }
+ if (bslide[i] > 0) {
+ ge_p1p1_to_p3(&u, &t);
+ ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+ } else if (bslide[i] < 0) {
+ ge_p1p1_to_p3(&u, &t);
+ ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+ }
- ge_p1p1_to_p2(r, &t);
- }
+ ge_p1p1_to_p2(r, &t);
+ }
}
-/* The set of scalars is \Z/l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-
-/* Input:
+/*
+ * The set of scalars is \Z/l
+ * where l = 2^252 + 27742317777372353535851937790883648493.
+ *
+ * Input:
* s[0]+256*s[1]+...+256^63*s[63] = s
*
* Output:
* s[0]+256*s[1]+...+256^31*s[31] = s mod l
* where l = 2^252 + 27742317777372353535851937790883648493.
- * Overwrites s in place. */
-static void sc_reduce(uint8_t *s) {
- int64_t s0 = 2097151 & load_3(s);
- int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
- int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
- int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
- int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
- int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
- int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
- int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
- int64_t s8 = 2097151 & load_3(s + 21);
- int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
- int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
- int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
- int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
- int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
- int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
- int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
- int64_t s16 = 2097151 & load_3(s + 42);
- int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
- int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
- int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
- int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
- int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
- int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
- int64_t s23 = (load_4(s + 60) >> 3);
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
+ * Overwrites s in place.
+*/
+static void x25519_sc_reduce(uint8_t *s)
+{
+ int64_t s0 = kBottom21Bits & load_3(s);
+ int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
+ int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
+ int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
+ int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
+ int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
+ int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
+ int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
+ int64_t s8 = kBottom21Bits & load_3(s + 21);
+ int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
+ int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
+ int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
+ int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
+ int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
+ int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
+ int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
+ int64_t s16 = kBottom21Bits & load_3(s + 42);
+ int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
+ int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
+ int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
+ int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
+ int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
+ int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
+ int64_t s23 = (load_4(s + 60) >> 3);
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+ int64_t carry10;
+ int64_t carry11;
+ int64_t carry12;
+ int64_t carry13;
+ int64_t carry14;
+ int64_t carry15;
+ int64_t carry16;
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+ s23 = 0;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+ s22 = 0;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+ s21 = 0;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+ s20 = 0;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+ s19 = 0;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+ s18 = 0;
+
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * (1 << 21);
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * (1 << 21);
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * (1 << 21);
+
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * (1 << 21);
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * (1 << 21);
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+ s17 = 0;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+ s16 = 0;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+ s15 = 0;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+ s14 = 0;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+ s13 = 0;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+
+ s[ 0] = (uint8_t) (s0 >> 0);
+ s[ 1] = (uint8_t) (s0 >> 8);
+ s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
+ s[ 3] = (uint8_t) (s1 >> 3);
+ s[ 4] = (uint8_t) (s1 >> 11);
+ s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
+ s[ 6] = (uint8_t) (s2 >> 6);
+ s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
+ s[ 8] = (uint8_t) (s3 >> 1);
+ s[ 9] = (uint8_t) (s3 >> 9);
+ s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
+ s[11] = (uint8_t) (s4 >> 4);
+ s[12] = (uint8_t) (s4 >> 12);
+ s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
+ s[14] = (uint8_t) (s5 >> 7);
+ s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
+ s[16] = (uint8_t) (s6 >> 2);
+ s[17] = (uint8_t) (s6 >> 10);
+ s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
+ s[19] = (uint8_t) (s7 >> 5);
+ s[20] = (uint8_t) (s7 >> 13);
+ s[21] = (uint8_t) (s8 >> 0);
+ s[22] = (uint8_t) (s8 >> 8);
+ s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
+ s[24] = (uint8_t) (s9 >> 3);
+ s[25] = (uint8_t) (s9 >> 11);
+ s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
+ s[27] = (uint8_t) (s10 >> 6);
+ s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
+ s[29] = (uint8_t) (s11 >> 1);
+ s[30] = (uint8_t) (s11 >> 9);
+ s[31] = (uint8_t) (s11 >> 17);
}
-/* Input:
+/*
+ * Input:
* a[0]+256*a[1]+...+256^31*a[31] = a
* b[0]+256*b[1]+...+256^31*b[31] = b
* c[0]+256*c[1]+...+256^31*c[31] = c
*
* Output:
* s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
+ * where l = 2^252 + 27742317777372353535851937790883648493.
