From 481a58e01943b873bcc361ed72299ef7d3a2655a Mon Sep 17 00:00:00 2001 From: "Jason A. Donenfeld" Date: Mon, 15 Jan 2018 11:34:31 +0100 Subject: curve25519: modularize implementation Signed-off-by: Jason A. Donenfeld --- src/crypto/curve25519-arm.h | 14 + src/crypto/curve25519-generic.h | 1038 +++++++++++++++++++++++++ src/crypto/curve25519-u128.h | 408 ++++++++++ src/crypto/curve25519-x86_64.h | 175 +++++ src/crypto/curve25519.c | 1615 +-------------------------------------- 5 files changed, 1640 insertions(+), 1610 deletions(-) create mode 100644 src/crypto/curve25519-arm.h create mode 100644 src/crypto/curve25519-generic.h create mode 100644 src/crypto/curve25519-u128.h create mode 100644 src/crypto/curve25519-x86_64.h diff --git a/src/crypto/curve25519-arm.h b/src/crypto/curve25519-arm.h new file mode 100644 index 0000000..4142e4e --- /dev/null +++ b/src/crypto/curve25519-arm.h @@ -0,0 +1,14 @@ +/* SPDX-License-Identifier: GPL-2.0 + * + * Copyright (C) 2015-2018 Jason A. Donenfeld . All Rights Reserved. + */ + +#include +#include +#include +asmlinkage void curve25519_neon(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]); +static bool curve25519_use_neon __read_mostly; +void __init curve25519_fpu_init(void) +{ + curve25519_use_neon = elf_hwcap & HWCAP_NEON; +} diff --git a/src/crypto/curve25519-generic.h b/src/crypto/curve25519-generic.h new file mode 100644 index 0000000..185b62e --- /dev/null +++ b/src/crypto/curve25519-generic.h @@ -0,0 +1,1038 @@ +/* SPDX-License-Identifier: GPL-2.0 + * + * Copyright (C) 2008 Google Inc. All Rights Reserved. + * Copyright (C) 2015-2018 Jason A. Donenfeld . All Rights Reserved. + * + * Original author: Adam Langley + */ + +#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 diff --git a/src/crypto/curve25519-u128.h b/src/crypto/curve25519-u128.h new file mode 100644 index 0000000..9f9ab20 --- /dev/null +++ b/src/crypto/curve25519-u128.h @@ -0,0 +1,408 @@ +/* SPDX-License-Identifier: GPL-2.0 + * + * Copyright (C) 2008 Google Inc. All Rights Reserved. + * Copyright (C) 2015-2018 Jason A. Donenfeld . All Rights Reserved. + * + * Original author: Adam Langley + */ + +typedef u64 limb; +typedef limb felem[5]; +typedef __uint128_t u128; + +/* Sum two numbers: output += in */ +static __always_inline void fsum(limb *output, const limb *in) +{ + output[0] += in[0]; + output[1] += in[1]; + output[2] += in[2]; + output[3] += in[3]; + output[4] += in[4]; +} + +/* Find the difference of two numbers: output = in - output + * (note the order of the arguments!) + * + * Assumes that out[i] < 2**52 + * On return, out[i] < 2**55 + */ +static __always_inline void fdifference_backwards(felem out, const felem in) +{ + /* 152 is 19 << 3 */ + static const limb two54m152 = (((limb)1) << 54) - 152; + static const limb two54m8 = (((limb)1) << 54) - 8; + + out[0] = in[0] + two54m152 - out[0]; + out[1] = in[1] + two54m8 - out[1]; + out[2] = in[2] + two54m8 - out[2]; + out[3] = in[3] + two54m8 - out[3]; + out[4] = in[4] + two54m8 - out[4]; +} + +/* Multiply a number by a scalar: output = in * scalar */ +static __always_inline void fscalar_product(felem output, const felem in, const limb scalar) +{ + u128 a; + + a = ((u128) in[0]) * scalar; + output[0] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[1]) * scalar + ((limb) (a >> 51)); + output[1] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[2]) * scalar + ((limb) (a >> 51)); + output[2] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[3]) * scalar + ((limb) (a >> 51)); + output[3] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[4]) * scalar + ((limb) (a >> 51)); + output[4] = ((limb)a) & 0x7ffffffffffffUL; + + output[0] += (a >> 51) * 19; +} + +/* Multiply two numbers: output = in2 * in + * + * output must be distinct to both inputs. The inputs are reduced coefficient + * form, the output is not. + * + * Assumes that in[i] < 2**55 and likewise for in2. + * On return, output[i] < 2**52 + */ +static __always_inline void fmul(felem output, const felem in2, const felem in) +{ + u128 t[5]; + limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + s0 = in2[0]; + s1 = in2[1]; + s2 = in2[2]; + s3 = in2[3]; + s4 = in2[4]; + + t[0] = ((u128) r0) * s0; + t[1] = ((u128) r0) * s1 + ((u128) r1) * s0; + t[2] = ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1; + t[3] = ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1; + t[4] = ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2; + + r4 *= 19; + r1 *= 19; + r2 *= 19; + r3 *= 19; + + t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2; + t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3; + t[2] += ((u128) r4) * s3 + ((u128) r3) * s4; + t[3] += ((u128) r4) * s4; + + r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); + t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); + t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); + t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); + t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; + r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; + r2 += c; + + output[0] = r0; + output[1] = r1; + output[2] = r2; + output[3] = r3; + output[4] = r4; +} + +static __always_inline void fsquare_times(felem output, const felem in, limb count) +{ + u128 t[5]; + limb r0, r1, r2, r3, r4, c; + limb d0, d1, d2, d4, d419; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + do { + d0 = r0 * 2; + d1 = r1 * 2; + d2 = r2 * 2 * 19; + d419 = r4 * 19; + d4 = d419 * 2; + + t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3 )); + t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19)); + t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3 )); + t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419 )); + t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2 )); + + r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); + t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); + t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); + t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); + t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; + r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; + r2 += c; + } while (--count); + + output[0] = r0; + output[1] = r1; + output[2] = r2; + output[3] = r3; + output[4] = r4; +} + +/* Load a little-endian 64-bit number */ +static inline limb load_limb(const u8 *in) +{ + return le64_to_cpu(*(__le64 *)in); +} + +static inline void store_limb(u8 *out, limb in) +{ + *(__le64 *)out = cpu_to_le64(in); +} + +/* Take a little-endian, 32-byte number and expand it into polynomial form */ +static inline void fexpand(limb *output, const u8 *in) +{ + output[0] = load_limb(in) & 0x7ffffffffffffUL; + output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL; + output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL; + output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL; + output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL; +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array + */ +static void fcontract(u8 *output, const felem input) +{ + u128 t[5]; + + t[0] = input[0]; + t[1] = input[1]; + t[2] = input[2]; + t[3] = input[3]; + t[4] = input[4]; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + + t[0] += 19; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + + t[0] += 0x8000000000000UL - 19; + t[1] += 0x8000000000000UL - 1; + t[2] += 0x8000000000000UL - 1; + t[3] += 0x8000000000000UL - 1; + t[4] += 0x8000000000000UL - 1; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[4] &= 0x7ffffffffffffUL; + + store_limb(output, t[0] | (t[1] << 51)); + store_limb(output+8, (t[1] >> 13) | (t[2] << 38)); + store_limb(output+16, (t[2] >> 26) | (t[3] << 25)); + store_limb(output+24, (t[3] >> 39) | (t[4] << 12)); +} + +/* 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 + */ +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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5]; + + memcpy(origx, x, 5 * sizeof(limb)); + fsum(x, z); + fdifference_backwards(z, origx); // does x - z + + memcpy(origxprime, xprime, sizeof(limb) * 5); + fsum(xprime, zprime); + fdifference_backwards(zprime, origxprime); + fmul(xxprime, xprime, z); + fmul(zzprime, x, zprime); + memcpy(origxprime, xxprime, sizeof(limb) * 5); + fsum(xxprime, zzprime); + fdifference_backwards(zzprime, origxprime); + fsquare_times(x3, xxprime, 1); + fsquare_times(zzzprime, zzprime, 1); + fmul(z3, zzzprime, qmqp); + + fsquare_times(xx, x, 1); + fsquare_times(zz, z, 1); + fmul(x2, xx, zz); + fdifference_backwards(zz, xx); // does zz = xx - zz + fscalar_product(zzz, zz, 121665); + fsum(zzz, xx); + fmul(z2, zz, zzz); +} + +/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements + * long. Perform the swap iff @swap is non-zero. + * + * This function performs the swap without leaking any side-channel + * information. + */ +static void swap_conditional(limb a[5], limb b[5], limb iswap) +{ + unsigned int i; + const limb swap = -iswap; + + for (i = 0; i < 5; ++i) { + const limb x = swap & (a[i] ^ b[i]); + + a[i] ^= x; + b[i] ^= x; + } +} + +/* 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[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0}; + limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; + limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1}; + limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; + + unsigned int i, j; + + memcpy(nqpqx, q, sizeof(limb) * 5); + + 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) * 5); + memcpy(resultz, nqz, sizeof(limb) * 5); +} + +static void crecip(felem out, const felem z) +{ + felem a, t0, b, c; + + /* 2 */ fsquare_times(a, z, 1); // a = 2 + /* 8 */ fsquare_times(t0, a, 2); + /* 9 */ fmul(b, t0, z); // b = 9 + /* 11 */ fmul(a, b, a); // a = 11 + /* 22 */ fsquare_times(t0, a, 1); + /* 2^5 - 2^0 = 31 */ fmul(b, t0, b); + /* 2^10 - 2^5 */ fsquare_times(t0, b, 5); + /* 2^10 - 2^0 */ fmul(b, t0, b); + /* 2^20 - 2^10 */ fsquare_times(t0, b, 10); + /* 2^20 - 2^0 */ fmul(c, t0, b); + /* 2^40 - 2^20 */ fsquare_times(t0, c, 20); + /* 2^40 - 2^0 */ fmul(t0, t0, c); + /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10); + /* 2^50 - 2^0 */ fmul(b, t0, b); + /* 2^100 - 2^50 */ fsquare_times(t0, b, 50); + /* 2^100 - 2^0 */ fmul(c, t0, b); + /* 2^200 - 2^100 */ fsquare_times(t0, c, 100); + /* 2^200 - 2^0 */ fmul(t0, t0, c); + /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50); + /* 2^250 - 2^0 */ fmul(t0, t0, b); + /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5); + /* 2^255 - 21 */ fmul(out, t0, a); +} + +static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) +{ + limb bp[5], x[5], z[5], zmone[5]; + 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; +} diff --git a/src/crypto/curve25519-x86_64.h b/src/crypto/curve25519-x86_64.h new file mode 100644 index 0000000..2d83d77 --- /dev/null +++ b/src/crypto/curve25519-x86_64.h @@ -0,0 +1,175 @@ +/* SPDX-License-Identifier: GPL-2.0 + * + * Copyright (C) 2015-2018 Jason A. Donenfeld . All Rights Reserved. + * + * Based on algorithms from Tung Chou + */ + +#include +#include +#include +#include +static bool curve25519_use_avx __read_mostly; +void __init curve25519_fpu_init(void) +{ +#ifndef CONFIG_UML + curve25519_use_avx = boot_cpu_has(X86_FEATURE_AVX) && cpu_has_xfeatures(XFEATURE_MASK_SSE | XFEATURE_MASK_YMM, NULL); +#endif +} + +typedef u64 fe[10]; +typedef u64 fe51[5]; +asmlinkage void curve25519_sandy2x_ladder(fe *, const u8 *); +asmlinkage void curve25519_sandy2x_ladder_base(fe *, const u8 *); +asmlinkage void curve25519_sandy2x_fe51_pack(u8 *, const fe51 *); +asmlinkage void curve25519_sandy2x_fe51_mul(fe51 *, const fe51 *, const fe51 *); +asmlinkage void curve25519_sandy2x_fe51_nsquare(fe51 *, const fe51 *, int); + +static inline u32 le24_to_cpupv(const u8 *in) +{ + return le16_to_cpup((__le16 *)in) | ((u32)in[2]) << 16; +} + +static inline void fe_frombytes(fe h, const u8 *s) +{ + u64 h0 = le32_to_cpup((__le32 *)s); + u64 h1 = le24_to_cpupv(s + 4) << 6; + u64 h2 = le24_to_cpupv(s + 7) << 5; + u64 h3 = le24_to_cpupv(s + 10) << 3; + u64 h4 = le24_to_cpupv(s + 13) << 2; + u64 h5 = le32_to_cpup((__le32 *)(s + 16)); + u64 h6 = le24_to_cpupv(s + 20) << 7; + u64 h7 = le24_to_cpupv(s + 23) << 5; + u64 h8 = le24_to_cpupv(s + 26) << 4; + u64 h9 = (le24_to_cpupv(s + 29) & 8388607) << 2; + u64 carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, carry9; + + carry9 = h9 >> 25; h0 += carry9 * 19; h9 &= 0x1FFFFFF; + carry1 = h1 >> 25; h2 += carry1; h1 &= 0x1FFFFFF; + carry3 = h3 >> 25; h4 += carry3; h3 &= 0x1FFFFFF; + carry5 = h5 >> 25; h6 += carry5; h5 &= 0x1FFFFFF; + carry7 = h7 >> 25; h8 += carry7; h7 &= 0x1FFFFFF; + + carry0 = h0 >> 26; h1 += carry0; h0 &= 0x3FFFFFF; + carry2 = h2 >> 26; h3 += carry2; h2 &= 0x3FFFFFF; + carry4 = h4 >> 26; h5 += carry4; h4 &= 0x3FFFFFF; + carry6 = h6 >> 26; h7 += carry6; h6 &= 0x3FFFFFF; + carry8 = h8 >> 26; h9 += carry8; h8 &= 0x3FFFFFF; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +static inline