diff --git a/crypto/Makefile b/crypto/Makefile index 0c2620aeb9..aae8be748f 100644 --- a/crypto/Makefile +++ b/crypto/Makefile @@ -52,6 +52,7 @@ ifeq ($(CONFIG_CRYPTO_CRYPTODEV),y) CRYPTO_CSRCS += key_wrap.c CRYPTO_CSRCS += siphash.c CRYPTO_CSRCS += hmac_buff.c + CRYPTO_CSRCS += curve25519.c endif # BLAKE2s hash algorithm diff --git a/crypto/curve25519.c b/crypto/curve25519.c new file mode 100644 index 0000000000..4820ccfe9a --- /dev/null +++ b/crypto/curve25519.c @@ -0,0 +1,1216 @@ +/**************************************************************************** + * crypto/curve25519.c + * $OpenBSD: curve25519.c,v 1.2 2020/07/22 13:54:30 tobhe Exp $ + * + * Copyright (C) 2018-2020 Jason A. Donenfeld . All Rights + * Reserved. + * Copyright (C) 2015-2016 The fiat-crypto Authors. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + * + * This contains two implementation: a machine-generated formally verified + * implementation of Curve25519 ECDH from: + * . Though originally machine + * generated, it has been tweaked to be suitable for use in the kernel. + * It is optimized for 32-bit machines and machines that cannot work + * efficiently with 128-bit integer types. + ****************************************************************************/ + +/**************************************************************************** + * Included Files + ****************************************************************************/ + +#include +#include +#include +#include + +/**************************************************************************** + * Private Type Definitions + ****************************************************************************/ + +/* fe means field element. Here the field is \Z/(2^255-19). An element t, + * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 + * t[3]+2^102 t[4]+...+2^230 t[9]. + * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc. + * Multiplication and carrying produce fe from fe_loose. + */ + +typedef struct fe +{ + uint32_t v[10]; +} fe; + +/* fe_loose limbs are bounded by + * 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc + * Addition and subtraction produce fe_loose from (fe, fe). + */ + +typedef struct fe_loose +{ + uint32_t v[10]; +} fe_loose; + +/**************************************************************************** + * Private Data + ****************************************************************************/ + +static const uint8_t g_null_point[CURVE25519_KEY_SIZE]; +static const uint8_t g_base_point[CURVE25519_KEY_SIZE] = +{ + 9 +}; + +/**************************************************************************** + * Private Functions + ****************************************************************************/ + +static uint32_t get_unaligned_le32(FAR const uint8_t *a) +{ + uint32_t l; + + memcpy(&l, a, sizeof(l)); + return letoh32(l); +} + +static void fe_frombytes_impl(uint32_t h[10], FAR const uint8_t *s) +{ + /* Ignores top bit of s. */ + + uint32_t a0 = get_unaligned_le32(s); + uint32_t a1 = get_unaligned_le32(s + 4); + uint32_t a2 = get_unaligned_le32(s + 8); + uint32_t a3 = get_unaligned_le32(s + 12); + uint32_t a4 = get_unaligned_le32(s + 16); + uint32_t a5 = get_unaligned_le32(s + 20); + uint32_t a6 = get_unaligned_le32(s + 24); + uint32_t a7 = get_unaligned_le32(s + 28); + + /* 26 used, 32 - 26 left. 26 */ + + h[0] = a0 & ((1 << 26) - 1); + + /* (32 - 26) + 19 = 6 + 19 = 25 */ + + h[1] = (a0 >> 26) | ((a1 & ((1 << 19) - 1)) << 6); + + /* (32 - 19) + 13 = 13 + 13 = 26 */ + + h[2] = (a1 >> 19) | ((a2 & ((1 << 13) - 1)) << 13); + + /* (32 - 13) + 6 = 19 + 6 = 25 */ + + h[3] = (a2 >> 13) | ((a3 & ((1 << 6) - 1)) << 19); + + /* (32 - 6) = 26 */ + + h[4] = (a3 >> 6); + + /* 25 */ + + h[5] = a4 & ((1 << 25) - 1); + + /* (32 - 25) + 19 = 7 + 19 = 26 */ + + h[6] = (a4 >> 25) | ((a5 & ((1 << 19) - 1)) << 7); + + /* (32 - 19) + 12 = 13 + 12 = 25 */ + + h[7] = (a5 >> 19) | ((a6 & ((1 << 12) - 1)) << 13); + + /* (32 - 12) + 6 = 20 + 6 = 26 */ + + h[8] = (a6 >> 12) | ((a7 & ((1 << 6) - 1)) << 20); + + /* 25 */ + + h[9] = (a7 >> 6) & ((1 << 25) - 1); +} + +static void fe_frombytes(FAR fe *h, FAR const uint8_t *s) +{ + fe_frombytes_impl(h->v, s); +} + +/* uint8_t c - bool */ + +static uint8_t /* bool */ +addcarryx_u25(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low) +{ + /* This function extracts 25 bits of result and 1 bit of carry + * (26 total), so a 32-bit intermediate is sufficient. + */ + + uint32_t x = a + b + c; + + *low = x & ((1 << 25) - 1); + return (x >> 25) & 1; +} + +/* uint8_t c - bool */ + +static uint8_t /* bool */ +addcarryx_u26(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low) +{ + /* This function extracts 26 bits of result and 1 bit of carry + * (27 total), so a 32-bit intermediate is sufficient. + */ + + uint32_t x = a + b + c; + + *low = x & ((1 << 26) - 1); + return (x >> 26) & 1; +} + +/* uint8_t c - bool */ + +static uint8_t /* bool */ +subborrow_u25(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low) +{ + /* This function extracts 25 bits of result and 1 bit of borrow + * (26 total), so a 32-bit intermediate is sufficient. + */ + + uint32_t x = a - b - c; + + *low = x & ((1 << 25) - 1); + return x >> 31; +} + +/* uint8_t c - bool */ + +static uint8_t /* bool */ +subborrow_u26(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low) +{ + /* This function extracts 26 bits of result and 1 bit of borrow + * (27 total), so a 32-bit intermediate is sufficient. + */ + + uint32_t x = a - b - c; + + *low = x & ((1 << 26) - 1); + return x >> 31; +} + +static uint32_t +cmovznz32(uint32_t t, uint32_t z, uint32_t nz) +{ + t = - !!t; /* all set if nonzero, 0 if 0 */ + return (t & nz) | ((~t) & z); +} + +static void fe_freeze(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x17 = in1[9]; + const uint32_t x18 = in1[8]; + const uint32_t x16 = in1[7]; + const uint32_t x14 = in1[6]; + const uint32_t x12 = in1[5]; + const uint32_t x10 = in1[4]; + const uint32_t x8 = in1[3]; + const uint32_t x6 = in1[2]; + const uint32_t x4 = in1[1]; + const uint32_t x2 = in1[0]; + uint32_t x20; + + /* bool */ + + uint8_t x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); + uint32_t x23; + + /* bool */ + + uint8_t x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); + uint32_t x26; + + /* bool */ + + uint8_t x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); + uint32_t x29; + + /* bool */ + + uint8_t x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); + uint32_t x32; + + /* bool */ + + uint8_t x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); + uint32_t x35; + + /* bool */ + + uint8_t x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); + uint32_t x38; + + /* bool */ + + uint8_t x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); + uint32_t x41; + + /* bool */ + + uint8_t x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); + uint32_t x44; + + /* bool */ + + uint8_t x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); + uint32_t x47; + + /* bool */ + + uint8_t x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); + uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff); + uint32_t x50 = (x49 & 0x3ffffed); + uint32_t x52; + + /* bool */ + + uint8_t x53 = addcarryx_u26(0x0, x20, x50, &x52); + uint32_t x54 = (x49 & 0x1ffffff); + uint32_t x56; + + /* bool */ + + uint8_t x57 = addcarryx_u25(x53, x23, x54, &x56); + uint32_t x58 = (x49 & 0x3ffffff); + uint32_t x60; + + /* bool */ + + uint8_t x61 = addcarryx_u26(x57, x26, x58, &x60); + uint32_t x62 = (x49 & 0x1ffffff); + uint32_t x64; + + /* bool */ + + uint8_t x65 = addcarryx_u25(x61, x29, x62, &x64); + uint32_t x66 = (x49 & 