+ */
static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
- const uint8_t *c) {
- int64_t a0 = 2097151 & load_3(a);
- int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
- int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
- int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
- int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
- int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
- int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
- int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
- int64_t a8 = 2097151 & load_3(a + 21);
- int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
- int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
- int64_t a11 = (load_4(a + 28) >> 7);
- int64_t b0 = 2097151 & load_3(b);
- int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
- int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
- int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
- int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
- int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
- int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
- int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
- int64_t b8 = 2097151 & load_3(b + 21);
- int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
- int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
- int64_t b11 = (load_4(b + 28) >> 7);
- int64_t c0 = 2097151 & load_3(c);
- int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
- int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
- int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
- int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
- int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
- int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
- int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
- int64_t c8 = 2097151 & load_3(c + 21);
- int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
- int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
- int64_t c11 = (load_4(c + 28) >> 7);
- int64_t s0;
- int64_t s1;
- int64_t s2;
- int64_t s3;
- int64_t s4;
- int64_t s5;
- int64_t s6;
- int64_t s7;
- int64_t s8;
- int64_t s9;
- int64_t s10;
- int64_t s11;
- int64_t s12;
- int64_t s13;
- int64_t s14;
- int64_t s15;
- int64_t s16;
- int64_t s17;
- int64_t s18;
- int64_t s19;
- int64_t s20;
- int64_t s21;
- int64_t s22;
- int64_t s23;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
- int64_t carry17;
- int64_t carry18;
- int64_t carry19;
- int64_t carry20;
- int64_t carry21;
- int64_t carry22;
-
- s0 = c0 + a0 * b0;
- s1 = c1 + a0 * b1 + a1 * b0;
- s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
- s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
- s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
- s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
- s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
- s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
- a6 * b1 + a7 * b0;
- s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
- a6 * b2 + a7 * b1 + a8 * b0;
- s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
- a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
- s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
- a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
- s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
- a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
- s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
- a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
- s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
- a9 * b4 + a10 * b3 + a11 * b2;
- s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
- a10 * b4 + a11 * b3;
- s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
- a11 * b4;
- s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
- s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
- s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
- s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
- s20 = a9 * b11 + a10 * b10 + a11 * b9;
- s21 = a10 * b11 + a11 * b10;
- s22 = a11 * b11;
- s23 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
- carry18 = (s18 + (1 << 20)) >> 21;
- s19 += carry18;
- s18 -= carry18 << 21;
- carry20 = (s20 + (1 << 20)) >> 21;
- s21 += carry20;
- s20 -= carry20 << 21;
- carry22 = (s22 + (1 << 20)) >> 21;
- s23 += carry22;
- s22 -= carry22 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
- carry17 = (s17 + (1 << 20)) >> 21;
- s18 += carry17;
- s17 -= carry17 << 21;
- carry19 = (s19 + (1 << 20)) >> 21;
- s20 += carry19;
- s19 -= carry19 << 21;
- carry21 = (s21 + (1 << 20)) >> 21;
- s22 += carry21;
- s21 -= carry21 << 21;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
- uint8_t seed[32];
- RAND_bytes(seed, 32);
-
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(seed, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- ge_p3 A;
- ge_scalarmult_base(&A, az);
- ge_p3_tobytes(out_public_key, &A);
-
- memcpy(out_private_key, seed, 32);
- memmove(out_private_key + 32, out_public_key, 32);
+ const uint8_t *c)
+{
+ int64_t a0 = kBottom21Bits & load_3(a);
+ int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
+ int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
+ int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
+ int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
+ int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
+ int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
+ int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