void fe51_invert(fe51 *r, const fe51 *x) +{ + fe51 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t; + + /* 2 */ curve25519_sandy2x_fe51_nsquare(&z2, x, 1); + /* 4 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2, 1); + /* 8 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 1); + /* 9 */ curve25519_sandy2x_fe51_mul(&z9, (const fe51 *)&t, x); + /* 11 */ curve25519_sandy2x_fe51_mul(&z11, (const fe51 *)&z9, (const fe51 *)&z2); + /* 22 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z11, 1); + /* 2^5 - 2^0 = 31 */ curve25519_sandy2x_fe51_mul(&z2_5_0, (const fe51 *)&t, (const fe51 *)&z9); + + /* 2^10 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_5_0, 5); + /* 2^10 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_10_0, (const fe51 *)&t, (const fe51 *)&z2_5_0); + + /* 2^20 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_10_0, 10); + /* 2^20 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_20_0, (const fe51 *)&t, (const fe51 *)&z2_10_0); + + /* 2^40 - 2^20 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_20_0, 20); + /* 2^40 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_20_0); + + /* 2^50 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 10); + /* 2^50 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_50_0, (const fe51 *)&t, (const fe51 *)&z2_10_0); + + /* 2^100 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_50_0, 50); + /* 2^100 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_100_0, (const fe51 *)&t, (const fe51 *)&z2_50_0); + + /* 2^200 - 2^100 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_100_0, 100); + /* 2^200 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_100_0); + + /* 2^250 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 50); + /* 2^250 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_50_0); + + /* 2^255 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 5); + /* 2^255 - 21 */ curve25519_sandy2x_fe51_mul(r, (const fe51 *)t, (const fe51 *)&z11); +} + +static void curve25519_sandy2x(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) +{ + u8 e[32]; + fe var[3]; + fe51 x_51, z_51; + + memcpy(e, secret, 32); + normalize_secret(e); +#define x1 var[0] +#define x2 var[1] +#define z2 var[2] + fe_frombytes(x1, basepoint); + curve25519_sandy2x_ladder(var, e); + z_51[0] = (z2[1] << 26) + z2[0]; + z_51[1] = (z2[3] << 26) + z2[2]; + z_51[2] = (z2[5] << 26) + z2[4]; + z_51[3] = (z2[7] << 26) + z2[6]; + z_51[4] = (z2[9] << 26) + z2[8]; + x_51[0] = (x2[1] << 26) + x2[0]; + x_51[1] = (x2[3] << 26) + x2[2]; + x_51[2] = (x2[5] << 26) + x2[4]; + x_51[3] = (x2[7] << 26) + x2[6]; + x_51[4] = (x2[9] << 26) + x2[8]; +#undef x1 +#undef x2 +#undef z2 + fe51_invert(&z_51, (const fe51 *)&z_51); + curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51); + curve25519_sandy2x_fe51_pack(mypublic, (const fe51 *)&x_51); + + memzero_explicit(e, sizeof(e)); + memzero_explicit(var, sizeof(var)); + memzero_explicit(x_51, sizeof(x_51)); + memzero_explicit(z_51, sizeof(z_51)); +} + +static void curve25519_sandy2x_base(u8 pub[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE]) +{ + u8 e[32]; + fe var[3]; + fe51 x_51, z_51; + + memcpy(e, secret, 32); + normalize_secret(e); + curve25519_sandy2x_ladder_base(var, e); +#define x2 var[0] +#define z2 var[1] + z_51[0] = (z2[1] << 26) + z2[0]; + z_51[1] = (z2[3] << 26) + z2[2]; + z_51[2] = (z2[5] << 26) + z2[4]; + z_51[3] = (z2[7] << 26) + z2[6]; + z_51[4] = (z2[9] << 26) + z2[8]; + x_51[0] = (x2[1] << 26) + x2[0]; + x_51[1] = (x2[3] << 26) + x2[2]; + x_51[2] = (x2[5] << 26) + x2[4]; + x_51[3] = (x2[7] << 26) + x2[6]; + x_51[4] = (x2[9] << 26) + x2[8]; +#undef x2 +#undef z2 + fe51_invert(&z_51, (const fe51 *)&z_51); + curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51); + curve25519_sandy2x_fe51_pack(pub, (const fe51 *)&x_51); + + memzero_explicit(e, sizeof(e)); + memzero_explicit(var, sizeof(var)); + memzero_explicit(x_51, sizeof(x_51)); + memzero_explicit(z_51, sizeof(z_51)); +} diff --git a/src/crypto/curve25519.c b/src/crypto/curve25519.c index e343c85..dd7f4bd 100644 --- a/src/crypto/curve25519.c +++ b/src/crypto/curve25519.c @@ -1,9 +1,6 @@ /* SPDX-License-Identifier: GPL-2.0 * - * Copyright (C) 2008 Google Inc. All Rights Reserved. * Copyright (C) 2015-2018 Jason A. Donenfeld . All Rights Reserved. - * - * Original