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linux/lib/crypto/curve25519-fiat32.c
Ard Biesheuvel 660bb8e1f8 crypto: lib/curve25519 - work around Clang stack spilling issue 
Arnd reports that the 32-bit generic library code for Curve25119 ends
up using an excessive amount of stack space when built with Clang:

  lib/crypto/curve25519-fiat32.c:756:6: error: stack frame size
      of 1384 bytes in function 'curve25519_generic'
      [-Werror,-Wframe-larger-than=]

Let's give some hints to the compiler regarding which routines should
not be inlined, to prevent it from running out of registers and spilling
to the stack. The resulting code performs identically under both GCC
and Clang, and makes the warning go away.

Suggested-by: Arnd Bergmann <arnd@arndb.de>
Signed-off-by: Ard Biesheuvel <ardb@kernel.org>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
2019-11-17 09:02:43 +08:00

864 lines
30 KiB
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// SPDX-License-Identifier: GPL-2.0 OR MIT
/*
* Copyright (C) 2015-2016 The fiat-crypto Authors.
* Copyright (C) 2018-2019 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
*
* This is a machine-generated formally verified implementation of Curve25519
* ECDH from: <https://github.com/mit-plv/fiat-crypto>. 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.
*/
#include <asm/unaligned.h>
#include <crypto/curve25519.h>
#include <linux/string.h>
/* 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 { u32 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 { u32 v[10]; } fe_loose;
static __always_inline void fe_frombytes_impl(u32 h[10], const u8 *s)
{
/* Ignores top bit of s. */
u32 a0 = get_unaligned_le32(s);
u32 a1 = get_unaligned_le32(s+4);
u32 a2 = get_unaligned_le32(s+8);
u32 a3 = get_unaligned_le32(s+12);
u32 a4 = get_unaligned_le32(s+16);
u32 a5 = get_unaligned_le32(s+20);
u32 a6 = get_unaligned_le32(s+24);
u32 a7 = get_unaligned_le32(s+28);
h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */
h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */
h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */
h[4] = (a3>> 6); /* (32- 6) = 26 */
h[5] = a4&((1<<25)-1); /* 25 */
h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */
h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */
h[9] = (a7>> 6)&((1<<25)-1); /* 25 */
}
static __always_inline void fe_frombytes(fe *h, const u8 *s)
{
fe_frombytes_impl(h->v, s);
}
static __always_inline u8 /*bool*/
addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
{
/* This function extracts 25 bits of result and 1 bit of carry
* (26 total), so a 32-bit intermediate is sufficient.
*/
u32 x = a + b + c;
*low = x & ((1 << 25) - 1);
return (x >> 25) & 1;
}
static __always_inline u8 /*bool*/
addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
{
/* This function extracts 26 bits of result and 1 bit of carry
* (27 total), so a 32-bit intermediate is sufficient.
*/
u32 x = a + b + c;
*low = x & ((1 << 26) - 1);
return (x >> 26) & 1;
}
static __always_inline u8 /*bool*/
subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
{
/* This function extracts 25 bits of result and 1 bit of borrow
* (26 total), so a 32-bit intermediate is sufficient.
*/
u32 x = a - b - c;
*low = x & ((1 << 25) - 1);
return x >> 31;
}
static __always_inline u8 /*bool*/
subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
{
/* This function extracts 26 bits of result and 1 bit of borrow
*(27 total), so a 32-bit intermediate is sufficient.