+ int64_t a8 = kBottom21Bits & load_3(a + 21);
+ int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
+ int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
+ int64_t a11 = (load_4(a + 28) >> 7);
+ int64_t b0 = kBottom21Bits & load_3(b);
+ int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
+ int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
+ int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
+ int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
+ int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
+ int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
+ int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
+ int64_t b8 = kBottom21Bits & load_3(b + 21);
+ int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
+ int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
+ int64_t b11 = (load_4(b + 28) >> 7);
+ int64_t c0 = kBottom21Bits & load_3(c);
+ int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
+ int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
+ int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
+ int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
+ int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
+ int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
+ int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
+ int64_t c8 = kBottom21Bits & load_3(c + 21);
+ int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
+ int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
+ int64_t c11 = (load_4(c + 28) >> 7);
+ int64_t s0;
+ int64_t s1;
+ int64_t s2;
+ int64_t s3;
+ int64_t s4;
+ int64_t s5;
+ int64_t s6;
+ int64_t s7;
+ int64_t s8;
+ int64_t s9;
+ int64_t s10;
+ int64_t s11;
+ int64_t s12;
+ int64_t s13;
+ int64_t s14;
+ int64_t s15;
+ int64_t s16;
+ int64_t s17;
+ int64_t s18;
+ int64_t s19;
+ int64_t s20;
+ int64_t s21;
+ int64_t s22;
+ int64_t s23;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+ int64_t carry10;
+ int64_t carry11;
+ int64_t carry12;
+ int64_t carry13;
+ int64_t carry14;
+ int64_t carry15;
+ int64_t carry16;
+ int64_t carry17;
+ int64_t carry18;
+ int64_t carry19;
+ int64_t carry20;
+ int64_t carry21;
+ int64_t carry22;
+
+ s0 = c0 + a0 * b0;
+ s1 = c1 + a0 * b1 + a1 * b0;
+ s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+ s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+ s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+ s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+ s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+ s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+ s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+ s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+ s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+ s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+ s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+ s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+ s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+ s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+ s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+ s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+ s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+ s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+ s20 = a9 * b11 + a10 * b10 + a11 * b9;
+ s21 = a10 * b11 + a11 * b10;
+ s22 = a11 * b11;
+ s23 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * (1 << 21);
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * (1 << 21);
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * (1 << 21);
+ carry18 = (s18 + (1 << 20)) >> 21;
+ s19 += carry18;
+ s18 -= carry18 * (1 << 21);
+ carry20 = (s20 + (1 << 20)) >> 21;
+ s21 += carry20;
+ s20 -= carry20 * (1 << 21);
+ carry22 = (s22 + (1 << 20)) >> 21;
+ s23 += carry22;
+ s22 -= carry22 * (1 << 21);
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * (1 << 21);
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * (1 << 21);
+ carry17 = (s17 + (1 << 20)) >> 21;
+ s18 += carry17;
+ s17 -= carry17 * (1 << 21);
+ carry19 = (s19 + (1 << 20)) >> 21;
+ s20 += carry19;
+ s19 -= carry19 * (1 << 21);
+ carry21 = (s21 + (1 << 20)) >> 21;
+ s22 += carry21;
+ s21 -= carry21 * (1 << 21);
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+ s23 = 0;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+ s22 = 0;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+ s21 = 0;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+ s20 = 0;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+ s19 = 0;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+ s18 = 0;
+
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * (1 << 21);
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * (1 << 21);
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * (1 << 21);
+
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * (1 << 21);
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * (1 << 21);
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+ s17 = 0;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+ s16 = 0;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+ s15 = 0;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+ s14 = 0;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+ s13 = 0;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 * (1 << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * (1 << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * (1 << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * (1 << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * (1 << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * (1 << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * (1 << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * (1 << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * (1 << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * (1 << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * (1 << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * (1 << 21);