author: Adam Langley */ #include "curve25519.h" @@ -13,11 +10,6 @@ #include #include -#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 - static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE]) { secret[0] &= 248; @@ -26,1615 +18,17 @@ static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE]) } #if defined(CONFIG_X86_64) && defined(CONFIG_AS_AVX) -#include -#include -#include -#include -static bool curve25519_use_avx __read_mostly; -void __init curve25519_fpu_init(void) -{ -#ifndef CONFIG_UML - curve25519_use_avx = boot_cpu_has(X86_FEATURE_AVX) && cpu_has_xfeatures(XFEATURE_MASK_SSE | XFEATURE_MASK_YMM, NULL); -#endif -} - -typedef u64 fe[10]; -typedef u64 fe51[5]; -asmlinkage void curve25519_sandy2x_ladder(fe *, const u8 *); -asmlinkage void curve25519_sandy2x_ladder_base(fe *, const u8 *); -asmlinkage void curve25519_sandy2x_fe51_pack(u8 *, const fe51 *); -asmlinkage void curve25519_sandy2x_fe51_mul(fe51 *, const fe51 *, const fe51 *); -asmlinkage void curve25519_sandy2x_fe51_nsquare(fe51 *, const fe51 *, int); - -static inline u32 le24_to_cpupv(const u8 *in) -{ - return le16_to_cpup((__le16 *)in) | ((u32)in[2]) << 16; -} - -static inline void fe_frombytes(fe h, const u8 *s) -{ - u64 h0 = le32_to_cpup((__le32 *)s); - u64 h1 = le24_to_cpupv(s + 4) << 6; - u64 h2 = le24_to_cpupv(s + 7) << 5; - u64 h3 = le24_to_cpupv(s + 10) << 3; - u64 h4 = le24_to_cpupv(s + 13) << 2; - u64 h5 = le32_to_cpup((__le32 *)(s + 16)); - u64 h6 = le24_to_cpupv(s + 20) << 7; - u64 h7 = le24_to_cpupv(s + 23) << 5; - u64 h8 = le24_to_cpupv(s + 26) << 4; - u64 h9 = (le24_to_cpupv(s + 29) & 8388607) << 2; - u64 carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, carry9; - - carry9 = h9 >> 25; h0 += carry9 * 19; h9 &= 0x1FFFFFF; - carry1 = h1 >> 25; h2 += carry1; h1 &= 0x1FFFFFF; - carry3 = h3 >> 25; h4 += carry3; h3 &= 0x1FFFFFF; - carry5 = h5 >> 25; h6 += carry5; h5 &= 0x1FFFFFF; - carry7 = h7 >> 25; h8 += carry7; h7 &= 0x1FFFFFF; - - carry0 = h0 >> 26; h1 += carry0; h0 &= 0x3FFFFFF; - carry2 = h2 >> 26; h3 += carry2; h2 &= 0x3FFFFFF; - carry4 = h4 >> 26; h5 += carry4; h4 &= 0x3FFFFFF; - carry6 = h6 >> 26; h7 += carry6; h6 &= 0x3FFFFFF; - carry8 = h8 >> 26; h9 += carry8; h8 &= 0x3FFFFFF; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -static inline void fe51_invert(fe51 *r, const fe51 *x) -{ - fe51 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t; - - /* 2 */ curve25519_sandy2x_fe51_nsquare(&z2, x, 1); - /* 4 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2, 1); - /* 8 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 1); - /* 9 */ curve25519_sandy2x_fe51_mul(&z9, (const fe51 *)&t, x); - /* 11 */ curve25519_sandy2x_fe51_mul(&z11, (const fe51 *)&z9, (const fe51 *)&z2); - /* 22 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z11, 1); - /* 2^5 - 2^0 = 31 */ curve25519_sandy2x_fe51_mul(&z2_5_0, (const fe51 *)&t, (const fe51 *)&z9); - - /* 2^10 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_5_0, 5); - /* 2^10 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_10_0, (const fe51 *)&t, (const fe51 *)&z2_5_0); - - /* 2^20 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_10_0, 10); - /* 2^20 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_20_0, (const fe51 *)&t, (const fe51 *)&z2_10_0); - - /* 2^40 - 2^20 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_20_0, 20); - /* 2^40 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_20_0); - - /* 2^50 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 10); - /* 2^50 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_50_0, (const fe51 *)&t, (const fe51 *)&z2_10_0); - - /* 2^100 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_50_0, 50); - /* 2^100 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_100_0, (const fe51 *)&t, (const fe51 *)&z2_50_0); - - /* 2^200 - 2^100 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_100_0, 100); - /* 2^200 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_100_0); - - /* 2^250 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 50); - /* 2^250 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_50_0); - - /* 2^255 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 5); - /* 2^255 - 21 */ curve25519_sandy2x_fe51_mul(r, (const fe51 *)t, (const fe51 *)&z11); -} - -static void