aboutsummaryrefslogtreecommitdiffstatshomepage
path: root/src/crypto/curve25519-generic.h
diff options
context:
space:
mode:
Diffstat (limited to 'src/crypto/curve25519-generic.h')
-rw-r--r--src/crypto/curve25519-generic.h1038
1 files changed, 0 insertions, 1038 deletions
diff --git a/src/crypto/curve25519-generic.h b/src/crypto/curve25519-generic.h
deleted file mode 100644
index 185b62e..0000000
--- a/src/crypto/curve25519-generic.h
+++ /dev/null
@@ -1,1038 +0,0 @@
-/* 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.
- *
- * Original author: Adam Langley <agl@imperialviolet.org>
- */
-
-#define ARCH_HAS_SEPARATE_IRQ_STACK
-#if (defined(CONFIG_MIPS) && LINUX_VERSION_CODE < KERNEL_VERSION(4, 11, 0)) || defined(CONFIG_ARM)
-#undef ARCH_HAS_SEPARATE_IRQ_STACK
-#endif
-
-typedef s64 limb;
-
-/* 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.
- */
-
-/* Sum two numbers: output += in */
-static void fsum(limb *output, const limb *in)
-{
- 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];
- }
-}
-
-/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!).
- */
-static void fdifference(limb *output, const limb *in)
-{
- unsigned int i;
-
- for (i = 0; i < 10; ++i)
- output[i] = in[i] - output[i];
-}
-
-/* Multiply a number by a scalar: output = in * scalar */
-static void fscalar_product(limb *output, const limb *in, const limb scalar)
-{
- unsigned int i;
-
- for (i = 0; i < 10; ++i)
- output[i] = in[i] * scalar;
-}
-
-/* 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) ((s32) in2[0])) * ((s32) in[0]);
- output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
- ((limb) ((s32) in2[1])) * ((s32) in[0]);
- output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[2]) +
- ((limb) ((s32) in2[2])) * ((s32) in[0]);
- output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
- ((limb) ((s32) in2[2])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[0]);
- output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
- 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[1])) +
- ((limb) ((s32) in2[0])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[0]);
- output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[0]);
- output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[1])) +
- ((limb) ((s32) in2[2])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[2]) +
- ((limb) ((s32) in2[0])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[0]);
- output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[0]);
- output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
- 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[1])) +
- ((limb) ((s32) in2[2])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[2]) +
- ((limb) ((s32) in2[0])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[0]);
- output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[4]) +
- ((limb) ((s32) in2[3])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[0]);
- output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
- ((limb) ((s32) in2[3])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[1])) +
- ((limb) ((s32) in2[4])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[4]) +
- ((limb) ((s32) in2[2])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[2]);
- output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[5]) +
- ((limb) ((s32) in2[4])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[4]) +
- ((limb) ((s32) in2[3])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[2]);
- output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
- 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[5]) +
- ((limb) ((s32) in2[3])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[3])) +
- ((limb) ((s32) in2[4])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[4]);
- output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[6]) +
- ((limb) ((s32) in2[5])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[5]) +
- ((limb) ((s32) in2[4])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[4]);
- output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
- ((limb) ((s32) in2[5])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[5])) +
- ((limb) ((s32) in2[6])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[6]);
- output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[7]) +
- ((limb) ((s32) in2[6])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[6]);
- output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[7]));
- output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[8]);
- output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) 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)
-{
- /* 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.
- */
- 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
-
-/* 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)
-{
- /* High word of v; no shift needed. */
- const u32 highword = (u32) (((u64) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const s32 sign = ((s32) highword) >> 31;
- /* Set to 0x3ffffff if v was negative; else set to 0. */
- const s32 roundoff = ((u32) sign) >> 6;
- /* Should return v / (1<<26) */
- return (v + roundoff) >> 26;
-}
-
-/* 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)
-{
- /* High word of v; no shift needed*/
- const u32 highword = (u32) (((u64) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const s32 sign = ((s32) highword) >> 31;
- /* Set to 0x1ffffff if v was negative; else set to 0. */
- const s32 roundoff = ((u32) sign) >> 7;
- /* Should return v / (1<<25) */
- return (v + roundoff) >> 25;
-}
-
-/* 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)
-{
- unsigned int i;
-
- output[10] = 0;
-
- 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];
-
- output[10] = 0;
-
- /* 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]);
-
- output[0] -= over << 26;
- output[1] += over;
- }
-
- /* 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.
