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-rw-r--r--contrib/examples/keygen-html/src/curve25519_generate.c1554
1 files changed, 769 insertions, 785 deletions
diff --git a/contrib/examples/keygen-html/src/curve25519_generate.c b/contrib/examples/keygen-html/src/curve25519_generate.c
index 20d3f91..1633275 100644
--- a/contrib/examples/keygen-html/src/curve25519_generate.c
+++ b/contrib/examples/keygen-html/src/curve25519_generate.c
@@ -1,869 +1,853 @@
/* SPDX-License-Identifier: GPL-2.0
*
- * Copyright (C) 2008 Google Inc. All Rights Reserved.
- * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ * Copyright (C) 2015-2016 The fiat-crypto Authors.
+ * Copyright (C) 2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * This is a machine-generated formally verified implementation of curve25519 DH from:
+ * https://github.com/mit-plv/fiat-crypto
*/
#include <emscripten.h>
+#ifndef __always_inline
+#define __always_inline __inline __attribute__((__always_inline__))
+#endif
+
+#ifndef __aligned
+#define __aligned(x) __attribute__((aligned(x)))
+#endif
+
+#if __BYTE_ORDER == __LITTLE_ENDIAN
+#define le32toh(x) (x)
+#else
+#define htole32(x) __builtin_bswap32(x)
+#endif
+
+
typedef unsigned long long uint64_t;
-typedef long long int64_t;
-typedef int int32_t;
typedef unsigned int uint32_t;
typedef unsigned char uint8_t;
-typedef int64_t limb;
+/* 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].
+ * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
+ * Multiplication and carrying produce fe from fe_loose.
+ */
+typedef struct fe { uint32_t v[10]; } fe;
-/* Field element representation:
- *
- * Field elements are written as an array of signed, 64-bit limbs, least
- * significant first. The value of the field element is:
- * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
- *
- * i.e. the limbs are 26, 25, 26, 25, ... bits wide.
+/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc.
+ * Addition and subtraction produce fe_loose from (fe, fe).
*/
+typedef struct fe_loose { uint32_t v[10]; } fe_loose;
-/* Sum two numbers: output += in */
-static void fsum(limb *output, const limb *in)
+static __always_inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s)
{
- unsigned int i;
-
- for (i = 0; i < 10; i += 2) {
- output[0 + i] = output[0 + i] + in[0 + i];
- output[1 + i] = output[1 + i] + in[1 + i];
- }
+ /* Ignores top bit of s. */
+ uint32_t a0 = le32toh(*(uint32_t *)(s));
+ uint32_t a1 = le32toh(*(uint32_t *)(s+4));
+ uint32_t a2 = le32toh(*(uint32_t *)(s+8));
+ uint32_t a3 = le32toh(*(uint32_t *)(s+12));
+ uint32_t a4 = le32toh(*(uint32_t *)(s+16));
+ uint32_t a5 = le32toh(*(uint32_t *)(s+20));
+ uint32_t a6 = le32toh(*(uint32_t *)(s+24));
+ uint32_t a7 = le32toh(*(uint32_t *)(s+28));
+ h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */
+ h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */
+ h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
+ h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */
+ h[4] = (a3>> 6); /* (32- 6) = 26 */
+ h[5] = a4&((1<<25)-1); /* 25 */
+ h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */
+ h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
+ h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */
+ h[9] = (a7>> 6)&((1<<25)-1); /* 25 */
}
-/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!).
- */
-static void fdifference(limb *output, const limb *in)
+static __always_inline void fe_frombytes(fe *h, const uint8_t *s)
{
- unsigned int i;
-
- for (i = 0; i < 10; ++i) {
- output[i] = in[i] - output[i];
- }
+ fe_frombytes_impl(h->v, s);
}
-/* Multiply a number by a scalar: output = in * scalar */
-static void fscalar_product(limb *output, const limb *in, const limb scalar)
+static __always_inline uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
{
- unsigned int i;
-
- for (i = 0; i < 10; ++i) {
- output[i] = in[i] * scalar;
- }
+ /* This function extracts 25 bits of result and 1 bit of carry (26 total), so
+ * a 32-bit intermediate is sufficient.
+ */
+ uint32_t x = a + b + c;
+ *low = x & ((1 << 25) - 1);
+ return (x >> 25) & 1;
}
-/* Multiply two numbers: output = in2 * in
- *
- * output must be distinct to both inputs. The inputs are reduced coefficient
- * form, the output is not.
- *
- * output[x] <= 14 * the largest product of the input limbs.
- */
-static void fproduct(limb *output, const limb *in2, const limb *in)
-{
- output[0] = ((limb) ((int32_t) in2[0])) * ((int32_t) in[0]);
- output[1] = ((limb) ((int32_t) in2[0])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[0]);
- output[2] = 2 * ((limb) ((int32_t) in2[1])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[0]);
- output[3] = ((limb) ((int32_t) in2[1])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[0]);
- output[4] = ((limb) ((int32_t) in2[2])) * ((int32_t) in[2]) +
- 2 * (((limb) ((int32_t) in2[1])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[1])) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[0]);
- output[5] = ((limb) ((int32_t) in2[2])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[0]);
- output[6] = 2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[1])) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[0]);
- output[7] = ((limb) ((int32_t) in2[3])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[0]);
- output[8] = ((limb) ((int32_t) in2[4])) * ((int32_t) in[4]) +
- 2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[1])) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[0]);
- output[9] = ((limb) ((int32_t) in2[4])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in2[0])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[0]);
- output[10] = 2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[1])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[1])) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[2]);
- output[11] = ((limb) ((int32_t) in2[5])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in2[2])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[2]);
- output[12] = ((limb) ((int32_t) in2[6])) * ((int32_t) in[6]) +
- 2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[3])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[3])) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[4]);
- output[13] = ((limb) ((int32_t) in2[6])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[7])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in2[4])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[4]);
- output[14] = 2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[5])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[5])) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[6]);
- output[15] = ((limb) ((int32_t) in2[7])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in2[8])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in2[6])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[6]);
- output[16] = ((limb) ((int32_t) in2[8])) * ((int32_t) in[8]) +
- 2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[7]));
- output[17] = ((limb) ((int32_t) in2[8])) * ((int32_t) in[9]) +
- ((limb) ((int32_t) in2[9])) * ((int32_t) in[8]);
- output[18] = 2 * ((limb) ((int32_t) in2[9])) * ((int32_t) in[9]);
-}
-
-/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
- *
- * On entry: |output[i]| < 14*2^54
- * On exit: |output[0..8]| < 280*2^54
- */
-static void freduce_degree(limb *output)
+static __always_inline uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
{
- /* Each of these shifts and adds ends up multiplying the value by 19.