0x3ffffff); + uint32_t x68; + + /* bool */ + + uint8_t x69 = addcarryx_u26(x65, x32, x66, &x68); + uint32_t x70 = (x49 & 0x1ffffff); + uint32_t x72; + + /* bool */ + + uint8_t x73 = addcarryx_u25(x69, x35, x70, &x72); + uint32_t x74 = (x49 & 0x3ffffff); + uint32_t x76; + + /* bool */ + + uint8_t x77 = addcarryx_u26(x73, x38, x74, &x76); + uint32_t x78 = (x49 & 0x1ffffff); + uint32_t x80; + + /* bool */ + + uint8_t x81 = addcarryx_u25(x77, x41, x78, &x80); + uint32_t x82 = (x49 & 0x3ffffff); + uint32_t x84; + + /* bool */ + + uint8_t x85 = addcarryx_u26(x81, x44, x82, &x84); + uint32_t x86 = (x49 & 0x1ffffff); + uint32_t x88; + + addcarryx_u25(x85, x47, x86, &x88); + + out[0] = x52; + out[1] = x56; + out[2] = x60; + out[3] = x64; + out[4] = x68; + out[5] = x72; + out[6] = x76; + out[7] = x80; + out[8] = x84; + out[9] = x88; +} + +static void fe_tobytes(uint8_t s[32], FAR const fe *f) +{ + uint32_t h[10]; + + fe_freeze(h, f->v); + s[0] = h[0] >> 0; + s[1] = h[0] >> 8; + s[2] = h[0] >> 16; + s[3] = (h[0] >> 24) | (h[1] << 2); + s[4] = h[1] >> 6; + s[5] = h[1] >> 14; + s[6] = (h[1] >> 22) | (h[2] << 3); + s[7] = h[2] >> 5; + s[8] = h[2] >> 13; + s[9] = (h[2] >> 21) | (h[3] << 5); + s[10] = h[3] >> 3; + s[11] = h[3] >> 11; + s[12] = (h[3] >> 19) | (h[4] << 6); + s[13] = h[4] >> 2; + s[14] = h[4] >> 10; + s[15] = h[4] >> 18; + s[16] = h[5] >> 0; + s[17] = h[5] >> 8; + s[18] = h[5] >> 16; + s[19] = (h[5] >> 24) | (h[6] << 1); + s[20] = h[6] >> 7; + s[21] = h[6] >> 15; + s[22] = (h[6] >> 23) | (h[7] << 3); + s[23] = h[7] >> 5; + s[24] = h[7] >> 13; + s[25] = (h[7] >> 21) | (h[8] << 4); + s[26] = h[8] >> 4; + s[27] = h[8] >> 12; + s[28] = (h[8] >> 20) | (h[9] << 6); + s[29] = h[9] >> 2; + s[30] = h[9] >> 10; + s[31] = h[9] >> 18; +} + +/* h = f */ + +static void fe_copy(FAR fe *h, FAR const fe *f) +{ + memmove(h, f, sizeof(uint32_t) * 10); +} + +static void fe_copy_lt(FAR fe_loose *h, FAR const fe *f) +{ + memmove(h, f, sizeof(uint32_t) * 10); +} + +/* h = 0 */ + +static void fe_0(FAR fe *h) +{ + memset(h, 0, sizeof(uint32_t) * 10); +} + +/* h = 1 */ + +static void fe_1(FAR fe *h) +{ + memset(h, 0, sizeof(uint32_t) * 10); + h->v[0] = 1; +} + +static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], + const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + + out[0] = (x5 + x23); + out[1] = (x7 + x25); + out[2] = (x9 + x27); + out[3] = (x11 + x29); + out[4] = (x13 + x31); + out[5] = (x15 + x33); + out[6] = (x17 + x35); + out[7] = (x19 + x37); + out[8] = (x21 + x39); + out[9] = (x20 + x38); +} + +/* h = f + g + * Can overlap h with f or g. + */ + +static void fe_add(FAR fe_loose *h, FAR const fe *f, FAR const fe *g) +{ + fe_add_impl(h->v, f->v, g->v); +} + +static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], + const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + + out[0] = ((0x7ffffda + x5) - x23); + out[1] = ((0x3fffffe + x7) - x25); + out[2] = ((0x7fffffe + x9) - x27); + out[3] = ((0x3fffffe + x11) - x29); + out[4] = ((0x7fffffe + x13) - x31); + out[5] = ((0x3fffffe + x15) - x33); + out[6] = ((0x7fffffe + x17) - x35); + out[7] = ((0x3fffffe + x19) - x37); + out[8] = ((0x7fffffe + x21) - x39); + out[9] = ((0x3fffffe + x20) - x38); +} + +/* h = f - g + * Can overlap h with f or g. + */ + +static void fe_sub(FAR fe_loose *h, FAR const fe *f, FAR const fe *g) +{ + fe_sub_impl(h->v, f->v, g->v); +} + +static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], + const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + uint64_t x40 = ((uint64_t)x23 * x5); + uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); + uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); + uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); + uint64_t x44 = (((((uint64_t)x27 * x9) + + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); + uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); + uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); + uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); + uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * + (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); + uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); + uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); + uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); + uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + + ((uint64_t)x39 * x13)); + uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); + uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + + ((uint64_t)x39 * x17)); + uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); + uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + + ((uint64_t)x38 * x19)))); + uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); + uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); + uint64_t x59 = (x48 + (x58 << 0x4)); + uint64_t x60 = (x59 + (x58 << 0x1)); + uint64_t x61 = (x60 + x58); + uint64_t x62 = (x47 + (x57 << 0x4)); + uint64_t x63 = (x62 + (x57 << 0x1)); + uint64_t x64 = (x63 + x57); + uint64_t x65 = (x46 + (x56 << 0x4)); + uint64_t x66 = (x65 + (x56 << 0x1)); + uint64_t x67 = (x66 + x56); + uint64_t x68 = (x45 + (x55 << 0x4)); + uint64_t x69 = (x68 + (x55 << 0x1)); + uint64_t x70 = (x69 + x55); + uint64_t x71 = (x44 + (x54 << 0x4)); + uint64_t x72 = (x71 + (x54 << 0x1)); + uint64_t x73 = (x72 + x54); + uint64_t x74 = (x43 + (x53 << 0x4)); + uint64_t x75 = (x74 + (x53 << 0x1)); + uint64_t x76 = (x75 + x53); + uint64_t x77 = (x42 + (x52 << 0x4)); + uint64_t x78 = (x77 + (x52 << 0x1)); + uint64_t x79 = (x78 + x52); + uint64_t x80 = (x41 + (x51 << 0x4)); + uint64_t x81 = (x80 + (x51 << 0x1)); + uint64_t x82 = (x81 + x51); + uint64_t x83 = (x40 + (x50 << 0x4)); + uint64_t x84 = (x83 + (x50 << 0x1)); + uint64_t x85 = (x84 + x50); + uint64_t x86 = (x85 >> 0x1a); + uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); + uint64_t x88 = (x86 + x82); + uint64_t x89 = (x88 >> 0x19); + uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); + uint64_t x91 = (x89 + x79); + uint64_t x92 = (x91 >> 0x1a); + uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); + uint64_t x94 = (x92 + x76); + uint64_t x95 = (x94 >> 0x19); + uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); + uint64_t x97 = (x95 + x73); + uint64_t x98 = (x97 >> 0x1a); + uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); + uint64_t x100 = (x98 + x70); + uint64_t x101 = (x100 >> 0x19); + uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); + uint64_t x103 = (x101 + x67); + uint64_t x104 = (x103 >> 0x1a); + uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); + uint64_t x106 = (x104 + x64); + uint64_t x107 = (x106 >> 0x19); + uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); + uint64_t x109 = (x107 + x61); + uint64_t x110 = (x109 >> 0x1a); + uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); + uint64_t x112 = (x110 + x49); + uint64_t x113 = (x112 >> 0x19); + uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); + uint64_t x115 = (x87 + (0x13 * x113)); + uint32_t x116 = (uint32_t)(x115 >> 0x1a); + uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); + uint32_t x118 = (x116 + x90); + uint32_t x119 = (x118 >> 0x19); + uint32_t x120 = (x118 & 0x1ffffff); + + out[0] = x117; + out[1] = x120; + out[2] = (x119 + x93); + out[3] = x96; + out[4] = x99; + out[5] = x102; + out[6] = x105; + out[7] = x108; + out[8] = x111; + out[9] = x114; +} + +static void fe_mul_ttt(FAR fe *h, FAR const fe *f, FAR const fe *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static void fe_mul_tlt(FAR fe *h, FAR const fe_loose *f, + FAR const fe *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static void fe_mul_tll(FAR