curve25519_sandy2x(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) -{ - u8 e[32]; - fe var[3]; - fe51 x_51, z_51; - - memcpy(e, secret, 32); - normalize_secret(e); -#define x1 var[0] -#define x2 var[1] -#define z2 var[2] - fe_frombytes(x1, basepoint); - curve25519_sandy2x_ladder(var, e); - z_51[0] = (z2[1] << 26) + z2[0]; - z_51[1] = (z2[3] << 26) + z2[2]; - z_51[2] = (z2[5] << 26) + z2[4]; - z_51[3] = (z2[7] << 26) + z2[6]; - z_51[4] = (z2[9] << 26) + z2[8]; - x_51[0] = (x2[1] << 26) + x2[0]; - x_51[1] = (x2[3] << 26) + x2[2]; - x_51[2] = (x2[5] << 26) + x2[4]; - x_51[3] = (x2[7] << 26) + x2[6]; - x_51[4] = (x2[9] << 26) + x2[8]; -#undef x1 -#undef x2 -#undef z2 - fe51_invert(&z_51, (const fe51 *)&z_51); - curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51); - curve25519_sandy2x_fe51_pack(mypublic, (const fe51 *)&x_51); - - memzero_explicit(e, sizeof(e)); - memzero_explicit(var, sizeof(var)); - memzero_explicit(x_51, sizeof(x_51)); - memzero_explicit(z_51, sizeof(z_51)); -} - -static void curve25519_sandy2x_base(u8 pub[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE]) -{ - u8 e[32]; - fe var[3]; - fe51 x_51, z_51; - - memcpy(e, secret, 32); - normalize_secret(e); - curve25519_sandy2x_ladder_base(var, e); -#define x2 var[0] -#define z2 var[1] - z_51[0] = (z2[1] << 26) + z2[0]; - z_51[1] = (z2[3] << 26) + z2[2]; - z_51[2] = (z2[5] << 26) + z2[4]; - z_51[3] = (z2[7] << 26) + z2[6]; - z_51[4] = (z2[9] << 26) + z2[8]; - x_51[0] = (x2[1] << 26) + x2[0]; - x_51[1] = (x2[3] << 26) + x2[2]; - x_51[2] = (x2[5] << 26) + x2[4]; - x_51[3] = (x2[7] << 26) + x2[6]; - x_51[4] = (x2[9] << 26) + x2[8]; -#undef x2 -#undef z2 - fe51_invert(&z_51, (const fe51 *)&z_51); - curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51); - curve25519_sandy2x_fe51_pack(pub, (const fe51 *)&x_51); - - memzero_explicit(e, sizeof(e)); - memzero_explicit(var, sizeof(var)); - memzero_explicit(x_51, sizeof(x_51)); - memzero_explicit(z_51, sizeof(z_51)); -} +#include "curve25519-x86_64.h" #elif IS_ENABLED(CONFIG_KERNEL_MODE_NEON) && defined(CONFIG_ARM) -#include -#include -#include -asmlinkage void curve25519_neon(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]); -static bool curve25519_use_neon __read_mostly; -void __init curve25519_fpu_init(void) -{ - curve25519_use_neon = elf_hwcap & HWCAP_NEON; -} +#include "curve25519-arm.h" #else void __init curve25519_fpu_init(void) { } #endif #if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__) -typedef u64 limb; -typedef limb felem[5]; -typedef __uint128_t u128; - -/* Sum two numbers: output += in */ -static __always_inline void fsum(limb *output, const limb *in) -{ - output[0] += in[0]; - output[1] += in[1]; - output[2] += in[2]; - output[3] += in[3]; - output[4] += in[4]; -} - -/* Find the difference of two numbers: output = in - output - * (note the order of the arguments!) - * - * Assumes that out[i] < 2**52 - * On return, out[i] < 2**55 - */ -static __always_inline void fdifference_backwards(felem out, const felem in) -{ - /* 152 is 19 << 3 */ - static const limb two54m152 = (((limb)1) << 54) - 152; - static const limb two54m8 = (((limb)1) << 54) - 8; - - out[0] = in[0] + two54m152 - out[0]; - out[1] = in[1] + two54m8 - out[1]; - out[2] = in[2] + two54m8 - out[2]; - out[3] = in[3] + two54m8 - out[3]; - out[4] = in[4] + two54m8 - out[4]; -} - -/* Multiply a number by a scalar: output = in * scalar */ -static __always_inline void fscalar_product(felem output, const felem in, const limb scalar) -{ - u128 a; - - a = ((u128) in[0]) * scalar; - output[0] = ((limb)a) & 0x7ffffffffffffUL; - - a = ((u128) in[1]) * scalar + ((limb) (a >> 51)); - output[1] = ((limb)a) & 0x7ffffffffffffUL; - - a = ((u128) in[2]) * scalar + ((limb) (a >> 51)); - output[2] = ((limb)a) & 0x7ffffffffffffUL; - - a = ((u128) in[3]) * scalar + ((limb) (a >> 51)); - output[3] = ((limb)a) & 0x7ffffffffffffUL; - - a = ((u128) in[4]) * scalar + ((limb) (a >> 51)); - output[4] = ((limb)a) & 0x7ffffffffffffUL; - - output[0] += (a >> 51) * 19; -} - -/* Multiply two numbers: output = in2 * in - * - * output must be distinct to both inputs. The inputs are reduced coefficient - * form, the output is not. - * - * Assumes that in[i] < 2**55 and likewise for in2. - * On return, output[i] < 2**52 - */ -static __always_inline void fmul(felem output, const felem