- *
- * For output[0..8], the absolute entry value is < 14*2^54 and we add, at
- * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54.
+ /* This function extracts 26 bits of result and 1 bit of carry (27 total), so
+ * a 32-bit intermediate is sufficient.
*/
- output[8] += output[18] << 4;
- output[8] += output[18] << 1;
- output[8] += output[18];
- output[7] += output[17] << 4;
- output[7] += output[17] << 1;
- output[7] += output[17];
- output[6] += output[16] << 4;
- output[6] += output[16] << 1;
- output[6] += output[16];
- output[5] += output[15] << 4;
- output[5] += output[15] << 1;
- output[5] += output[15];
- output[4] += output[14] << 4;
- output[4] += output[14] << 1;
- output[4] += output[14];
- output[3] += output[13] << 4;
- output[3] += output[13] << 1;
- output[3] += output[13];
- output[2] += output[12] << 4;
- output[2] += output[12] << 1;
- output[2] += output[12];
- output[1] += output[11] << 4;
- output[1] += output[11] << 1;
- output[1] += output[11];
- output[0] += output[10] << 4;
- output[0] += output[10] << 1;
- output[0] += output[10];
-}
-
-#if (-1 & 3) != 3
-#error "This code only works on a two's complement system"
-#endif
+ uint32_t x = a + b + c;
+ *low = x & ((1 << 26) - 1);
+ return (x >> 26) & 1;
+}
-/* return v / 2^26, using only shifts and adds.
- *
- * On entry: v can take any value.
- */
-static inline limb div_by_2_26(const limb v)
+static __always_inline uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
{
- /* High word of v; no shift needed. */
- const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const int32_t sign = ((int32_t) highword) >> 31;
- /* Set to 0x3ffffff if v was negative; else set to 0. */
- const int32_t roundoff = ((uint32_t) sign) >> 6;
- /* Should return v / (1<<26) */
- return (v + roundoff) >> 26;
+ /* This function extracts 25 bits of result and 1 bit of borrow (26 total), so
+ * a 32-bit intermediate is sufficient.
+ */
+ uint32_t x = a - b - c;
+ *low = x & ((1 << 25) - 1);
+ return x >> 31;
}
-/* return v / (2^25), using only shifts and adds.
- *
- * On entry: v can take any value.
- */
-static inline limb div_by_2_25(const limb v)
+static __always_inline uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
{
- /* High word of v; no shift needed*/
- const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const int32_t sign = ((int32_t) highword) >> 31;
- /* Set to 0x1ffffff if v was negative; else set to 0. */
- const int32_t roundoff = ((uint32_t) sign) >> 7;
- /* Should return v / (1<<25) */
- return (v + roundoff) >> 25;
+ /* This function extracts 26 bits of result and 1 bit of borrow (27 total), so
+ * a 32-bit intermediate is sufficient.
+ */
+ uint32_t x = a - b - c;
+ *low = x & ((1 << 26) - 1);
+ return x >> 31;
}
-/* Reduce all coefficients of the short form input so that |x| < 2^26.
- *
- * On entry: |output[i]| < 280*2^54
- */
-static void freduce_coefficients(limb *output)
+static __always_inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz)
{
- unsigned int i;
-
- output[10] = 0;
+ t = -!!t; /* all set if nonzero, 0 if 0 */
+ return (t&nz) | ((~t)&z);
+}
- for (i = 0; i < 10; i += 2) {
- limb over = div_by_2_26(output[i]);
- /* The entry condition (that |output[i]| < 280*2^54) means that over is, at
- * most, 280*2^28 in the first iteration of this loop. This is added to the
- * next limb and we can approximate the resulting bound of that limb by
- * 281*2^54.
- */
- output[i] -= over << 26;
- output[i+1] += over;
-
- /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
- * 281*2^29. When this is added to the next limb, the resulting bound can
- * be approximated as 281*2^54.
- *
- * For subsequent iterations of the loop, 281*2^54 remains a conservative
- * bound and no overflow occurs.