fe *h, FAR const fe_loose *f, + FAR const fe_loose *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x17 = in1[9]; + const uint32_t x18 = in1[8]; + const uint32_t x16 = in1[7]; + const uint32_t x14 = in1[6]; + const uint32_t x12 = in1[5]; + const uint32_t x10 = in1[4]; + const uint32_t x8 = in1[3]; + const uint32_t x6 = in1[2]; + const uint32_t x4 = in1[1]; + const uint32_t x2 = in1[0]; + uint64_t x19 = ((uint64_t)x2 * x2); + uint64_t x20 = ((uint64_t)(0x2 * x2) * x4); + uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6))); + uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8))); + uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + + ((uint64_t)(0x2 * x2) * x10)); + uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12))); + uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12))); + uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16))); + uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + + ((uint64_t)x8 * x12)))))); + uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + + ((uint64_t)x2 * x17))); + uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + + ((uint64_t)x4 * x17))))); + uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17))); + uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17)))))); + uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + + ((uint64_t)x10 * x17))); + uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + + ((uint64_t)(0x2 * x12) * x17))); + uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17))); + uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17)); + uint64_t x36 = ((uint64_t)(0x2 * x18) * x17); + uint64_t x37 = ((uint64_t)(0x2 * x17) * x17); + uint64_t x38 = (x27 + (x37 << 0x4)); + uint64_t x39 = (x38 + (x37 << 0x1)); + uint64_t x40 = (x39 + x37); + uint64_t x41 = (x26 + (x36 << 0x4)); + uint64_t x42 = (x41 + (x36 << 0x1)); + uint64_t x43 = (x42 + x36); + uint64_t x44 = (x25 + (x35 << 0x4)); + uint64_t x45 = (x44 + (x35 << 0x1)); + uint64_t x46 = (x45 + x35); + uint64_t x47 = (x24 + (x34 << 0x4)); + uint64_t x48 = (x47 + (x34 << 0x1)); + uint64_t x49 = (x48 + x34); + uint64_t x50 = (x23 + (x33 << 0x4)); + uint64_t x51 = (x50 + (x33 << 0x1)); + uint64_t x52 = (x51 + x33); + uint64_t x53 = (x22 + (x32 << 0x4)); + uint64_t x54 = (x53 + (x32 << 0x1)); + uint64_t x55 = (x54 + x32); + uint64_t x56 = (x21 + (x31 << 0x4)); + uint64_t x57 = (x56 + (x31 << 0x1)); + uint64_t x58 = (x57 + x31); + uint64_t x59 = (x20 + (x30 << 0x4)); + uint64_t x60 = (x59 + (x30 << 0x1)); + uint64_t x61 = (x60 + x30); + uint64_t x62 = (x19 + (x29 << 0x4)); + uint64_t x63 = (x62 + (x29 << 0x1)); + uint64_t x64 = (x63 + x29); + uint64_t x65 = (x64 >> 0x1a); + uint32_t x66 = ((uint32_t)x64 & 0x3ffffff); + uint64_t x67 = (x65 + x61); + uint64_t x68 = (x67 >> 0x19); + uint32_t x69 = ((uint32_t)x67 & 0x1ffffff); + uint64_t x70 = (x68 + x58); + uint64_t x71 = (x70 >> 0x1a); + uint32_t x72 = ((uint32_t)x70 & 0x3ffffff); + uint64_t x73 = (x71 + x55); + uint64_t x74 = (x73 >> 0x19); + uint32_t x75 = ((uint32_t)x73 & 0x1ffffff); + uint64_t x76 = (x74 + x52); + uint64_t x77 = (x76 >> 0x1a); + uint32_t x78 = ((uint32_t)x76 & 0x3ffffff); + uint64_t x79 = (x77 + x49); + uint64_t x80 = (x79 >> 0x19); + uint32_t x81 = ((uint32_t)x79 & 0x1ffffff); + uint64_t x82 = (x80 + x46); + uint64_t x83 = (x82 >> 0x1a); + uint32_t x84 = ((uint32_t)x82 & 0x3ffffff); + uint64_t x85 = (x83 + x43); + uint64_t x86 = (x85 >> 0x19); + uint32_t x87 = ((uint32_t)x85 & 0x1ffffff); + uint64_t x88 = (x86 + x40); + uint64_t x89 = (x88 >> 0x1a); + uint32_t x90 = ((uint32_t)x88 & 0x3ffffff); + uint64_t x91 = (x89 + x28); + uint64_t x92 = (x91 >> 0x19); + uint32_t x93 = ((uint32_t)x91 & 0x1ffffff); + uint64_t x94 = (x66 + (0x13 * x92)); + uint32_t x95 = (uint32_t)(x94 >> 0x1a); + uint32_t x96 = ((uint32_t)x94 & 0x3ffffff); + uint32_t