+
+ s[ 0] = (uint8_t) (s0 >> 0);
+ s[ 1] = (uint8_t) (s0 >> 8);
+ s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
+ s[ 3] = (uint8_t) (s1 >> 3);
+ s[ 4] = (uint8_t) (s1 >> 11);
+ s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
+ s[ 6] = (uint8_t) (s2 >> 6);
+ s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
+ s[ 8] = (uint8_t) (s3 >> 1);
+ s[ 9] = (uint8_t) (s3 >> 9);
+ s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
+ s[11] = (uint8_t) (s4 >> 4);
+ s[12] = (uint8_t) (s4 >> 12);
+ s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
+ s[14] = (uint8_t) (s5 >> 7);
+ s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
+ s[16] = (uint8_t) (s6 >> 2);
+ s[17] = (uint8_t) (s6 >> 10);
+ s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
+ s[19] = (uint8_t) (s7 >> 5);
+ s[20] = (uint8_t) (s7 >> 13);
+ s[21] = (uint8_t) (s8 >> 0);
+ s[22] = (uint8_t) (s8 >> 8);
+ s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
+ s[24] = (uint8_t) (s9 >> 3);
+ s[25] = (uint8_t) (s9 >> 11);
+ s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
+ s[27] = (uint8_t) (s10 >> 6);
+ s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
+ s[29] = (uint8_t) (s11 >> 1);
+ s[30] = (uint8_t) (s11 >> 9);
+ s[31] = (uint8_t) (s11 >> 17);
}
int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
- const uint8_t private_key[64]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(private_key, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, az + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t nonce[SHA512_DIGEST_LENGTH];
- SHA512_Final(nonce, &hash_ctx);
-
- sc_reduce(nonce);
- ge_p3 R;
- ge_scalarmult_base(&R, nonce);
- ge_p3_tobytes(out_sig, &R);
-
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, out_sig, 32);
- SHA512_Update(&hash_ctx, private_key + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t hram[SHA512_DIGEST_LENGTH];
- SHA512_Final(hram, &hash_ctx);
-
- sc_reduce(hram);
- sc_muladd(out_sig + 32, hram, az, nonce);
-
- return 1;
+ const uint8_t public_key[32], const uint8_t private_key[32],
+ OPENSSL_CTX *libctx, const char *propq)
+{
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ uint8_t nonce[SHA512_DIGEST_LENGTH];
+ ge_p3 R;
+ uint8_t hram[SHA512_DIGEST_LENGTH];
+ EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
+ EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
+ unsigned int sz;
+ int res = 0;
+
+ if (sha512 == NULL || hash_ctx == NULL)
+ goto err;
+
+ if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
+ || !EVP_DigestUpdate(hash_ctx, private_key, 32)
+ || !EVP_DigestFinal_ex(hash_ctx, az, &sz))
+ goto err;
+
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
+
+ if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
+ || !EVP_DigestUpdate(hash_ctx, az + 32, 32)
+ || !EVP_DigestUpdate(hash_ctx, message, message_len)
+ || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
+ goto err;
+
+ x25519_sc_reduce(nonce);
+ ge_scalarmult_base(&R, nonce);
+ ge_p3_tobytes(out_sig, &R);
+
+ if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
+ || !EVP_DigestUpdate(hash_ctx, out_sig, 32)
+ || !EVP_DigestUpdate(hash_ctx, public_key, 32)
+ || !EVP_DigestUpdate(hash_ctx, message, message_len)
+ || !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
+ goto err;
+
+ x25519_sc_reduce(hram);
+ sc_muladd(out_sig + 32, hram, az, nonce);
+
+ res = 1;
+err:
+ OPENSSL_cleanse(nonce, sizeof(nonce));
+ OPENSSL_cleanse(az, sizeof(az));
+ EVP_MD_free(sha512);
+ EVP_MD_CTX_free(hash_ctx);
+ return res;
}
-int ED25519_verify(const uint8_t *message, size_t message_len,
- const uint8_t signature[64], const uint8_t public_key[32]) {
- ge_p3 A;
- if ((signature[63] & 224) != 0 ||
- ge_frombytes_negate_vartime(&A, public_key) != 0) {
- return 0;
- }
-
- uint8_t pkcopy[32];
- memcpy(pkcopy, public_key, 32);
- uint8_t rcopy[32];
- memcpy(rcopy, signature, 32);
- uint8_t scopy[32];
- memcpy(scopy, signature + 32, 32);
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, signature, 32);
- SHA512_Update(&hash_ctx, public_key, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t h[SHA512_DIGEST_LENGTH];
- SHA512_Final(h, &hash_ctx);
-
- sc_reduce(h);
-
- ge_p2 R;
- ge_double_scalarmult_vartime(&R, h, &A, scopy);
+static const char allzeroes[15];
- uint8_t rcheck[32];
- ge_tobytes(rcheck, &R);
-
- return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
-}
+int ED25519_verify(const uint8_t *message, size_t message_len,
+ const uint8_t signature[64], const uint8_t public_key[32],
+ OPENSSL_CTX *libctx, const char *propq)
+{
+ int i;
+ ge_p3 A;
+ const uint8_t *r, *s;
+ EVP_MD *sha512;
+ EVP_MD_CTX *hash_ctx = NULL;
+ unsigned int sz;
+ int res = 0;
+ ge_p2 R;
+ uint8_t rcheck[32];
+ uint8_t h[SHA512_DIGEST_LENGTH];
+ /* 27742317777372353535851937790883648493 in little endian format */
+ const uint8_t l_low[16] = {
+ 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
+ 0xDE, 0xF9, 0xDE, 0x14
+ };
+
+ r = signature;
+ s = signature + 32;
+
+ /*
+ * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
+ *
+ * If not the signature is publicly invalid. Since it's public we can do the
+ * check in variable time.