in2, const felem in) -{ - u128 t[5]; - limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c; - - r0 = in[0]; - r1 = in[1]; - r2 = in[2]; - r3 = in[3]; - r4 = in[4]; - - s0 = in2[0]; - s1 = in2[1]; - s2 = in2[2]; - s3 = in2[3]; - s4 = in2[4]; - - t[0] = ((u128) r0) * s0; - t[1] = ((u128) r0) * s1 + ((u128) r1) * s0; - t[2] = ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1; - t[3] = ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1; - t[4] = ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2; - - r4 *= 19; - r1 *= 19; - r2 *= 19; - r3 *= 19; - - t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2; - t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3; - t[2] += ((u128) r4) * s3 + ((u128) r3) * s4; - t[3] += ((u128) r4) * s4; - - r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); - t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); - t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); - t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); - t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); - r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; - r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; - r2 += c; - - output[0] = r0; - output[1] = r1; - output[2] = r2; - output[3] = r3; - output[4] = r4; -} - -static __always_inline void fsquare_times(felem output, const felem in, limb count) -{ - u128 t[5]; - limb r0, r1, r2, r3, r4, c; - limb d0, d1, d2, d4, d419; - - r0 = in[0]; - r1 = in[1]; - r2 = in[2]; - r3 = in[3]; - r4 = in[4]; - - do { - d0 = r0 * 2; - d1 = r1 * 2; - d2 = r2 * 2 * 19; - d419 = r4 * 19; - d4 = d419 * 2; - - t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3 )); - t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19)); - t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3 )); - t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419 )); - t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2 )); - - r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); - t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); - t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); - t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); - t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); - r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; - r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; - r2 += c; - } while (--count); - - output[0] = r0; - output[1] = r1; - output[2] = r2; - output[3] = r3; - output[4] = r4; -} - -/* Load a little-endian 64-bit number */ -static inline limb load_limb(const u8 *in) -{ - return le64_to_cpu(*(__le64 *)in); -} - -static inline void store_limb(u8 *out, limb in) -{ - *(__le64 *)out = cpu_to_le64(in); -} - -/* Take a little-endian, 32-byte number and expand it into polynomial form */ -static inline void fexpand(limb *output, const u8 *in) -{ - output[0] = load_limb(in) & 0x7ffffffffffffUL; - output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL; - output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL; - output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL; - output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL; -} - -/* Take a fully reduced polynomial form number and contract it into a - * little-endian, 32-byte array - */ -static void fcontract(u8 *output, const felem input) -{ - u128 t[5]; - - t[0] = input[0]; - t[1] = input[1]; - t[2] = input[2]; - t[3] = input[3]; - t[4] = input[4]; - - t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; - t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; - t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; - t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; - t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; - - t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; - t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; - t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; - t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; - t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; - - /* now t is between 0 and 2^255-1, properly carried. */ - /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ - - t[0] += 19; - - t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; - t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; - t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; - t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; - t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; - - /* now