*/
u32 x = a - b - c;
*low = x & ((1 << 26) - 1);
return x >> 31;
}
static __always_inline u32 cmovznz32(u32 t, u32 z, u32 nz)
{
t = -!!t; /* all set if nonzero, 0 if 0 */
return (t&nz) | ((~t)&z);
}
static __always_inline void fe_freeze(u32 out[10], const u32 in1[10])
{
{ const u32 x17 = in1[9];
{ const u32 x18 = in1[8];
{ const u32 x16 = in1[7];
{ const u32 x14 = in1[6];
{ const u32 x12 = in1[5];
{ const u32 x10 = in1[4];
{ const u32 x8 = in1[3];
{ const u32 x6 = in1[2];
{ const u32 x4 = in1[1];
{ const u32 x2 = in1[0];
{ u32 x20; u8/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
{ u32 x23; u8/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
{ u32 x26; u8/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
{ u32 x29; u8/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
{ u32 x32; u8/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
{ u32 x35; u8/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
{ u32 x38; u8/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
{ u32 x41; u8/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
{ u32 x44; u8/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
{ u32 x47; u8/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
{ u32 x49 = cmovznz32(x48, 0x0, 0xffffffff);
{ u32 x50 = (x49 & 0x3ffffed);
{ u32 x52; u8/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
{ u32 x54 = (x49 & 0x1ffffff);
{ u32 x56; u8/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
{ u32 x58 = (x49 & 0x3ffffff);
{ u32 x60; u8/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
{ u32 x62 = (x49 & 0x1ffffff);
{ u32 x64; u8/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
{ u32 x66 = (x49 & 0x3ffffff);
{ u32 x68; u8/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
{ u32 x70 = (x49 & 0x1ffffff);
{ u32 x72; u8/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
{ u32 x74 = (x49 & 0x3ffffff);
{ u32 x76; u8/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
{ u32 x78 = (x49 & 0x1ffffff);
{ u32 x80; u8/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
{ u32 x82 = (x49 & 0x3ffffff);
{ u32 x84; u8/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
{ u32 x86 = (x49 & 0x1ffffff);
{ u32 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 __always_inline void fe_tobytes(u8 s[32], const fe *f)
{
u32 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 __always_inline void fe_copy(fe *h, const fe *f)
{
memmove(h, f, sizeof(u32) * 10);
}
static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
{
memmove(h, f, sizeof(u32) * 10);
}
/* h = 0 */
static __always_inline void fe_0(fe *h)
{
memset(h, 0, sizeof(u32) * 10);
}
/* h = 1 */
static __always_inline void fe_1(fe *h)
{
memset(h, 0, sizeof(u32) * 10);
h->v[0] = 1;
}
static noinline void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
{
{ const u32 x20 = in1[9];
{ const u32 x21 = in1[8];
{ const u32 x19 = in1[7];
{ const u32 x17 = in1[6];
{ const u32 x15 = in1[5];
{ const u32 x13 = in1[4];
{ const u32 x11 = in1[3];
{ const u32 x9 = in1[2];
