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-rw-r--r--crypto/ec/curve25519.c5457
1 files changed, 5457 insertions, 0 deletions
diff --git a/crypto/ec/curve25519.c b/crypto/ec/curve25519.c
new file mode 100644
index 000000000000..abe9b9cbf6dd
--- /dev/null
+++ b/crypto/ec/curve25519.c
@@ -0,0 +1,5457 @@
+/*
+ * Copyright 2016-2018 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+#include <string.h>
+#include "ec_lcl.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(__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,
+ * 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. */
+typedef int32_t fe[10];
+
+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 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 + (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.
+ *
+ * Write p=2^255-19; q=floor(h/p).
+ * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+ *
+ * Proof:
+ * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+ * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+ *
+ * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+ * Then 0<y<1.
+ *
+ * Write r=h-pq.
+ * Have 0<=r<=p-1=2^255-20.
+ * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+ *
+ * Write x=r+19(2^-255)r+y.
+ * 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;
+
+ 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);
+}
+
+/* h = 0 */
+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;
+}
+
+/* h = f + g
+ * Can overlap h with f or g.
+ *
+ * Preconditions:
+ * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ * |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 = f - g
+ * Can overlap h with f or g.
+ *
+ * Preconditions:
+ * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ * |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 = f * g
+ * Can overlap h with f or g.
+ *
+ * Preconditions:
+ * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ *
+ * Postconditions:
+ * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+ *
+ * Notes on implementation strategy:
+ *
+ * Using schoolbook multiplication.
+ * Karatsuba would save a little in some cost models.
+ *
+ * Most multiplications by 2 and 19 are 32-bit precomputations;
+ * cheaper than 64-bit postcomputations.
+ *
+ * There is one remaining multiplication by 19 in the carry chain;
+ * one *19 precomputation can be merged into this,
+ * but the resulting data flow is considerably less clean.
+ *
+ * There are 12 carries below.
+ * 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 + (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
+ * Can overlap h with f.
+ *
+ * Preconditions:
+ * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ *
+ * 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 + (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;
+
+ /*
+ * 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);
+
+ /* 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);
+ 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);
+ for (i = 1; i < 5; ++i) {
+ fe_sq(t1, t1);
+ }
+
+ /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+ fe_mul(out, t1, t0);
+}
+
+/* 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];
+ }
+}
+
+/* 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;
+ }
+}
+
+/* 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};
+ fe_tobytes(s, f);
+
+ return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+}
+
+/* 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;
+}
+
+/* h = 2 * f * f
+ * Can overlap h with f.
+ *
+ * Preconditions:
+ * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ *
+ * 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 + (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);
+ 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_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) {
+ fe_sq(t1, t1);
+ }
+ fe_mul(t0, t1, t0);
+ fe_sq(t0, t0);
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t0, t0);
+ }
+ fe_mul(out, t0, z);
+}
+
+/* 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.