- */
- over = div_by_2_25(output[i+1]);
- output[i+1] -= over << 25;
- output[i+2] += over;
- }
- /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
- output[0] += output[10] << 4;
- output[0] += output[10] << 1;
- output[0] += output[10];
+static __always_inline void fe_freeze(uint32_t out[10], const uint32_t in1[10])
+{
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
+ { uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
+ { uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
+ { uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
+ { uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
+ { uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
+ { uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
+ { uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
+ { uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
+ { uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
+ { uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
+ { uint32_t x50 = (x49 & 0x3ffffed);
+ { uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
+ { uint32_t x54 = (x49 & 0x1ffffff);
+ { uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
+ { uint32_t x58 = (x49 & 0x3ffffff);
+ { uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
+ { uint32_t x62 = (x49 & 0x1ffffff);
+ { uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
+ { uint32_t x66 = (x49 & 0x3ffffff);
+ { uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
+ { uint32_t x70 = (x49 & 0x1ffffff);
+ { uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
+ { uint32_t x74 = (x49 & 0x3ffffff);
+ { uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
+ { uint32_t x78 = (x49 & 0x1ffffff);
+ { uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
+ { uint32_t x82 = (x49 & 0x3ffffff);
+ { uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
+ { uint32_t x86 = (x49 & 0x1ffffff);
+ { uint32_t x88; addcarryx_u25(x85, x47, x86, &x88);
+ out[0] = x52;
+ out[1] = x56;
+ out[2] = x60;
+ out[3] = x64;
+ out[4] = x68;
+ out[5] = x72;
+ out[6] = x76;
+ out[7] = x80;
+ out[8] = x84;
+ out[9] = x88;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
- output[10] = 0;
+static __always_inline void fe_tobytes(uint8_t s[32], const fe *f)
+{
+ uint32_t h[10];
+ fe_freeze(h, f->v);
+ s[0] = h[0] >> 0;
+ s[1] = h[0] >> 8;
+ s[2] = h[0] >> 16;
+ s[3] = (h[0] >> 24) | (h[1] << 2);
+ s[4] = h[1] >> 6;
+ s[5] = h[1] >> 14;
+ s[6] = (h[1] >> 22) | (h[2] << 3);
+ s[7] = h[2] >> 5;
+ s[8] = h[2] >> 13;
+ s[9] = (h[2] >> 21) | (h[3] << 5);
+ s[10] = h[3] >> 3;
+ s[11] = h[3] >> 11;
+ s[12] = (h[3] >> 19) | (h[4] << 6);
+ s[13] = h[4] >> 2;
+ s[14] = h[4] >> 10;
+ s[15] = h[4] >> 18;
+ s[16] = h[5] >> 0;
+ s[17] = h[5] >> 8;
+ s[18] = h[5] >> 16;
+ s[19] = (h[5] >> 24) | (h[6] << 1);
+ s[20] = h[6] >> 7;
+ s[21] = h[6] >> 15;
+ s[22] = (h[6] >> 23) | (h[7] << 3);
+ s[23] = h[7] >> 5;
+ s[24] = h[7] >> 13;
+ s[25] = (h[7] >> 21) | (h[8] << 4);
+ s[26] = h[8] >> 4;
+ s[27] = h[8] >> 12;
+ s[28] = (h[8] >> 20) | (h[9] << 6);
+ s[29] = h[9] >> 2;
+ s[30] = h[9] >> 10;
+ s[31] = h[9] >> 18;
+}
- /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
- * So |over| will be no more than 2^16.
- */
- {
- limb over = div_by_2_26(output[0]);
+/* h = f */
+static __always_inline void fe_copy(fe *h, const fe *f)
+{
+ __builtin_memmove(h, f, sizeof(uint32_t) * 10);
+}
- output[0] -= over << 26;
- output[1] += over;
- }
+static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
+{
+ __builtin_memmove(h, f, sizeof(uint32_t) * 10);
+}
- /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
- * bound on |output[1]| is sufficient to meet our needs.
- */
+/* h = 0 */
+static __always_inline void fe_0(fe *h)
+{
+ __builtin_memset(h, 0, sizeof(uint32_t) * 10);
}
-/* A helpful wrapper around fproduct: output = in * in2.
- *
- * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
- *
- * output must be distinct to both inputs. The output is reduced degree
- * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26.
- */
-static void fmul(limb *output, const limb *in, const limb *in2)
+/* h = 1 */
+static __always_inline void fe_1(fe *h)
{
- limb t[19];
+ __builtin_memset(h, 0, sizeof(uint32_t) * 10);
+ h->v[0] = 1;
+}
- fproduct(t, in, in2);
- /* |t[i]| < 14*2^54 */
- freduce_degree(t);
- freduce_coefficients(t);
- /* |t[i]| < 2^26 */
- __builtin_memcpy(output, t, sizeof(limb) * 10);
+static __always_inline void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
+{
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = (x5 + x23);
+ out[1] = (x7 + x25);
+ out[2] = (x9 + x27);
+ out[3] = (x11 + x29);
+ out[4] = (x13 + x31);
+ out[5] = (x15 + x33);
+ out[6] = (x17 + x35);
+ out[7] = (x19 + x37);
+ out[8] = (x21 + x39);
+ out[9] = (x20 + x38);
+ }}}}}}}}}}}}}}}}}}}}
}
-/* Square a number: output = in**2
- *
- * output must be distinct from the input. The inputs are reduced coefficient
- * form, the output is not.
- *
- * output[x] <= 14 * the largest product of the input limbs.
+/* h = f + g
+ * Can overlap h with f or g.
*/
-static void fsquare_inner(limb *output, const limb *in)
-{
- output[0] = ((limb) ((int32_t) in[0])) * ((int32_t) in[0]);
- output[1] = 2 * ((limb) ((int32_t) in[0])) * ((int32_t) in[1]);
- output[2] = 2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[1]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[2]));
- output[3] = 2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[2]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[3]));
- output[4] = ((limb) ((int32_t) in[2])) * ((int32_t) in[2]) +
- 4 * ((limb) ((int32_t) in[1])) * ((int32_t) in[3]) +
- 2 * ((limb) ((int32_t) in[0])) * ((int32_t) in[4]);
- output[5] = 2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in[1])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[5]));
- output[6] = 2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[3]) +
- ((limb) ((int32_t) in[2])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[6]) +
- 2 * ((limb) ((int32_t) in[1])) * ((int32_t) in[5]));
- output[7] = 2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[4]) +
- ((limb) ((int32_t) in[2])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in[1])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[7]));
- output[8] = ((limb) ((int32_t) in[4])) * ((int32_t) in[4]) +
- 2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[8]) +
- 2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[3])) * ((int32_t) in[5])));
- output[9] = 2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in[3])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in[2])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[1])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in[0])) * ((int32_t) in[9]));
- output[10] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[5]) +
- ((limb) ((int32_t) in[4])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in[2])) * ((int32_t) in[8]) +
- 2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[1])) * ((int32_t) in[9])));
- output[11] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[6]) +
- ((limb) ((int32_t) in[4])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[3])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in[2])) * ((int32_t) in[9]));
- output[12] = ((limb) ((int32_t) in[6])) * ((int32_t) in[6]) +
- 2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[8]) +
- 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[3])) * ((int32_t) in[9])));
- output[13] = 2 * (((limb) ((int32_t) in[6])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[5])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in[4])) * ((int32_t) in[9]));
- output[14] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[7]) +
- ((limb) ((int32_t) in[6])) * ((int32_t) in[8]) +
- 2 * ((limb) ((int32_t) in[5])) * ((int32_t) in[9]));
- output[15] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[8]) +
- ((limb) ((int32_t) in[6])) * ((int32_t) in[9]));
- output[16] = ((limb) ((int32_t) in[8])) * ((int32_t) in[8]) +
- 4 * ((limb) ((int32_t) in[7])) * ((int32_t) in[9]);
- output[17] = 2 * ((limb) ((int32_t) in[8])) * ((int32_t) in[9]);
- output[18] = 2 * ((limb) ((int32_t) in[9])) * ((int32_t) in[9]);
-}
-
-/* fsquare sets output = in^2.