{ const u32 x7 = in1[1];
{ const u32 x5 = in1[0];
{ const u32 x38 = in2[9];
{ const u32 x39 = in2[8];
{ const u32 x37 = in2[7];
{ const u32 x35 = in2[6];
{ const u32 x33 = in2[5];
{ const u32 x31 = in2[4];
{ const u32 x29 = in2[3];
{ const u32 x27 = in2[2];
{ const u32 x25 = in2[1];
{ const u32 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 __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
{
fe_add_impl(h->v, f->v, g->v);
}
static noinline void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
{
{ const u32 x20 = in1[9];
{ const u32 x21 = in1[8];
{ const u32 x19 = in1[7];
{ const u32 x17 = in1[6];
{ const u32 x15 = in1[5];
{ const u32 x13 = in1[4];
{ const u32 x11 = in1[3];
{ const u32 x9 = in1[2];
{ const u32 x7 = in1[1];
{ const u32 x5 = in1[0];
{ const u32 x38 = in2[9];
{ const u32 x39 = in2[8];
{ const u32 x37 = in2[7];
{ const u32 x35 = in2[6];
{ const u32 x33 = in2[5];
{ const u32 x31 = in2[4];
{ const u32 x29 = in2[3];
{ const u32 x27 = in2[2];
{ const u32 x25 = in2[1];
{ const u32 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 __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
{
fe_sub_impl(h->v, f->v, g->v);
}
static noinline void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
{
{ const u32 x20 = in1[9];
{ const u32 x21 = in1[8];
{ const u32 x19 = in1[7];
{ const u32 x17 = in1[6];
{ const u32 x15 = in1[5];
{ const u32 x13 = in1[4];
{ const u32 x11 = in1[3];
{ const u32 x9 = in1[2];
{ const u32 x7 = in1[1];
{ const u32 x5 = in1[0];
{ const u32 x38 = in2[9];
{ const u32 x39 = in2[8];
{ const u32 x37 = in2[7];
{ const u32 x35 = in2[6];
{ const u32 x33 = in2[5];
{ const u32 x31 = in2[4];
{ const u32 x29 = in2[3];
{ const u32 x27 = in2[2];
{ const u32 x25 = in2[1];
{ const u32 x23 = in2[0];
{ u64 x40 = ((u64)x23 * x5);
{ u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
{ u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
{ u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
{ u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
{ u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
{ u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
{ u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5));
{ u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5));
{ u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5));
{ u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9));
{ u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9));
{ u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
{ u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
{ u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
{ u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
{ u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
{ u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
{ u64 x58 = ((u64)(0x2 * x38) * x20);
{ u64 x59 = (x48 + (x58 << 0x4));
{ u64 x60 = (x59 + (x58 << 0x1));
{ u64 x61 = (x60 + x58);
{ u64 x62 = (x47 + (x57 << 0x4));
{ u64 x63 = (x62 + (x57 << 0x1));
{ u64 x64 = (x63 + x57);
{ u64 x65 = (x46 + (x56 << 0x4));