- */
-}
-
-/* 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)
-{
- limb t[19];
-
- fproduct(t, in, in2);
- /* |t[i]| < 14*2^54 */
- freduce_degree(t);
- freduce_coefficients(t);
- /* |t[i]| < 2^26 */
- memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* 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.
- */
-static void fsquare_inner(limb *output, const limb *in)
-{
- output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
- output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
- output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
- ((limb) ((s32) in[0])) * ((s32) in[2]));
- output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
- ((limb) ((s32) in[0])) * ((s32) in[3]));
- output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
- 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
- 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
- output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
- ((limb) ((s32) in[1])) * ((s32) in[4]) +
- ((limb) ((s32) in[0])) * ((s32) in[5]));
- output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
- ((limb) ((s32) in[2])) * ((s32) in[4]) +
- ((limb) ((s32) in[0])) * ((s32) in[6]) +
- 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
- output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
- ((limb) ((s32) in[2])) * ((s32) in[5]) +
- ((limb) ((s32) in[1])) * ((s32) in[6]) +
- ((limb) ((s32) in[0])) * ((s32) in[7]));
- output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
- 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
- ((limb) ((s32) in[0])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[5])));
- output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
- ((limb) ((s32) in[3])) * ((s32) in[6]) +
- ((limb) ((s32) in[2])) * ((s32) in[7]) +
- ((limb) ((s32) in[1])) * ((s32) in[8]) +
- ((limb) ((s32) in[0])) * ((s32) in[9]));
- output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
- ((limb) ((s32) in[4])) * ((s32) in[6]) +
- ((limb) ((s32) in[2])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
- ((limb) ((s32) in[1])) * ((s32) in[9])));
- output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
- ((limb) ((s32) in[4])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[8]) +
- ((limb) ((s32) in[2])) * ((s32) in[9]));
- output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
- 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[9])));
- output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
- ((limb) ((s32) in[5])) * ((s32) in[8]) +
- ((limb) ((s32) in[4])) * ((s32) in[9]));
- output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
- ((limb) ((s32) in[6])) * ((s32) in[8]) +
- 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
- output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
- ((limb) ((s32) in[6])) * ((s32) in[9]));
- output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
- 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
- output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
- output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) 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)
-{
- 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 */
- memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static inline void fexpand(limb *output, const u8 *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
-
-/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
-static s32 s32_eq(s32 a, s32 b)
-{
- a = ~(a ^ b);
- a &= a << 16;
- a &= a << 8;
- a &= a << 4;
- a &= a << 2;
- a &= a << 1;
- return a >> 31;
-}
-
-/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
- * both non-negative.
- */
-static s32 s32_gte(s32 a, s32 b)
-{
- a -= b;
- /* a >= 0 iff a >= b. */
- return ~(a >> 31);
-}
-
-/* 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(u8 *output, limb *input_limbs)
-{
- int i;
- int j;
- s32 input[10];
- s32 mask;
-
- /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
- 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 s32 mask = input[i] >> 31;
- const s32 carry = -((input[i] & mask) >> 25);
-
- input[i] = input[i] + (carry << 25);
- input[i+1] = input[i+1] - carry;
- } else {
- const s32 mask = input[i] >> 31;
- const s32 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 s32 mask = input[9] >> 31;
- const s32 carry = -((input[9] & mask) >> 25);
-
- input[9] = input[9] + (carry << 25);
- input[0] = input[0] - (carry * 19);
- }
-
- /* 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.