- *
- * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
- * 2^27.
- *
- * On exit: The |output| argument is in reduced coefficients form (indeed, one
- * need only provide storage for 10 limbs) and |out[i]| < 2^26.
- */
-static void fsquare(limb *output, const limb *in)
+static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
{
- limb t[19];
-
- fsquare_inner(t, in);
- /* |t[i]| < 14*2^54 because the largest product of two limbs will be <
- * 2^(27+27) and fsquare_inner adds together, at most, 14 of those
- * products.
- */
- freduce_degree(t);
- freduce_coefficients(t);
- /* |t[i]| < 2^26 */
- __builtin_memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static void fexpand(limb *output, const uint8_t *input)
-{
-#define F(n, start, shift, mask) \
- output[n] = ((((limb) input[start + 0]) | \
- ((limb) input[start + 1]) << 8 | \
- ((limb) input[start + 2]) << 16 | \
- ((limb) input[start + 3]) << 24) >> shift) & mask;
- F(0, 0, 0, 0x3ffffff);
- F(1, 3, 2, 0x1ffffff);
- F(2, 6, 3, 0x3ffffff);
- F(3, 9, 5, 0x1ffffff);
- F(4, 12, 6, 0x3ffffff);
- F(5, 16, 0, 0x1ffffff);
- F(6, 19, 1, 0x3ffffff);
- F(7, 22, 3, 0x1ffffff);
- F(8, 25, 4, 0x3ffffff);
- F(9, 28, 6, 0x1ffffff);
-#undef F
-}
-
-#if (-32 >> 1) != -16
-#error "This code only works when >> does sign-extension on negative numbers"
-#endif
+ fe_add_impl(h->v, f->v, g->v);
+}
-/* int32_t_eq returns 0xffffffff iff a == b and zero otherwise. */
-static int32_t int32_t_eq(int32_t a, int32_t b)
+static __always_inline void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
{
- a = ~(a ^ b);
- a &= a << 16;
- a &= a << 8;
- a &= a << 4;
- a &= a << 2;
- a &= a << 1;
- return a >> 31;
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = ((0x7ffffda + x5) - x23);
+ out[1] = ((0x3fffffe + x7) - x25);
+ out[2] = ((0x7fffffe + x9) - x27);
+ out[3] = ((0x3fffffe + x11) - x29);
+ out[4] = ((0x7fffffe + x13) - x31);
+ out[5] = ((0x3fffffe + x15) - x33);
+ out[6] = ((0x7fffffe + x17) - x35);
+ out[7] = ((0x3fffffe + x19) - x37);
+ out[8] = ((0x7fffffe + x21) - x39);
+ out[9] = ((0x3fffffe + x20) - x38);
+ }}}}}}}}}}}}}}}}}}}}
}
-/* int32_t_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
- * both non-negative.
+/* h = f - g
+ * Can overlap h with f or g.
*/
-static int32_t int32_t_gte(int32_t a, int32_t b)
+static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
{
- a -= b;
- /* a >= 0 iff a >= b. */
- return ~(a >> 31);
+ fe_sub_impl(h->v, f->v, g->v);
}
-/* Take a fully reduced polynomial form number and contract it into a
- * little-endian, 32-byte array.
- *
- * On entry: |input_limbs[i]| < 2^26
- */
-static void fcontract(uint8_t *output, limb *input_limbs)
+static __always_inline void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
{
- int i;
- int j;
- int32_t input[10];
- int32_t mask;
-
- /* |input_limbs[i]| < 2^26, so it's valid to convert to an int32_t. */
- for (i = 0; i < 10; i++) {
- input[i] = input_limbs[i];
- }
-
- for (j = 0; j < 2; ++j) {
- for (i = 0; i < 9; ++i) {
- if ((i & 1) == 1) {
- /* This calculation is a time-invariant way to make input[i]
- * non-negative by borrowing from the next-larger limb.
- */
- const int32_t mask = input[i] >> 31;
- const int32_t carry = -((input[i] & mask) >> 25);
-
- input[i] = input[i] + (carry << 25);
- input[i+1] = input[i+1] - carry;
- } else {
- const int32_t mask = input[i] >> 31;
- const int32_t carry = -((input[i] & mask) >> 26);
-
- input[i] = input[i] + (carry << 26);
- input[i+1] = input[i+1] - carry;
- }
- }
-
- /* There's no greater limb for input[9] to borrow from, but we can multiply
- * by 19 and borrow from input[0], which is valid mod 2^255-19.
- */
- {
- const int32_t mask = input[9] >> 31;
- const int32_t carry = -((input[9] & mask) >> 25);
-
- input[9] = input[9] + (carry << 25);
- input[0] = input[0] - (carry * 19);
- }
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
- /* After the first iteration, input[1..9] are non-negative and fit within
- * 25 or 26 bits, depending on position. However, input[0] may be
- * negative.