{ u64 x66 = (x65 + (x56 << 0x1));
{ u64 x67 = (x66 + x56);
{ u64 x68 = (x45 + (x55 << 0x4));
{ u64 x69 = (x68 + (x55 << 0x1));
{ u64 x70 = (x69 + x55);
{ u64 x71 = (x44 + (x54 << 0x4));
{ u64 x72 = (x71 + (x54 << 0x1));
{ u64 x73 = (x72 + x54);
{ u64 x74 = (x43 + (x53 << 0x4));
{ u64 x75 = (x74 + (x53 << 0x1));
{ u64 x76 = (x75 + x53);
{ u64 x77 = (x42 + (x52 << 0x4));
{ u64 x78 = (x77 + (x52 << 0x1));
{ u64 x79 = (x78 + x52);
{ u64 x80 = (x41 + (x51 << 0x4));
{ u64 x81 = (x80 + (x51 << 0x1));
{ u64 x82 = (x81 + x51);
{ u64 x83 = (x40 + (x50 << 0x4));
{ u64 x84 = (x83 + (x50 << 0x1));
{ u64 x85 = (x84 + x50);
{ u64 x86 = (x85 >> 0x1a);
{ u32 x87 = ((u32)x85 & 0x3ffffff);
{ u64 x88 = (x86 + x82);
{ u64 x89 = (x88 >> 0x19);
{ u32 x90 = ((u32)x88 & 0x1ffffff);
{ u64 x91 = (x89 + x79);
{ u64 x92 = (x91 >> 0x1a);
{ u32 x93 = ((u32)x91 & 0x3ffffff);
{ u64 x94 = (x92 + x76);
{ u64 x95 = (x94 >> 0x19);
{ u32 x96 = ((u32)x94 & 0x1ffffff);
{ u64 x97 = (x95 + x73);
{ u64 x98 = (x97 >> 0x1a);
{ u32 x99 = ((u32)x97 & 0x3ffffff);
{ u64 x100 = (x98 + x70);
{ u64 x101 = (x100 >> 0x19);
{ u32 x102 = ((u32)x100 & 0x1ffffff);
{ u64 x103 = (x101 + x67);
{ u64 x104 = (x103 >> 0x1a);
{ u32 x105 = ((u32)x103 & 0x3ffffff);
{ u64 x106 = (x104 + x64);
{ u64 x107 = (x106 >> 0x19);
{ u32 x108 = ((u32)x106 & 0x1ffffff);
{ u64 x109 = (x107 + x61);
{ u64 x110 = (x109 >> 0x1a);
{ u32 x111 = ((u32)x109 & 0x3ffffff);
{ u64 x112 = (x110 + x49);
{ u64 x113 = (x112 >> 0x19);
{ u32 x114 = ((u32)x112 & 0x1ffffff);
{ u64 x115 = (x87 + (0x13 * x113));
{ u32 x116 = (u32) (x115 >> 0x1a);
{ u32 x117 = ((u32)x115 & 0x3ffffff);
{ u32 x118 = (x116 + x90);
{ u32 x119 = (x118 >> 0x19);
{ u32 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 __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
{
fe_mul_impl(h->v, f->v, g->v);
}
static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
{
fe_mul_impl(h->v, f->v, g->v);
}
static __always_inline void
fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
{
fe_mul_impl(h->v, f->v, g->v);
}
static noinline void fe_sqr_impl(u32 out[10], const u32 in1[10])
{
{ const u32 x17 = in1[9];
{ const u32 x18 = in1[8];
{ const u32 x16 = in1[7];
{ const u32 x14 = in1[6];
{ const u32 x12 = in1[5];
{ const u32 x10 = in1[4];
{ const u32 x8 = in1[3];
{ const u32 x6 = in1[2];
{ const u32 x4 = in1[1];
{ const u32 x2 = in1[0];
{ u64 x19 = ((u64)x2 * x2);
{ u64 x20 = ((u64)(0x2 * x2) * x4);
{ u64 x21 = (0x2 * (((u64)x4 * x4) + ((u64)x2 * x6)));
{ u64 x22 = (0x2 * (((u64)x4 * x6) + ((u64)x2 * x8)));
{ u64 x23 = ((((u64)x6 * x6) + ((u64)(0x4 * x4) * x8)) + ((u64)(0x2 * x2) * x10));
{ u64 x24 = (0x2 * ((((u64)x6 * x8) + ((u64)x4 * x10)) + ((u64)x2 * x12)));
{ u64 x25 = (0x2 * (((((u64)x8 * x8) + ((u64)x6 * x10)) + ((u64)x2 * x14)) + ((u64)(0x2 * x4) * x12)));
{ u64 x26 = (0x2 * (((((u64)x8 * x10) + ((u64)x6 * x12)) + ((u64)x4 * x14)) + ((u64)x2 * x16)));
{ u64 x27 = (((u64)x10 * x10) + (0x2 * ((((u64)x6 * x14) + ((u64)x2 * x18)) + (0x2 * (((u64)x4 * x16) + ((u64)x8 * x12))))));