x97 = (x95 + x69); + uint32_t x98 = (x97 >> 0x19); + uint32_t x99 = (x97 & 0x1ffffff); + + out[0] = x96; + out[1] = x99; + out[2] = (x98 + x72); + out[3] = x75; + out[4] = x78; + out[5] = x81; + out[6] = x84; + out[7] = x87; + out[8] = x90; + out[9] = x93; +} + +static void fe_sq_tl(FAR fe *h, FAR const fe_loose *f) +{ + fe_sqr_impl(h->v, f->v); +} + +static void fe_sq_tt(FAR fe *h, FAR const fe *f) +{ + fe_sqr_impl(h->v, f->v); +} + +static void fe_loose_invert(FAR fe *out, FAR const fe_loose *z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq_tl(&t0, z); + fe_sq_tt(&t1, &t0); + for (i = 1; i < 2; ++i) + { + fe_sq_tt(&t1, &t1); + } + + fe_mul_tlt(&t1, z, &t1); + fe_mul_ttt(&t0, &t0, &t1); + fe_sq_tt(&t2, &t0); + fe_mul_ttt(&t1, &t1, &t2); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 5; ++i) + { + fe_sq_tt(&t2, &t2); + } + + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 10; ++i) + { + fe_sq_tt(&t2, &t2); + } + + fe_mul_ttt(&t2, &t2, &t1); + fe_sq_tt(&t3, &t2); + for (i = 1; i < 20; ++i) + { + fe_sq_tt(&t3, &t3); + } + + fe_mul_ttt(&t2, &t3, &t2); + fe_sq_tt(&t2, &t2); + for (i = 1; i < 10; ++i) + { + fe_sq_tt(&t2, &t2); + } + + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 50; ++i) + { + fe_sq_tt(&t2, &t2); + } + + fe_mul_ttt(&t2, &t2, &t1); + fe_sq_tt(&t3, &t2); + for (i = 1; i < 100; ++i) + { + fe_sq_tt(&t3, &t3); + } + + fe_mul_ttt(&t2, &t3, &t2); + fe_sq_tt(&t2, &t2); + for (i = 1; i < 50; ++i) + { + fe_sq_tt(&t2, &t2); + } + + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t1, &t1); + for (i = 1; i < 5; ++i) + { + fe_sq_tt(&t1, &t1); + } + + fe_mul_ttt(out, &t1, &t0); +} + +static void fe_invert(FAR fe *out, FAR const fe *z) +{ + fe_loose l; + + fe_copy_lt(&l, z); + fe_loose_invert(out, &l); +} + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1} + */ + +static void fe_cswap(FAR fe *f, FAR fe *g, unsigned int b) +{ + unsigned i; + + b = 0 - b; + for (i = 0; i < 10; i++) + { + uint32_t x = f->v[i] ^ g->v[i]; + x &= b; + f->v[i] ^= x; + g->v[i] ^= x; + } +} + +/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0. */ + +static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = 0; + const uint32_t x39 = 0; + const uint32_t x37 = 0; + const uint32_t x35 = 0; + const uint32_t x33 = 0; + const uint32_t x31 = 0; + const uint32_t x29 = 0; + const uint32_t x27 = 0; + const uint32_t x25 = 0; + const uint32_t x23 = 121666; + uint64_t x40 = ((uint64_t)x23 * x5); + uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); + uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + + ((uint64_t)x27 * x5)); + uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); + uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + + ((uint64_t)x31 * x5)); + uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); + uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); + uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); + uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * + (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); + uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); + uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); + uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); + uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * + (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); + uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); + uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + + ((uint64_t)x39 * x17)); + uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); + uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * + (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); + uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); + uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); + uint64_t x59 = (x48 + (x58 << 0x4)); + uint64_t x60 = (x59 + (x58 << 0x1)); + uint64_t x61 = (x60 + x58); + uint64_t x62 = (x47 + (x57 << 0x4)); + uint64_t x63 = (x62 + (x57 << 0x1)); + uint64_t x64 = (x63 + x57); + uint64_t x65 = (x46 + (x56 << 0x4)); + uint64_t x66 = (x65 + (x56 << 0x1)); + uint64_t x67 = (x66 + x56); + uint64_t x68 = (x45 + (x55 << 0x4)); + uint64_t x69 = (x68 + (x55 << 0x1)); + uint64_t x70 = (x69 + x55); + uint64_t x71 = (x44 + (x54 << 0x4)); + uint64_t x72 = (x71 + (x54 << 0x1)); + uint64_t x73 = (x72 + x54); + uint64_t x74 = (x43 + (x53 << 0x4)); + uint64_t x75 = (x74 + (x53 << 0x1)); + uint64_t x76 = (x75 + x53); + uint64_t x77 = (x42 + (x52 << 0x4)); + uint64_t x78 = (x77 + (x52 << 0x1)); + uint64_t x79 = (x78 + x52); + uint64_t x80 = (x41 + (x51 << 0x4)); + uint64_t x81 = (x80 + (x51 << 0x1)); + uint64_t x82 = (x81 + x51); + uint64_t x83 = (x40 + (x50 << 0x4)); + uint64_t x84 = (x83 + (x50 << 0x1)); + uint64_t x85 = (x84 + x50); + uint64_t x86 = (x85 >> 0x1a); + uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); + uint64_t x88 = (x86 + x82); + uint64_t x89 = (x88 >> 0x19); + uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); + uint64_t x91 = (x89 + x79); + uint64_t x92 = (x91 >> 0x1a); + uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); + uint64_t x94 = (x92 + x76); + uint64_t x95 = (x94 >> 0x19); + uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); + uint64_t x97 = (x95 + x73); + uint64_t x98 = (x97 >> 0x1a); + uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); + uint64_t x100 = (x98 + x70); + uint64_t x101 = (x100 >> 0x19); + uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); + uint64_t x103 = (x101 + x67); + uint64_t x104 = (x103 >> 0x1a); + uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); + uint64_t x106 = (x104 + x64); + uint64_t x107 = (x106 >> 0x19); + uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); + uint64_t x109 = (x107 + x61); + uint64_t x110 = (x109 >> 0x1a); + uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); + uint64_t x112 = (x110 + x49); + uint64_t x113 = (x112 >> 0x19); + uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); + uint64_t x115 = (x87 + (0x13 * x113)); + uint32_t x116 = (uint32_t)(x115 >> 0x1a); + uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); + uint32_t x118 = (x116 + x90); + uint32_t x119 = (x118 >> 0x19); + uint32_t x120 = (x118 & 0x1ffffff); + + out[0] = x117; + out[1] = x120; + out[2] = (x119 + x93); + out[3] = x96; + out[4] = x99; + out[5] = x102; + out[6] = x105; + out[7] = x108; + out[8] = x111; + out[9] = x114; +} + +static void fe_mul121666(FAR fe *h, FAR const fe_loose *f) +{ + fe_mul_121666_impl(h->v, f->v); +} + +/**************************************************************************** + * Public Functions + ****************************************************************************/ + +int curve25519(uint8_t out[CURVE25519_KEY_SIZE], + const uint8_t scalar[CURVE25519_KEY_SIZE], + const uint8_t point[CURVE25519_KEY_SIZE]) +{ + fe x1, x2, z2, x3, z3; + fe_loose x2l, z2l, x3l; + unsigned swap = 0; + int pos; + uint8_t e[32]; + + memcpy(e, scalar, 32); + curve25519_clamp_secret(e); + + /* The following implementation was transcribed to Coq and proven to + * correspond to unary scalar multiplication in affine coordinates given + * that x1 != 0 is the x coordinate of some point on the curve. It was + * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives + * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was + * quantified over the underlying field, so it applies to Curve25519 + * itself and the quadratic twist of Curve25519. It was not proven in + * Coq that prime-field arithmetic correctly simulates extension-field + * arithmetic on prime-field values. The decoding of the byte array + * representation of e was not considered. + * + * Specification of Montgomery