- */
- }
-
- /* 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 s32 mask = input[0] >> 31;
- const s32 carry = -((input[0] & mask) >> 26);
-
- input[0] = input[0] + (carry << 26);
- input[1] = input[1] - carry;
- }
-
- /* 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 s32 carry = input[i] >> 25;
-
- input[i] &= 0x1ffffff;
- input[i+1] += carry;
- } else {
- const s32 carry = input[i] >> 26;
-
- input[i] &= 0x3ffffff;
- input[i+1] += carry;
- }
- }
-
- {
- const s32 carry = input[9] >> 25;
-
- input[9] &= 0x1ffffff;
- input[0] += 19*carry;
- }
- }
-
- /* 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.
- */
-
- /* 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 = s32_gte(input[0], 0x3ffffed);
- for (i = 1; i < 10; i++) {
- if ((i & 1) == 1) {
- mask &= s32_eq(input[i], 0x1ffffff);
- } else {
- mask &= s32_eq(input[i], 0x3ffffff);
- }
- }
-
- /* 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;
- }
- }
-
- 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
-}
-
-/* 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[19], limb b[19], limb iswap)
-{
- unsigned int i;
- const s32 swap = (s32) -iswap;
-
- for (i = 0; i < 10; ++i) {
- const s32 x = swap & (((s32)a[i]) ^ ((s32)b[i]));
-
- a[i] = ((s32)a[i]) ^ x;
- b[i] = ((s32)b[i]) ^ x;
- }
-}
-
-static void crecip(limb *out, const limb *z)
-{
- 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;
-
- /* 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);
-}
-
-
-#ifdef ARCH_HAS_SEPARATE_IRQ_STACK
-/* 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];
-
- memcpy(origx, x, 10 * sizeof(limb));
- fsum(x, z);
- /* |x[i]| < 2^27 */
- fdifference(z, origx); /* does x - z */
- /* |z[i]| < 2^27 */
-
- 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 */
- 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 */
- memcpy(x3, xxxprime, sizeof(limb) * 10);
- 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 */
- 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 */
-}
-
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- * 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)
- */
-static void cmult(limb *resultx, limb *resultz, const u8 *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;
-
- memcpy(nqpqx, q, sizeof(limb) * 10);
-
- for (i = 0; i < 32; ++i) {
- u8 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;
- }
- }
-
- memcpy(resultx, nqx, sizeof(limb) * 10);
- memcpy(resultz, nqz, sizeof(limb) * 10);
-}
-
-static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- limb bp[10], x[10], z[11], zmone[10];
- u8 e[32];
-
- memcpy(e, secret, 32);
- normalize_secret(e);
-
- fexpand(bp, basepoint);
- cmult(x, z, e, bp);
- crecip(zmone, z);
- fmul(z, x, zmone);
- fcontract(mypublic, z);
-
- memzero_explicit(e, sizeof(e));
- memzero_explicit(bp, sizeof(bp));
- memzero_explicit(x, sizeof(x));
- memzero_explicit(z, sizeof(z));
- memzero_explicit(zmone, sizeof(zmone));
-
- return true;
-}
-#else
-struct other_stack {
- limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
- limb a[19], b[19], c[19], d[19], e[19], f[19], g[19], h[19];
- limb bp[10], x[10], z[11], zmone[10];
- u8 ee[32];
-};
-
-/* 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(struct other_stack *s,
- 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' */)