{ u64 x28 = (0x2 * ((((((u64)x10 * x12) + ((u64)x8 * x14)) + ((u64)x6 * x16)) + ((u64)x4 * x18)) + ((u64)x2 * x17)));
{ u64 x29 = (0x2 * (((((u64)x12 * x12) + ((u64)x10 * x14)) + ((u64)x6 * x18)) + (0x2 * (((u64)x8 * x16) + ((u64)x4 * x17)))));
{ u64 x30 = (0x2 * (((((u64)x12 * x14) + ((u64)x10 * x16)) + ((u64)x8 * x18)) + ((u64)x6 * x17)));
{ u64 x31 = (((u64)x14 * x14) + (0x2 * (((u64)x10 * x18) + (0x2 * (((u64)x12 * x16) + ((u64)x8 * x17))))));
{ u64 x32 = (0x2 * ((((u64)x14 * x16) + ((u64)x12 * x18)) + ((u64)x10 * x17)));
{ u64 x33 = (0x2 * ((((u64)x16 * x16) + ((u64)x14 * x18)) + ((u64)(0x2 * x12) * x17)));
{ u64 x34 = (0x2 * (((u64)x16 * x18) + ((u64)x14 * x17)));
{ u64 x35 = (((u64)x18 * x18) + ((u64)(0x4 * x16) * x17));
{ u64 x36 = ((u64)(0x2 * x18) * x17);
{ u64 x37 = ((u64)(0x2 * x17) * x17);
{ u64 x38 = (x27 + (x37 << 0x4));
{ u64 x39 = (x38 + (x37 << 0x1));
{ u64 x40 = (x39 + x37);
{ u64 x41 = (x26 + (x36 << 0x4));
{ u64 x42 = (x41 + (x36 << 0x1));
{ u64 x43 = (x42 + x36);
{ u64 x44 = (x25 + (x35 << 0x4));
{ u64 x45 = (x44 + (x35 << 0x1));
{ u64 x46 = (x45 + x35);
{ u64 x47 = (x24 + (x34 << 0x4));
{ u64 x48 = (x47 + (x34 << 0x1));
{ u64 x49 = (x48 + x34);
{ u64 x50 = (x23 + (x33 << 0x4));
{ u64 x51 = (x50 + (x33 << 0x1));
{ u64 x52 = (x51 + x33);
{ u64 x53 = (x22 + (x32 << 0x4));
{ u64 x54 = (x53 + (x32 << 0x1));
{ u64 x55 = (x54 + x32);
{ u64 x56 = (x21 + (x31 << 0x4));
{ u64 x57 = (x56 + (x31 << 0x1));
{ u64 x58 = (x57 + x31);
{ u64 x59 = (x20 + (x30 << 0x4));
{ u64 x60 = (x59 + (x30 << 0x1));
{ u64 x61 = (x60 + x30);
{ u64 x62 = (x19 + (x29 << 0x4));
{ u64 x63 = (x62 + (x29 << 0x1));
{ u64 x64 = (x63 + x29);
{ u64 x65 = (x64 >> 0x1a);
{ u32 x66 = ((u32)x64 & 0x3ffffff);
{ u64 x67 = (x65 + x61);
{ u64 x68 = (x67 >> 0x19);
{ u32 x69 = ((u32)x67 & 0x1ffffff);
{ u64 x70 = (x68 + x58);
{ u64 x71 = (x70 >> 0x1a);
{ u32 x72 = ((u32)x70 & 0x3ffffff);
{ u64 x73 = (x71 + x55);
{ u64 x74 = (x73 >> 0x19);
{ u32 x75 = ((u32)x73 & 0x1ffffff);
{ u64 x76 = (x74 + x52);
{ u64 x77 = (x76 >> 0x1a);
{ u32 x78 = ((u32)x76 & 0x3ffffff);
{ u64 x79 = (x77 + x49);
{ u64 x80 = (x79 >> 0x19);
{ u32 x81 = ((u32)x79 & 0x1ffffff);
{ u64 x82 = (x80 + x46);
{ u64 x83 = (x82 >> 0x1a);
{ u32 x84 = ((u32)x82 & 0x3ffffff);
{ u64 x85 = (x83 + x43);
{ u64 x86 = (x85 >> 0x19);
{ u32 x87 = ((u32)x85 & 0x1ffffff);
{ u64 x88 = (x86 + x40);
{ u64 x89 = (x88 >> 0x1a);
{ u32 x90 = ((u32)x88 & 0x3ffffff);
{ u64 x91 = (x89 + x28);
{ u64 x92 = (x91 >> 0x19);
{ u32 x93 = ((u32)x91 & 0x1ffffff);
{ u64 x94 = (x66 + (0x13 * x92));
{ u32 x95 = (u32) (x94 >> 0x1a);
{ u32 x96 = ((u32)x94 & 0x3ffffff);
{ u32 x97 = (x95 + x69);
{ u32 x98 = (x97 >> 0x19);
{ u32 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 __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
{
fe_sqr_impl(h->v, f->v);
}
static __always_inline void fe_sq_tt(fe *h, const fe *f)
{
fe_sqr_impl(h->v, f->v);
}