curves in affine coordinates: + * + * + * Proof that these form a group that is isomorphic to a Weierstrass + * curve: + * + * + * Coq transcription and correctness proof of the loop + * (where scalarbits=255): + * + * + * preconditions: 0 <= e < 2^255 (not necessarily e < order), + * fe_invert(0) = 0 + */ + + fe_frombytes(&x1, point); + fe_1(&x2); + fe_0(&z2); + fe_copy(&x3, &x1); + fe_1(&z3); + + for (pos = 254; pos >= 0; --pos) + { + fe tmp0, tmp1; + fe_loose tmp0l, tmp1l; + + /* loop invariant as of right before the test, for the case + * where x1 != 0: + * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 + * is nonzero + * let r := e >> (pos+1) in the following equalities of + * projective points: + * to_xz (r*P) === if swap then (x3, z3) else (x2, z2) + * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) + * x1 is the nonzero x coordinate of the nonzero + * point (r*P-(r+1)*P) + */ + + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(&x2, &x3, swap); + fe_cswap(&z2, &z3, swap); + swap = b; + + /* Coq transcription of ladderstep formula (called from + * transcribed loop): + * \ + * + * x1 != 0 + * \ + * x1 = 0 + * + */ + + fe_sub(&tmp0l, &x3, &z3); + fe_sub(&tmp1l, &x2, &z2); + fe_add(&x2l, &x2, &z2); + fe_add(&z2l, &x3, &z3); + fe_mul_tll(&z3, &tmp0l, &x2l); + fe_mul_tll(&z2, &z2l, &tmp1l); + fe_sq_tl(&tmp0, &tmp1l); + fe_sq_tl(&tmp1, &x2l); + fe_add(&x3l, &z3, &z2); + fe_sub(&z2l, &z3, &z2); + fe_mul_ttt(&x2, &tmp1, &tmp0); + fe_sub(&tmp1l, &tmp1, &tmp0); + fe_sq_tl(&z2, &z2l); + fe_mul121666(&z3, &tmp1l); + fe_sq_tl(&x3, &x3l); + fe_add(&tmp0l, &tmp0, &z3); + fe_mul_ttt(&z3, &x1, &z2); + fe_mul_tll(&z2, &tmp1l, &tmp0l); + } + + /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) + * else (x2, z2) + */ + + fe_cswap(&x2, &x3, swap); + fe_cswap(&z2, &z3, swap); + + fe_invert(&z2, &z2); + fe_mul_ttt(&x2, &x2, &z2); + fe_tobytes(out, &x2); + + explicit_bzero(&x1, sizeof(x1)); + explicit_bzero(&x2, sizeof(x2)); + explicit_bzero(&z2, sizeof(z2)); + explicit_bzero(&x3, sizeof(x3)); + explicit_bzero(&z3, sizeof(z3)); + explicit_bzero(&x2l, sizeof(x2l)); + explicit_bzero(&z2l, sizeof(z2l)); + explicit_bzero(&x3l, sizeof(x3l)); + explicit_bzero(&e, sizeof(e)); + return timingsafe_bcmp(out, g_null_point, CURVE25519_KEY_SIZE); +} + +int curve25519_generate_public(uint8_t pub[CURVE25519_KEY_SIZE], + const uint8_t secret[CURVE25519_KEY_SIZE]) +{ + if (timingsafe_bcmp(secret, g_null_point, CURVE25519_KEY_SIZE) == 0) + { + return 0; + } + + return curve25519(pub, secret, g_base_point); +} diff --git a/include/crypto/curve25519.h b/include/crypto/curve25519.h new file mode 100644 index 0000000000..d5d239895e --- /dev/null +++ b/include/crypto/curve25519.h @@ -0,0 +1,45 @@ +/**************************************************************************** + * include/crypto/curve25519.h + * $OpenBSD: curve25519.h,v 1.2 2020/07/22 13:54:30 tobhe Exp $ + * + * Copyright (C) 2019-2020 Matt Dunwoodie + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + ****************************************************************************/ + +#ifndef __INCLUDE_CRYPTO_CURVE25519_H +#define __INCLUDE_CRYPTO_CURVE25519_H + +#define CURVE25519_KEY_SIZE 32 + +int curve25519(uint8_t out[CURVE25519_KEY_SIZE], + const uint8_t scalar[CURVE25519_KEY_SIZE], + const uint8_t point[CURVE25519_KEY_SIZE]); + +int curve25519_generate_public(uint8_t pub[CURVE25519_KEY_SIZE], + const uint8_t secret[CURVE25519_KEY_SIZE]); + +static inline void +curve25519_clamp_secret(uint8_t secret[CURVE25519_KEY_SIZE]) +{ + secret[0] &= 248; + secret[31] = (secret[31] & 127) | 64; +} + +static inline void +curve25519_generate_secret(uint8_t secret[CURVE25519_KEY_SIZE]) +{ + arc4random_buf(secret, CURVE25519_KEY_SIZE); + curve25519_clamp_secret(secret); +} +#endif /* __INCLUDE_CRYPTO_CURVE25519_H */