- */
- }
+static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
+{
+ fe_mul_impl(h->v, f->v, g->v);
+}
- /* The first borrow-propagation pass above ended with every limb
- except (possibly) input[0] non-negative.
- If input[0] was negative after the first pass, then it was because of a
- carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
- one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
- In the second pass, each limb is decreased by at most one. Thus the second
- borrow-propagation pass could only have wrapped around to decrease
- input[0] again if the first pass left input[0] negative *and* input[1]
- through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
- and this last borrow-propagation step will leave input[1] non-negative. */
- {
- const int32_t mask = input[0] >> 31;
- const int32_t carry = -((input[0] & mask) >> 26);
-
- input[0] = input[0] + (carry << 26);
- input[1] = input[1] - carry;
- }
+static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
+{
+ fe_mul_impl(h->v, f->v, g->v);
+}
- /* All input[i] are now non-negative. However, there might be values between
- * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide.
- */
- for (j = 0; j < 2; j++) {
- for (i = 0; i < 9; i++) {
- if ((i & 1) == 1) {
- const int32_t carry = input[i] >> 25;
-
- input[i] &= 0x1ffffff;
- input[i+1] += carry;
- } else {
- const int32_t carry = input[i] >> 26;
-
- input[i] &= 0x3ffffff;
- input[i+1] += carry;
- }
- }
-
- {
- const int32_t carry = input[9] >> 25;
-
- input[9] &= 0x1ffffff;
- input[0] += 19*carry;
- }
- }
+static __always_inline void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
+{
+ fe_mul_impl(h->v, f->v, g->v);
+}
- /* If the first carry-chain pass, just above, ended up with a carry from
- * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
- * < 2^26 + 2*19, because the carry was, at most, two.
- *
- * If the second pass carried from input[9] again then input[0] is < 2*19 and
- * the input[9] -> input[0] carry didn't push input[0] out of bounds.
- */
+static __always_inline void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10])
+{
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint64_t x19 = ((uint64_t)x2 * x2);
+ { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
+ { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
+ { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
+ { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
+ { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
+ { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
+ { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
+ { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
+ { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
+ { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
+ { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
+ { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
+ { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
+ { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
+ { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
+ { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
+ { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
+ { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
+ { uint64_t x38 = (x27 + (x37 << 0x4));
+ { uint64_t x39 = (x38 + (x37 << 0x1));
+ { uint64_t x40 = (x39 + x37);
+ { uint64_t x41 = (x26 + (x36 << 0x4));
+ { uint64_t x42 = (x41 + (x36 << 0x1));
+ { uint64_t x43 = (x42 + x36);
+ { uint64_t x44 = (x25 + (x35 << 0x4));
+ { uint64_t x45 = (x44 + (x35 << 0x1));
+ { uint64_t x46 = (x45 + x35);
+ { uint64_t x47 = (x24 + (x34 << 0x4));
+ { uint64_t x48 = (x47 + (x34 << 0x1));
+ { uint64_t x49 = (x48 + x34);
+ { uint64_t x50 = (x23 + (x33 << 0x4));
+ { uint64_t x51 = (x50 + (x33 << 0x1));
+ { uint64_t x52 = (x51 + x33);
+ { uint64_t x53 = (x22 + (x32 << 0x4));
+ { uint64_t x54 = (x53 + (x32 << 0x1));
+ { uint64_t x55 = (x54 + x32);
+ { uint64_t x56 = (x21 + (x31 << 0x4));
+ { uint64_t x57 = (x56 + (x31 << 0x1));
+ { uint64_t x58 = (x57 + x31);
+ { uint64_t x59 = (x20 + (x30 << 0x4));
+ { uint64_t x60 = (x59 + (x30 << 0x1));
+ { uint64_t x61 = (x60 + x30);
+ { uint64_t x62 = (x19 + (x29 << 0x4));
+ { uint64_t x63 = (x62 + (x29 << 0x1));
+ { uint64_t x64 = (x63 + x29);
+ { uint64_t x65 = (x64 >> 0x1a);
+ { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
+ { uint64_t x67 = (x65 + x61);
+ { uint64_t x68 = (x67 >> 0x19);
+ { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
+ { uint64_t x70 = (x68 + x58);
+ { uint64_t x71 = (x70 >> 0x1a);
+ { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
+ { uint64_t x73 = (x71 + x55);
+ { uint64_t x74 = (x73 >> 0x19);
+ { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
+ { uint64_t x76 = (x74 + x52);
+ { uint64_t x77 = (x76 >> 0x1a);
+ { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
+ { uint64_t x79 = (x77 + x49);
+ { uint64_t x80 = (x79 >> 0x19);
+ { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
+ { uint64_t x82 = (x80 + x46);
+ { uint64_t x83 = (x82 >> 0x1a);
+ { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
+ { uint64_t x85 = (x83 + x43);
+ { uint64_t x86 = (x85 >> 0x19);
+ { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
+ { uint64_t x88 = (x86 + x40);
+ { uint64_t x89 = (x88 >> 0x1a);
+ { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
+ { uint64_t x91 = (x89 + x28);
+ { uint64_t x92 = (x91 >> 0x19);
+ { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
+ { uint64_t x94 = (x66 + (0x13 * x92));
+ { uint32_t x95 = (uint32_t) (x94 >> 0x1a);
+ { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
+ { uint32_t x97 = (x95 + x69);
+ { uint32_t x98 = (x97 >> 0x19);
+ { uint32_t x99 = (x97 & 0x1ffffff);
+ out[0] = x96;
+ out[1] = x99;
+ out[2] = (x98 + x72);
+ out[3] = x75;
+ out[4] = x78;
+ out[5] = x81;
+ out[6] = x84;
+ out[7] = x87;
+ out[8] = x90;
+ out[9] = x93;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
- /* It still remains the case that input might be between 2^255-19 and 2^255.