static __always_inline void fe_loose_invert(fe *out, 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 __always_inline void fe_invert(fe *out, 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 noinline void fe_cswap(fe *f, fe *g, unsigned int b)
{
unsigned i;
b = 0 - b;
for (i = 0; i < 10; i++) {
u32 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 __always_inline void fe_mul_121666_impl(u32 out[10], const u32 in1[10])
{
{ const u32 x20 = in1[9];
{ const u32 x21 = in1[8];
{ const u32 x19 = in1[7];
{ const u32 x17 = in1[6];
{ const u32 x15 = in1[5];
{ const u32 x13 = in1[4];
{ const u32 x11 = in1[3];
{ const u32 x9 = in1[2];
{ const u32 x7 = in1[1];
{ const u32 x5 = in1[0];
{ const u32 x38 = 0;
{ const u32 x39 = 0;
{ const u32 x37 = 0;
{ const u32 x35 = 0;
{ const u32 x33 = 0;
{ const u32 x31 = 0;
{ const u32 x29 = 0;
{ const u32 x27 = 0;
{ const u32 x25 = 0;
{ const u32 x23 = 121666;
{ u64 x40 = ((u64)x23 * x5);
{ u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
{ u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
{ u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
{ u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
{ u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
{ u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
{ u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5));
{ u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5));
{ u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5));
{ u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9));
{ u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9));
{ u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
{ u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
{ u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
{ u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
{ u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
{ u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
{ u64 x58 = ((u64)(0x2 * x38) * x20);
{ u64 x59 = (x48 + (x58 << 0x4));
{ u64 x60 = (x59 + (x58 << 0x1));
{ u64 x61 = (x60 + x58);
{ u64 x62 = (x47 + (x57 << 0x4));
{ u64 x63 = (x62 + (x57 << 0x1));
{ u64 x64 = (x63 + x57);
{ u64 x65 = (x46 + (x56 << 0x4));
{ u64 x66 = (x65 + (x56 << 0x1));
{ u64 x67 = (x66 + x56);
{ u64 x68 = (x45 + (x55 << 0x4));
{ u64 x69 = (x68 + (x55 << 0x1));
{ u64 x70 = (x69 + x55);
{ u64 x71 = (x44 + (x54 << 0x4));
{ u64 x72 = (x71 + (x54 << 0x1));
{ u64 x73 = (x72 + x54);
{ u64 x74 = (x43 + (x53 << 0x4));
{ u64 x75 = (x74 + (x53 << 0x1));
{ u64 x76 = (x75 + x53);
{ u64 x77 = (x42 + (x52 << 0x4));
{ u64 x78 = (x77 + (x52 << 0x1));
{ u64 x79 = (x78 + x52);
{ u64 x80 = (x41 + (x51 << 0x4));
{ u64 x81 = (x80 + (x51 << 0x1));
{ u64 x82 = (x81 + x51);
{ u64 x83 = (x40 + (x50 << 0x4));
{ u64 x84 = (x83 + (x50 << 0x1));
{ u64 x85 = (x84 + x50);
{ u64 x86 = (x85 >> 0x1a);
{ u32 x87 = ((u32)x85 & 0x3ffffff);
{ u64 x88 = (x86 + x82);
{ u64 x89 = (x88 >> 0x19);
{ u32 x90 = ((u32)x88 & 0x1ffffff);
{ u64 x91 = (x89 + x79);
{ u64 x92 = (x91 >> 0x1a);
{ u32 x93 = ((u32)x91 & 0x3ffffff);
{ u64 x94 = (x92 + x76);
{ u64 x95 = (x94 >> 0x19);