+ *
+ * Representations:
+ * 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) */
+
+typedef struct {
+ fe X;
+ fe Y;
+ fe Z;
+} ge_p2;
+
+typedef struct {
+ fe X;
+ fe Y;
+ fe Z;
+ fe T;
+} ge_p3;
+
+typedef struct {
+ fe X;
+ fe Y;
+ fe Z;
+ fe T;
+} ge_p1p1;
+
+typedef struct {
+ fe yplusx;
+ fe yminusx;
+ fe xy2d;
+} ge_precomp;
+
+typedef struct {
+ 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;
+
+ 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 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_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 */
+ if (fe_isnonzero(check)) {
+ return -1;
+ }
+ fe_mul(h->X, h->X, sqrtm1);
+ }
+
+ if (fe_isnegative(h->X) != (s[31] >> 7)) {
+ fe_neg(h->X, h->X);
+ }
+
+ 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_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);
+}
+
+/* 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 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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);
+}
+
+/* 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 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, 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);
+}
+
+/* k25519Precomp[i][j] = (j+1)*256^i*B */
+static const ge_precomp k25519Precomp[32][8] = {
+ {
+ {
+ {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
+ 27544626, -11754271, -6079156, 2047605},
+ {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
+ 5043384, 19500929, -15469378},
+ {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
+ 29287919, 11864899, -24514362, -4438546},
+ },
+ {
+ {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
+ -11717903, -3814571, -358445, -10211303},
+ {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
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+ },
+ {
+ {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
+ -6679750, -12670638, 24350578, -13450001},
+ {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
+ -31536088, -10406836, 8317860, 12352766},
+ {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
+ -23552096, -2287550, 20712163, 6719373},
+ },
+ {
+ {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
+ -3763210, 26224235, -3297458},
+ {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
+ 21728352, 9493610, 18620611, -16428628},
+ {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
+ -5269471, -9725556, -30701573, -16479657},
+ },
+ {
+ {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
+ 12248509, -5240639, 13735342, 1934062},
+ {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
+ -15136294, -3765346, -21277997, 5473616},
+ {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
+ -7125085, 12469656, 29111212, -5451014},
+ },
+ {
+ {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
+ 24367466, 6388839, -10295587, 452383},
+ {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
+ -24236251, -5915248, 15766062, 8407814},
+ {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
+ -8917023, -4388953, -8067909, 2276718},
+ },
+ {
+ {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
+ -23827587, 5096219, 22740376, -7303417},
+ {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
+ 24051124, 13742383, -15637599, 13295222},
+ {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
+ -17720195, -4612972, -4451357, -14669444},
+ },
+ {
+ {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
+ -2469266, -4141880, 7770569, 9620597},
+ {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
+ -1694323, -33502340, -14767970},
+ {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
+ 1220118, 30494170, -11440799},
+ },
+ {
+ {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
+ -26739026, 926050, -1684339, -13333647},
+ {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
+ 9021034, 9078865, 3353509, 4033511},
+ {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
+ 23161163, 8839127, 27485041, 7356032},
+ },
+ },
+ {
+ {
+ {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
+ 2625015, 28431036, -16771834},
+ {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
+ -22545972, 14150565, 15970762, 4099461},
+ {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
+ 13617293, -9937143, 11465739, 8317062},
+ },
+ {
+ {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
+ 14898637, 3848455, 20969334, -5157516},
+ {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
+ -21610826, -3649888, 11177095, 14989547},
+ {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
+ 13515641, 2581286, -28487508, 9930240},
+ },
+ {
+ {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
+ 18345767, -13403753, 16291481, -5314038},
+ {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
+ 6957617, 4368891, 9788741},
+ {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
+ -21722536, -8613148, 16250552, -11111103},
+ },
+ {
+ {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
+ 10604807, -30190403, 4782747},
+ {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
+ -9981571, 4383045, 22546403, 437323},
+ {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
+ 27343084, 2786261, -30633590, -14097016},
+ },
+ {
+ {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
+ -19690631, 2355319, -19284671, -6114373},
+ {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
+ 18952177, 15496498, -29380133, 11754228},
+ {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
+ 7141596, 11724556, 22761615, -10134141},
+ },
+ {
+ {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
+ -28741185, -12227393, 32851222, 11717399},
+ {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
+ 31474879, 3483633, -1193175, -4030831},
+ {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
+ 33142652, 6546660, -19985279, -3948376},
+ },
+ {
+ {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
+ -8537131, -12833048, -30772034, -15486313},