- * In this case, input[1..9] must take their maximum value and input[0] must
- * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed.
- */
- mask = int32_t_gte(input[0], 0x3ffffed);
- for (i = 1; i < 10; i++) {
- if ((i & 1) == 1) {
- mask &= int32_t_eq(input[i], 0x1ffffff);
- } else {
- mask &= int32_t_eq(input[i], 0x3ffffff);
- }
- }
+static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
+{
+ fe_sqr_impl(h->v, f->v);
+}
- /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
- * this conditionally subtracts 2^255-19.
- */
- input[0] -= mask & 0x3ffffed;
-
- for (i = 1; i < 10; i++) {
- if ((i & 1) == 1) {
- input[i] -= mask & 0x1ffffff;
- } else {
- input[i] -= mask & 0x3ffffff;
- }
- }
+static __always_inline void fe_sq_tt(fe *h, const fe *f)
+{
+ fe_sqr_impl(h->v, f->v);
+}
- input[1] <<= 2;
- input[2] <<= 3;
- input[3] <<= 5;
- input[4] <<= 6;
- input[6] <<= 1;
- input[7] <<= 3;
- input[8] <<= 4;
- input[9] <<= 6;
-#define F(i, s) \
- output[s+0] |= input[i] & 0xff; \
- output[s+1] = (input[i] >> 8) & 0xff; \
- output[s+2] = (input[i] >> 16) & 0xff; \
- output[s+3] = (input[i] >> 24) & 0xff;
- output[0] = 0;
- output[16] = 0;
- F(0, 0);
- F(1, 3);
- F(2, 6);
- F(3, 9);
- F(4, 12);
- F(5, 16);
- F(6, 19);
- F(7, 22);
- F(8, 25);
- F(9, 28);
-#undef F
-}
-
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- * x2 z3: long form
- * x3 z3: long form
- * x z: short form, destroyed
- * xprime zprime: short form, destroyed
- * qmqp: short form, preserved
- *
- * On entry and exit, the absolute value of the limbs of all inputs and outputs
- * are < 2^26.
- */
-static void fmonty(limb *x2, limb *z2, /* output 2Q */
- limb *x3, limb *z3, /* output Q + Q' */
- limb *x, limb *z, /* input Q */
- limb *xprime, limb *zprime, /* input Q' */
-
- const limb *qmqp /* input Q - Q' */)
-{
- limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
- zzprime[19], zzzprime[19], xxxprime[19];
-
- __builtin_memcpy(origx, x, 10 * sizeof(limb));
- fsum(x, z);
- /* |x[i]| < 2^27 */
- fdifference(z, origx); /* does x - z */
- /* |z[i]| < 2^27 */
-
- __builtin_memcpy(origxprime, xprime, sizeof(limb) * 10);
- fsum(xprime, zprime);
- /* |xprime[i]| < 2^27 */
- fdifference(zprime, origxprime);
- /* |zprime[i]| < 2^27 */
- fproduct(xxprime, xprime, z);
- /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
- * 2^(27+27) and fproduct adds together, at most, 14 of those products.
- * (Approximating that to 2^58 doesn't work out.)
- */
- fproduct(zzprime, x, zprime);
- /* |zzprime[i]| < 14*2^54 */
- freduce_degree(xxprime);
- freduce_coefficients(xxprime);
- /* |xxprime[i]| < 2^26 */
- freduce_degree(zzprime);
- freduce_coefficients(zzprime);
- /* |zzprime[i]| < 2^26 */
- __builtin_memcpy(origxprime, xxprime, sizeof(limb) * 10);
- fsum(xxprime, zzprime);
- /* |xxprime[i]| < 2^27 */
- fdifference(zzprime, origxprime);
- /* |zzprime[i]| < 2^27 */
- fsquare(xxxprime, xxprime);
- /* |xxxprime[i]| < 2^26 */
- fsquare(zzzprime, zzprime);
- /* |zzzprime[i]| < 2^26 */
- fproduct(zzprime, zzzprime, qmqp);
- /* |zzprime[i]| < 14*2^52 */
- freduce_degree(zzprime);
- freduce_coefficients(zzprime);
- /* |zzprime[i]| < 2^26 */
- __builtin_memcpy(x3, xxxprime, sizeof(limb) * 10);
- __builtin_memcpy(z3, zzprime, sizeof(limb) * 10);
-
- fsquare(xx, x);
- /* |xx[i]| < 2^26 */
- fsquare(zz, z);
- /* |zz[i]| < 2^26 */
- fproduct(x2, xx, zz);
- /* |x2[i]| < 14*2^52 */
- freduce_degree(x2);
- freduce_coefficients(x2);
- /* |x2[i]| < 2^26 */
- fdifference(zz, xx); // does zz = xx - zz
- /* |zz[i]| < 2^27 */
- __builtin_memset(zzz + 10, 0, sizeof(limb) * 9);
- fscalar_product(zzz, zz, 121665);
- /* |zzz[i]| < 2^(27+17) */
- /* No need to call freduce_degree here:
- fscalar_product doesn't increase the degree of its input. */
- freduce_coefficients(zzz);
- /* |zzz[i]| < 2^26 */
- fsum(zzz, xx);
- /* |zzz[i]| < 2^27 */
- fproduct(z2, zz, zzz);
- /* |z2[i]| < 14*2^(26+27) */
- freduce_degree(z2);
- freduce_coefficients(z2);
- /* |z2|i| < 2^26 */
-}
-
-/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
- * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
- * side-channel attacks.
- *
- * NOTE that this function requires that 'iswap' be 1 or 0; other values give
- * wrong results. Also, the two limb arrays must be in reduced-coefficient,
- * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
- * and all all values in a[0..9],b[0..9] must have magnitude less than
- * INT32_MAX.