between 19 and 2^255-1 in both cases, and offset by 19. */ - - t[0] += 0x8000000000000UL - 19; - t[1] += 0x8000000000000UL - 1; - t[2] += 0x8000000000000UL - 1; - t[3] += 0x8000000000000UL - 1; - t[4] += 0x8000000000000UL - 1; - - /* now between 2^255 and 2^256-20, and offset by 2^255. */ - - t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; - t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; - t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; - t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; - t[4] &= 0x7ffffffffffffUL; - - store_limb(output, t[0] | (t[1] << 51)); - store_limb(output+8, (t[1] >> 13) | (t[2] << 38)); - store_limb(output+16, (t[2] >> 26) | (t[3] << 25)); - store_limb(output+24, (t[3] >> 39) | (t[4] << 12)); -} - -/* 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 - */ -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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5]; - - memcpy(origx, x, 5 * sizeof(limb)); - fsum(x, z); - fdifference_backwards(z, origx); // does x - z - - memcpy(origxprime, xprime, sizeof(limb) * 5); - fsum(xprime, zprime); - fdifference_backwards(zprime, origxprime); - fmul(xxprime, xprime, z); - fmul(zzprime, x, zprime); - memcpy(origxprime, xxprime, sizeof(limb) * 5); - fsum(xxprime, zzprime); - fdifference_backwards(zzprime, origxprime); - fsquare_times(x3, xxprime, 1); - fsquare_times(zzzprime, zzprime, 1); - fmul(z3, zzzprime, qmqp); - - fsquare_times(xx, x, 1); - fsquare_times(zz, z, 1); - fmul(x2, xx, zz); - fdifference_backwards(zz, xx); // does zz = xx - zz - fscalar_product(zzz, zz, 121665); - fsum(zzz, xx); - fmul(z2, zz, zzz); -} - -/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements - * long. Perform the swap iff @swap is non-zero. - * - * This function performs the swap without leaking any side-channel - * information. - */ -static void swap_conditional(limb a[5], limb b[5], limb iswap) -{ - unsigned int i; - const limb swap = -iswap; - - for (i = 0; i < 5; ++i) { - const limb x = swap & (a[i] ^ b[i]); - - a[i] ^= x; - b[i] ^= x; - } -} - -/* 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[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0}; - limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; - limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1}; - limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; - - unsigned int i, j; - - memcpy(nqpqx, q, sizeof(limb) * 5); - - 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) * 5); - memcpy(resultz, nqz, sizeof(limb) * 5); -} - -static void crecip(felem out, const felem z) -{ - felem a, t0, b, c; - - /* 2 */ fsquare_times(a, z, 1); // a = 2 - /* 8 */ fsquare_times(t0, a, 2); - /* 9 */ fmul(b, t0, z); // b = 9 - /* 11 */ fmul(a, b, a); // a = 11 - /* 22 */ fsquare_times(t0, a, 1); - /* 2^5 - 2^0 = 31 */ fmul(b, t0, b); - /* 2^10 - 2^5 */ fsquare_times(t0, b, 5); - /* 2^10 - 2^0 */ fmul(b, t0, b); - /* 2^20 - 2^10 */ fsquare_times(t0, b, 10); - /* 2^20 - 2^0 */ fmul(c, t0, b); - /* 2^40 - 2^20 */ fsquare_times(t0, c, 20); - /* 2^40 - 2^0 */ fmul(t0, t0, c); - /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10); - /* 2^50 - 2^0 */ fmul(b, t0, b); - /* 2^100 - 2^50 */ fsquare_times(t0, b, 50); - /* 2^100 - 2^0 */ fmul(c, t0, b); - /* 2^200 - 2^100 */ fsquare_times(t0, c, 100); - /* 2^200 - 2^0 */ fmul(t0, t0, c); - /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50); - /* 2^250 - 2^0 */ fmul(t0, t0, b); - /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5); - /* 2^255 - 21 */ fmul(out, t0, a); -} - -static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) -{ - limb bp[5], x[5], z[5], zmone[5]; - 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; -} +#include "curve25519-u128.h" #else -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 +#include "curve25519-generic.h" #endif static const u8 null_point[CURVE25519_POINT_SIZE] = { 0 }; @@ -1642,6 +36,7 @@ static const u8 null_point[CURVE25519_POINT_SIZE] = { 0 }; bool curve25519(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) { bool ret = true; + #if defined(CONFIG_X86_64) && defined(CONFIG_AS_AVX) if (curve25519_use_avx && irq_fpu_usable()) { kernel_fpu_begin(); -- cgit v1.2.3