{ u32 x96 = ((u32)x94 & 0x1ffffff);
{ u64 x97 = (x95 + x73);
{ u64 x98 = (x97 >> 0x1a);
{ u32 x99 = ((u32)x97 & 0x3ffffff);
{ u64 x100 = (x98 + x70);
{ u64 x101 = (x100 >> 0x19);
{ u32 x102 = ((u32)x100 & 0x1ffffff);
{ u64 x103 = (x101 + x67);
{ u64 x104 = (x103 >> 0x1a);
{ u32 x105 = ((u32)x103 & 0x3ffffff);
{ u64 x106 = (x104 + x64);
{ u64 x107 = (x106 >> 0x19);
{ u32 x108 = ((u32)x106 & 0x1ffffff);
{ u64 x109 = (x107 + x61);
{ u64 x110 = (x109 >> 0x1a);
{ u32 x111 = ((u32)x109 & 0x3ffffff);
{ u64 x112 = (x110 + x49);
{ u64 x113 = (x112 >> 0x19);
{ u32 x114 = ((u32)x112 & 0x1ffffff);
{ u64 x115 = (x87 + (0x13 * x113));
{ u32 x116 = (u32) (x115 >> 0x1a);
{ u32 x117 = ((u32)x115 & 0x3ffffff);
{ u32 x118 = (x116 + x90);
{ u32 x119 = (x118 >> 0x19);
{ u32 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 __always_inline void fe_mul121666(fe *h, const fe_loose *f)
{
fe_mul_121666_impl(h->v, f->v);
}
void curve25519_generic(u8 out[CURVE25519_KEY_SIZE],
const u8 scalar[CURVE25519_KEY_SIZE],
const u8 point[CURVE25519_KEY_SIZE])
{
fe x1, x2, z2, x3, z3;
fe_loose x2l, z2l, x3l;
unsigned swap = 0;
int pos;
u8 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:
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
*
* Proof that these form a group that is isomorphic to a Weierstrass
* curve:
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
*
* Coq transcription and correctness proof of the loop
* (where scalarbits=255):
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
* preconditions: 0 <= e < 2^255 (not necessarily e < order),
* fe_invert(0) = 0
*/
fe_frombytes(&x1, point);
fe_1(&x2);
fe_0(&z2);
fe_copy(&x3, &x1);
fe_1(&z3);
for (pos = 254; pos >= 0; --pos) {
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):
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
* <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
* x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
* x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
*/
fe_sub(&tmp0l, &x3, &z3);
fe_sub(&tmp1l, &x2, &z2);
fe_add(&x2l, &x2, &z2);
fe_add(&z2l, &x3, &z3);
fe_mul_tll(&z3, &tmp0l, &x2l);
fe_mul_tll(&z2, &z2l, &tmp1l);
fe_sq_tl(&tmp0, &tmp1l);
fe_sq_tl(&tmp1, &x2l);
fe_add(&x3l, &z3, &z2);
fe_sub(&z2l, &z3, &z2);
fe_mul_ttt(&x2, &tmp1, &tmp0);
fe_sub(&tmp1l, &tmp1, &tmp0);
fe_sq_tl(&z2, &z2l);
fe_mul121666(&z3, &tmp1l);
fe_sq_tl(&x3, &x3l);
fe_add(&tmp0l, &tmp0, &z3);
fe_mul_ttt(&z3, &x1, &z2);
fe_mul_tll(&z2, &tmp1l, &tmp0l);
}
/* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
* else (x2, z2)
*/
fe_cswap(&x2, &x3, swap);
fe_cswap(&z2, &z3, swap);
fe_invert(&z2, &z2);
fe_mul_ttt(&x2, &x2, &z2);
fe_tobytes(out, &x2);
memzero_explicit(&x1, sizeof(x1));
memzero_explicit(&x2, sizeof(x2));
memzero_explicit(&z2, sizeof(z2));
memzero_explicit(&x3, sizeof(x3));
memzero_explicit(&z3, sizeof(z3));
memzero_explicit(&x2l, sizeof(x2l));
memzero_explicit(&z2l, sizeof(z2l));
memzero_explicit(&x3l, sizeof(x3l));
memzero_explicit(&e, sizeof(e));
}
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