+ {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
+ -31135347, -16049879, 10928917, 3011958},
+ {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
+ -30831056, -12805180, 18008031, 10258577},
+ },
+ {
+ {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
+ -1853465, 1367120, 25127874, 6671743},
+ {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
+ 21382910, 11042292, 25838796, 4642684},
+ {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
+ 30468147, -13900640, 18423289, 4177476},
+ },
+ },
+};
+
+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 - ((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
+ * 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);
+ 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;
+ }
+ } else {
+ break;
+ }
+ }
+ }
+ }
+ }
+}
+
+static const ge_precomp Bi[8] = {
+ {
+ {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
+ -11754271, -6079156, 2047605},
+ {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
+ 5043384, 19500929, -15469378},
+ {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
+ 11864899, -24514362, -4438546},
+ },
+ {
+ {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
+ -14772189, 28944400, -1550024},
+ {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
+ -11775962, 7689662, 11199574},
+ {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
+ 10017326, -17749093, -9920357},
+ },
+ {
+ {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
+ 14515107, -15438304, 10819380},
+ {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
+ 12483688, -12668491, 5581306},
+ {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
+ 13850243, -23678021, -15815942},
+ },
+ {
+ {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
+ 5230134, -23952439, -15175766},
+ {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
+ 16520125, 30598449, 7715701},
+ {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
+ 1370708, 29794553, -1409300},
+ },
+ {
+ {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
+ -1361450, -13062696, 13821877},
+ {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
+ -7212327, 18853322, -14220951},
+ {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
+ -10431137, 2207753, -3209784},
+ },
+ {
+ {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
+ -663000, -31111463, -16132436},
+ {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
+ 15725684, 171356, 6466918},
+ {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
+ -14088058, -30714912, 16193877},
+ },
+ {
+ {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
+ 4729455, -18074513, 9256800},
+ {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
+ 9761698, -19827198, 630305},
+ {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
+ -15960994, -2449256, -14291300},
+ },
+ {
+ {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
+ 15033784, 25105118, -7894876},
+ {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
+ 1573892, -2625887, 2198790, -15804619},
+ {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
+ -16236442, -32461234, -12290683},
+ },
+};
+
+/* 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. */
+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);
+
+ 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]);
+ }
+
+ ge_p1p1_to_p2(r, &t);
+ }
+}
+
+/* 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 x25519_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 * (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:
+ * 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. */
+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 * (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 public_key[32], const uint8_t private_key[32]) {
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ uint8_t nonce[SHA512_DIGEST_LENGTH];
+ ge_p3 R;
+ uint8_t hram[SHA512_DIGEST_LENGTH];
+ SHA512_CTX hash_ctx;
+
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, private_key, 32);
+ SHA512_Final(az, &hash_ctx);
+
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
+
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, az + 32, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ SHA512_Final(nonce, &hash_ctx);
+
+ x25519_sc_reduce(nonce);
+ 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, public_key, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ SHA512_Final(hram, &hash_ctx);
+
+ x25519_sc_reduce(hram);
+ sc_muladd(out_sig + 32, hram, az, nonce);
+
+ OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
+ OPENSSL_cleanse(nonce, sizeof(nonce));
+ OPENSSL_cleanse(az, sizeof(az));
+
+ return 1;
+}
+
+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;
+ uint8_t rcopy[32];
+ uint8_t scopy[32];
+ SHA512_CTX hash_ctx;
+ ge_p2 R;
+ uint8_t rcheck[32];
+ uint8_t h[SHA512_DIGEST_LENGTH];
+
+ if ((signature[63] & 224) != 0 ||
+ ge_frombytes_vartime(&A, public_key) != 0) {
+ return 0;
+ }
+
+ fe_neg(A.X, A.X);
+ fe_neg(A.T, A.T);
+
+ memcpy(rcopy, signature, 32);
+ memcpy(scopy, signature + 32, 32);
+
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, signature, 32);
+ SHA512_Update(&hash_ctx, public_key, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ SHA512_Final(h, &hash_ctx);
+
+ x25519_sc_reduce(h);
+
+ ge_double_scalarmult_vartime(&R, h, &A, scopy);
+
+ ge_tobytes(rcheck, &R);
+
+ return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
+}
+
+void ED25519_public_from_private(uint8_t out_public_key[32],
+ const uint8_t private_key[32]) {
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ ge_p3 A;
+
+ SHA512(private_key, 32, az);
+
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
+
+ ge_scalarmult_base(&A, az);
+ ge_p3_tobytes(out_public_key, &A);
+
+ OPENSSL_cleanse(az, sizeof(az));
+}
+
+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;
+}
+
+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;
+
+ 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));
+}