-{
- memcpy(s->origx, x, 10 * sizeof(limb));
- fsum(x, z);
- /* |x[i]| < 2^27 */
- fdifference(z, s->origx); /* does x - z */
- /* |z[i]| < 2^27 */
-
- memcpy(s->origxprime, xprime, sizeof(limb) * 10);
- fsum(xprime, zprime);
- /* |xprime[i]| < 2^27 */
- fdifference(zprime, s->origxprime);
- /* |zprime[i]| < 2^27 */
- fproduct(s->xxprime, xprime, z);
- /* |s->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(s->zzprime, x, zprime);
- /* |s->zzprime[i]| < 14*2^54 */
- freduce_degree(s->xxprime);
- freduce_coefficients(s->xxprime);
- /* |s->xxprime[i]| < 2^26 */
- freduce_degree(s->zzprime);
- freduce_coefficients(s->zzprime);
- /* |s->zzprime[i]| < 2^26 */
- memcpy(s->origxprime, s->xxprime, sizeof(limb) * 10);
- fsum(s->xxprime, s->zzprime);
- /* |s->xxprime[i]| < 2^27 */
- fdifference(s->zzprime, s->origxprime);
- /* |s->zzprime[i]| < 2^27 */
- fsquare(s->xxxprime, s->xxprime);
- /* |s->xxxprime[i]| < 2^26 */
- fsquare(s->zzzprime, s->zzprime);
- /* |s->zzzprime[i]| < 2^26 */
- fproduct(s->zzprime, s->zzzprime, qmqp);
- /* |s->zzprime[i]| < 14*2^52 */
- freduce_degree(s->zzprime);
- freduce_coefficients(s->zzprime);
- /* |s->zzprime[i]| < 2^26 */
- memcpy(x3, s->xxxprime, sizeof(limb) * 10);
- memcpy(z3, s->zzprime, sizeof(limb) * 10);
-
- fsquare(s->xx, x);
- /* |s->xx[i]| < 2^26 */
- fsquare(s->zz, z);
- /* |s->zz[i]| < 2^26 */
- fproduct(x2, s->xx, s->zz);
- /* |x2[i]| < 14*2^52 */
- freduce_degree(x2);
- freduce_coefficients(x2);
- /* |x2[i]| < 2^26 */
- fdifference(s->zz, s->xx); // does s->zz = s->xx - s->zz
- /* |s->zz[i]| < 2^27 */
- memset(s->zzz + 10, 0, sizeof(limb) * 9);
- fscalar_product(s->zzz, s->zz, 121665);
- /* |s->zzz[i]| < 2^(27+17) */
- /* No need to call freduce_degree here:
- fscalar_product doesn't increase the degree of its input. */
- freduce_coefficients(s->zzz);
- /* |s->zzz[i]| < 2^26 */
- fsum(s->zzz, s->xx);
- /* |s->zzz[i]| < 2^27 */
- fproduct(z2, s->zz, s->zzz);
- /* |z2[i]| < 14*2^(26+27) */
- freduce_degree(z2);
- freduce_coefficients(z2);
- /* |z2|i| < 2^26 */
-}
-
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- * 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)
- */
-static void cmult(struct other_stack *s, limb *resultx, limb *resultz, const u8 *n, const limb *q)
-{
- unsigned int i, j;
- limb *nqpqx = s->a, *nqpqz = s->b, *nqx = s->c, *nqz = s->d, *t;
- limb *nqpqx2 = s->e, *nqpqz2 = s->f, *nqx2 = s->g, *nqz2 = s->h;
-
- *nqpqz = *nqx = *nqpqz2 = *nqz2 = 1;
- memcpy(nqpqx, q, sizeof(limb) * 10);
-
- for (i = 0; i < 32; ++i) {
- u8 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(s,
- 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;
- }
- }
-
- memcpy(resultx, nqx, sizeof(limb) * 10);
- memcpy(resultz, nqz, sizeof(limb) * 10);
-}
-
-static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- struct other_stack *s = kzalloc(sizeof(struct other_stack), GFP_KERNEL);
-
- if (unlikely(!s))
- return false;
-
- memcpy(s->ee, secret, 32);
- normalize_secret(s->ee);
-
- fexpand(s->bp, basepoint);
- cmult(s, s->x, s->z, s->ee, s->bp);
- crecip(s->zmone, s->z);
- fmul(s->z, s->x, s->zmone);
- fcontract(mypublic, s->z);
-
- kzfree(s);
- return true;
-}
-#endif
Copyright © 1996 – 2023 Jason A. Donenfeld. All Rights Reverse Engineered.