+ *
+ * First check the most significant byte
+ */
+ if (s[31] > 0x10)
+ return 0;
+ if (s[31] == 0x10) {
+ /*
+ * Most significant byte indicates a value close to 2^252 so check the
+ * rest
+ */
+ if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
+ return 0;
+ for (i = 15; i >= 0; i--) {
+ if (s[i] < l_low[i])
+ break;
+ if (s[i] > l_low[i])
+ return 0;
+ }
+ if (i < 0)
+ return 0;
+ }
-#endif /* Ed25519 */
+ if (ge_frombytes_vartime(&A, public_key) != 0) {
+ return 0;
+ }
+ fe_neg(A.X, A.X);
+ fe_neg(A.T, A.T);
-#if defined(OPENSSL_X25519_X86_64)
+ sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
+ if (sha512 == NULL)
+ return 0;
+ hash_ctx = EVP_MD_CTX_new();
+ if (hash_ctx == NULL)
+ goto err;
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
- x25519_x86_64(out, scalar, point);
-}
+ if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
+ || !EVP_DigestUpdate(hash_ctx, r, 32)
+ || !EVP_DigestUpdate(hash_ctx, public_key, 32)
+ || !EVP_DigestUpdate(hash_ctx, message, message_len)
+ || !EVP_DigestFinal_ex(hash_ctx, h, &sz))
+ goto err;
-#else
+ x25519_sc_reduce(h);
-/* Replace (f,g) with (g,f) if b == 1;
- * replace (f,g) with (f,g) if b == 0.
- *
- * Preconditions: b in {0,1}. */
-static void fe_cswap(fe f, fe g, unsigned int b) {
- size_t i;
- b = 0-b;
- for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
- x &= b;
- f[i] ^= x;
- g[i] ^= x;
- }
-}
+ ge_double_scalarmult_vartime(&R, h, &A, s);
-/* h = f * 121666
- * Can overlap h with f.
- *
- * Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
- *
- * Postconditions:
- * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
-static void fe_mul121666(fe h, fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int64_t h0 = f0 * (int64_t) 121666;
- int64_t h1 = f1 * (int64_t) 121666;
- int64_t h2 = f2 * (int64_t) 121666;
- int64_t h3 = f3 * (int64_t) 121666;
- int64_t h4 = f4 * (int64_t) 121666;
- int64_t h5 = f5 * (int64_t) 121666;
- int64_t h6 = f6 * (int64_t) 121666;
- int64_t h7 = f7 * (int64_t) 121666;
- int64_t h8 = f8 * (int64_t) 121666;
- int64_t h9 = f9 * (int64_t) 121666;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
-
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
+ ge_tobytes(rcheck, &R);
-static void x25519_scalar_mult_generic(uint8_t out[32],
- const uint8_t scalar[32],
- const uint8_t point[32]) {
- fe x1, x2, z2, x3, z3, tmp0, tmp1;
- uint8_t e[32];
- unsigned swap = 0;
- int pos;
-
- memcpy(e, scalar, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
- fe_frombytes(x1, point);
- fe_1(x2);
- fe_0(z2);
- fe_copy(x3, x1);
- fe_1(z3);
-
- for (pos = 254; pos >= 0; --pos) {
- unsigned b = 1 & (e[pos / 8] >> (pos & 7));
- swap ^= b;
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
- swap = b;
- fe_sub(tmp0, x3, z3);
- fe_sub(tmp1, x2, z2);
- fe_add(x2, x2, z2);
- fe_add(z2, x3, z3);
- fe_mul(z3, tmp0, x2);
- fe_mul(z2, z2, tmp1);
- fe_sq(tmp0, tmp1);
- fe_sq(tmp1, x2);
- fe_add(x3, z3, z2);
- fe_sub(z2, z3, z2);
- fe_mul(x2, tmp1, tmp0);
- fe_sub(tmp1, tmp1, tmp0);
- fe_sq(z2, z2);
- fe_mul121666(z3, tmp1);
- fe_sq(x3, x3);
- fe_add(tmp0, tmp0, z3);
- fe_mul(z3, x1, z2);
- fe_mul(z2, tmp1, tmp0);
- }
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
-
- fe_invert(z2, z2);
- fe_mul(x2, x2, z2);
- fe_tobytes(out, x2);
+ res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