- */
-static void swap_conditional(limb a[static 19], limb b[static 19], limb iswap)
+static __always_inline void fe_loose_invert(fe *out, const fe_loose *z)
{
- unsigned int i;
- const int32_t swap = (int32_t) -iswap;
+ fe t0;
+ fe t1;
+ fe t2;
+ fe t3;
+ int i;
- for (i = 0; i < 10; ++i) {
- const int32_t x = swap & (((int32_t)a[i]) ^ ((int32_t)b[i]));
+ fe_sq_tl(&t0, z);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 2; ++i)
+ fe_sq_tt(&t1, &t1);
+ fe_mul_tlt(&t1, z, &t1);
+ fe_mul_ttt(&t0, &t0, &t1);
+ fe_sq_tt(&t2, &t0);
+ fe_mul_ttt(&t1, &t1, &t2);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 5; ++i)
+ fe_sq_tt(&t2, &t2);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 10; ++i)
+ fe_sq_tt(&t2, &t2);
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
+ for (i = 1; i < 20; ++i)
+ fe_sq_tt(&t3, &t3);
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
+ for (i = 1; i < 10; ++i)
+ fe_sq_tt(&t2, &t2);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 50; ++i)
+ fe_sq_tt(&t2, &t2);
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
+ for (i = 1; i < 100; ++i)
+ fe_sq_tt(&t3, &t3);
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
+ for (i = 1; i < 50; ++i)
+ fe_sq_tt(&t2, &t2);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
+ for (i = 1; i < 5; ++i)
+ fe_sq_tt(&t1, &t1);
+ fe_mul_ttt(out, &t1, &t0);
+}
- a[i] = ((int32_t)a[i]) ^ x;
- b[i] = ((int32_t)b[i]) ^ x;
- }
+static __always_inline void fe_invert(fe *out, const fe *z)
+{
+ fe_loose l;
+ fe_copy_lt(&l, z);
+ fe_loose_invert(out, &l);
}
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
+/* Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
*
- * resultx/resultz: the x coordinate of the resulting curve point (short form)
- * n: a little endian, 32-byte number
- * q: a point of the curve (short form)
+ * Preconditions: b in {0,1}
*/
-static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
-{
- limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
- limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
- limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
- limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
-
- unsigned int i, j;
-
- __builtin_memcpy(nqpqx, q, sizeof(limb) * 10);
-
- for (i = 0; i < 32; ++i) {
- uint8_t byte = n[31 - i];
-
- for (j = 0; j < 8; ++j) {
- const limb bit = byte >> 7;
-
- swap_conditional(nqx, nqpqx, bit);
- swap_conditional(nqz, nqpqz, bit);
- fmonty(nqx2, nqz2,
- nqpqx2, nqpqz2,
- nqx, nqz,
- nqpqx, nqpqz,
- q);
- swap_conditional(nqx2, nqpqx2, bit);
- swap_conditional(nqz2, nqpqz2, bit);
-
- t = nqx;
- nqx = nqx2;
- nqx2 = t;
- t = nqz;
- nqz = nqz2;
- nqz2 = t;
- t = nqpqx;
- nqpqx = nqpqx2;
- nqpqx2 = t;
- t = nqpqz;
- nqpqz = nqpqz2;
- nqpqz2 = t;
-
- byte <<= 1;
- }
+static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b)
+{
+ unsigned i;
+ b = 0-b;
+ for (i = 0; i < 10; i++) {
+ uint32_t x = f->v[i] ^ g->v[i];
+ x &= b;
+ f->v[i] ^= x;
+ g->v[i] ^= x;
}
+}
- __builtin_memcpy(resultx, nqx, sizeof(limb) * 10);
- __builtin_memcpy(resultz, nqz, sizeof(limb) * 10);
+/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
+static __always_inline void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10])
+{
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = 0;
+ { const uint32_t x39 = 0;
+ { const uint32_t x37 = 0;
+ { const uint32_t x35 = 0;
+ { const uint32_t x33 = 0;
+ { const uint32_t x31 = 0;
+ { const uint32_t x29 = 0;
+ { const uint32_t x27 = 0;
+ { const uint32_t x25 = 0;
+ { const uint32_t x23 = 121666;
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}
-static void crecip(limb *out, const limb *z)
+static __always_inline void fe_mul121666(fe *h, const fe_loose *f)
{
- limb z2[10];
- limb z9[10];
- limb z11[10];
- limb z2_5_0[10];
- limb z2_10_0[10];
- limb z2_20_0[10];
- limb z2_50_0[10];
- limb z2_100_0[10];
- limb t0[10];
- limb t1[10];
- int i;
+ fe_mul_121666_impl(h->v, f->v);
+}
- /* 2 */ fsquare(z2, z);
- /* 4 */ fsquare(t1, z2);
- /* 8 */ fsquare(t0, t1);
- /* 9 */ fmul(z9, t0, z);
- /* 11 */ fmul(z11, z9, z2);
- /* 22 */ fsquare(t0, z11);
- /* 2^5 - 2^0 = 31 */ fmul(z2_5_0, t0, z9);
-
- /* 2^6 - 2^1 */ fsquare(t0, z2_5_0);
- /* 2^7 - 2^2 */ fsquare(t1, t0);
- /* 2^8 - 2^3 */ fsquare(t0, t1);
- /* 2^9 - 2^4 */ fsquare(t1, t0);
- /* 2^10 - 2^5 */ fsquare(t0, t1);
- /* 2^10 - 2^0 */ fmul(z2_10_0, t0, z2_5_0);
-
- /* 2^11 - 2^1 */ fsquare(t0, z2_10_0);
- /* 2^12 - 2^2 */ fsquare(t1, t0);
- /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
- /* 2^20 - 2^0 */ fmul(z2_20_0, t1, z2_10_0);
-
- /* 2^21 - 2^1 */ fsquare(t0, z2_20_0);
- /* 2^22 - 2^2 */ fsquare(t1, t0);
- /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
- /* 2^40 - 2^0 */ fmul(t0, t1, z2_20_0);
-
- /* 2^41 - 2^1 */ fsquare(t1, t0);
- /* 2^42 - 2^2 */ fsquare(t0, t1);
- /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