+err:
+ EVP_MD_free(sha512);
+ EVP_MD_CTX_free(hash_ctx);
+ return res;
}
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
-#if defined(OPENSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- x25519_NEON(out, scalar, point);
- return;
- }
-#endif
+int ED25519_public_from_private(OPENSSL_CTX *ctx, uint8_t out_public_key[32],
+ const uint8_t private_key[32])
+{
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ ge_p3 A;
+ int r;
+ EVP_MD *sha512 = NULL;
+
+ sha512 = EVP_MD_fetch(ctx, SN_sha512, NULL);
+ if (sha512 == NULL)
+ return 0;
+ r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
+ EVP_MD_free(sha512);
+ if (!r) {
+ OPENSSL_cleanse(az, sizeof(az));
+ return 0;
+ }
- x25519_scalar_mult_generic(out, scalar, point);
-}
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
-#endif /* OPENSSL_X25519_X86_64 */
+ ge_scalarmult_base(&A, az);
+ ge_p3_tobytes(out_public_key, &A);
-#if 0
-void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
- RAND_bytes(out_private_key, 32);
- X25519_public_from_private(out_public_value, out_private_key);
+ OPENSSL_cleanse(az, sizeof(az));
+ return 1;
}
-#endif
-
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
- const uint8_t peer_public_value[32]) {
- static const uint8_t kZeros[32] = {0};
- x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
- /* The all-zero output results when the input is a point of small order. */
- return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
-}
-
-#if 0
-
-#if defined(OPENSSL_X25519_X86_64)
-
-/* When |OPENSSL_X25519_X86_64| is set, base point multiplication is done with
- * the Montgomery ladder because it's faster. Otherwise it's done using the
- * Ed25519 tables. */
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
+ const uint8_t peer_public_value[32])
+{
+ static const uint8_t kZeros[32] = {0};
+ x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
+ /* The all-zero output results when the input is a point of small order. */
+ return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}
-#else
-
void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
- uint8_t e[32];
- ge_p3 A;
- fe zplusy, zminusy, zminusy_inv;
-
-#if defined(OPENSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
- return;
- }
-#endif
-
- memcpy(e, private_key, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
-
- ge_scalarmult_base(&A, e);
-
- /* We only need the u-coordinate of the curve25519 point. The map is
- * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
- fe_add(zplusy, A.Z, A.Y);
- fe_sub(zminusy, A.Z, A.Y);
- fe_invert(zminusy_inv, zminusy);
- fe_mul(zplusy, zplusy, zminusy_inv);
- fe_tobytes(out_public_value, zplusy);
+ const uint8_t private_key[32])
+{
+ uint8_t e[32];
+ ge_p3 A;
+ fe zplusy, zminusy, zminusy_inv;
+
+ memcpy(e, private_key, 32);
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+
+ ge_scalarmult_base(&A, e);
+
+ /*
+ * We only need the u-coordinate of the curve25519 point.
+ * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
+ * u=(Z+Y)/(Z-Y).
+ */
+ fe_add(zplusy, A.Z, A.Y);
+ fe_sub(zminusy, A.Z, A.Y);
+ fe_invert(zminusy_inv, zminusy);
+ fe_mul(zplusy, zplusy, zminusy_inv);
+ fe_tobytes(out_public_value, zplusy);
+
+ OPENSSL_cleanse(e, sizeof(e));
}
-
-#endif /* OPENSSL_X25519_X86_64 */
-
-#endif
projects / openssl.git / blobdiff