- /* 2^50 - 2^0 */ fmul(z2_50_0, t0, z2_10_0);
-
- /* 2^51 - 2^1 */ fsquare(t0, z2_50_0);
- /* 2^52 - 2^2 */ fsquare(t1, t0);
- /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
- /* 2^100 - 2^0 */ fmul(z2_100_0, t1, z2_50_0);
-
- /* 2^101 - 2^1 */ fsquare(t1, z2_100_0);
- /* 2^102 - 2^2 */ fsquare(t0, t1);
- /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
- /* 2^200 - 2^0 */ fmul(t1, t0, z2_100_0);
-
- /* 2^201 - 2^1 */ fsquare(t0, t1);
- /* 2^202 - 2^2 */ fsquare(t1, t0);
- /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
- /* 2^250 - 2^0 */ fmul(t0, t1, z2_50_0);
-
- /* 2^251 - 2^1 */ fsquare(t1, t0);
- /* 2^252 - 2^2 */ fsquare(t0, t1);
- /* 2^253 - 2^3 */ fsquare(t1, t0);
- /* 2^254 - 2^4 */ fsquare(t0, t1);
- /* 2^255 - 2^5 */ fsquare(t1, t0);
- /* 2^255 - 21 */ fmul(out, t1, z11);
-}
-
-static inline void curve25519_normalize_secret(uint8_t secret[static 32])
+static __always_inline void normalize_secret(uint8_t secret[static 32])
{
secret[0] &= 248;
secret[31] &= 127;
secret[31] |= 64;
}
-static inline void curve25519(uint8_t mypublic[static 32], const uint8_t secret[static 32], const uint8_t basepoint[static 32])
+
+static void curve25519(uint8_t out[static 32], const uint8_t scalar[static 32], const uint8_t point[static 32])
{
- limb bp[10], x[10], z[11], zmone[10];
+ fe x1, x2, z2, x3, z3, tmp0, tmp1;
+ fe_loose x2l, z2l, x3l, tmp0l, tmp1l;
+ unsigned swap = 0;
+ int pos;
uint8_t e[32];
- __builtin_memcpy(e, secret, 32);
- curve25519_normalize_secret(e);
+ __builtin_memcpy(e, scalar, 32);
+ normalize_secret(e);
+
+ /* The following implementation was transcribed to Coq and proven to
+ * correspond to unary scalar multiplication in affine coordinates given that
+ * x1 != 0 is the x coordinate of some point on the curve. It was also checked
+ * in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2
+ * = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the
+ * underlying field, so it applies to Curve25519 itself and the quadratic
+ * twist of Curve25519. It was not proven in Coq that prime-field arithmetic
+ * correctly simulates extension-field arithmetic on prime-field values.
+ * The decoding of the byte array representation of e was not considered.
+ * Specification of Montgomery curves in affine coordinates:
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
+ * Proof that these form a group that is isomorphic to a Weierstrass curve:
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
+ * Coq transcription and correctness proof of the loop (where scalarbits=255):
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
+ * preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0
+ */
+ fe_frombytes(&x1, point);
+ fe_1(&x2);
+ fe_0(&z2);
+ fe_copy(&x3, &x1);
+ fe_1(&z3);
+
+ for (pos = 254; pos >= 0; --pos) {
+ /* loop invariant as of right before the test, for the case where x1 != 0:
+ * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero
+ * let r := e >> (pos+1) in the following equalities of projective points:
+ * to_xz (r*P) === if swap then (x3, z3) else (x2, z2)
+ * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
+ * x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P)
+ */
+ unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+ swap ^= b;
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
+ swap = b;
+ /* Coq transcription of ladderstep formula (called from transcribed loop):
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
+ * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
+ * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
+ * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
+ */
+ fe_sub(&tmp0l, &x3, &z3);
+ fe_sub(&tmp1l, &x2, &z2);
+ fe_add(&x2l, &x2, &z2);
+ fe_add(&z2l, &x3, &z3);
+ fe_mul_tll(&z3, &tmp0l, &x2l);
+ fe_mul_tll(&z2, &z2l, &tmp1l);
+ fe_sq_tl(&tmp0, &tmp1l);
+ fe_sq_tl(&tmp1, &x2l);
+ fe_add(&x3l, &z3, &z2);
+ fe_sub(&z2l, &z3, &z2);
+ fe_mul_ttt(&x2, &tmp1, &tmp0);
+ fe_sub(&tmp1l, &tmp1, &tmp0);
+ fe_sq_tl(&z2, &z2l);
+ fe_mul121666(&z3, &tmp1l);
+ fe_sq_tl(&x3, &x3l);
+ fe_add(&tmp0l, &tmp0, &z3);
+ fe_mul_ttt(&z3, &x1, &z2);
+ fe_mul_tll(&z2, &tmp1l, &tmp0l);
+ }
+ /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2) */
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
- fexpand(bp, basepoint);
- cmult(x, z, e, bp);
- crecip(zmone, z);
- fmul(z, x, zmone);
- fcontract(mypublic, z);
+ fe_invert(&z2, &z2);
+ fe_mul_ttt(&x2, &x2, &z2);
+ fe_tobytes(out, &x2);
}
EMSCRIPTEN_KEEPALIVE void curve25519_generate_public(uint8_t public[static 32], const uint8_t private[static 32])
@@ -889,7 +873,7 @@ EMSCRIPTEN_KEEPALIVE void curve25519_generate_private(uint8_t private[static 32]
for (i = 0; i < 32; ++i)
private[i] = EM_ASM_INT_V({ return Module.getRandomValue(); });
- curve25519_normalize_secret(private);
+ normalize_secret(private);
}
static inline void encode_base64(char dest[4], const uint8_t src[3])