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research-lab/source-code/RingCT/crypto-ops.c
shnoe bfb18a0eed Added MiniNero and RingCT code
2016-02-05 13:22:13 -07:00

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// Copyright (c) 2014-2015, The Monero Project
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other
// materials provided with the distribution.
//
// 3. Neither the name of the copyright holder nor the names of its contributors may be
// used to endorse or promote products derived from this software without specific
// prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers
#include <assert.h>
#include <stdint.h>
#include "warnings.h"
#include "crypto-ops.h"
//DISABLE_VS_WARNINGS(4146 4244)
/* Predeclarations */
static void fe_mul(fe, const fe, const fe);
static void fe_sq(fe, const fe);
static void fe_tobytes(unsigned char *, const fe);
static int fe_isnonzero(const fe);
static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_p2_0(ge_p2 *);
static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *);
static void ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *);
static void fe_divpowm1(fe, const fe, const fe);
/*
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].
Bounds on each t[i] vary depending on context.
*/
/*
h = 0
*/
void fe_0(fe h)
{
h[0] = 0;
h[1] = 0;
h[2] = 0;
h[3] = 0;
h[4] = 0;
h[5] = 0;
h[6] = 0;
h[7] = 0;
h[8] = 0;
h[9] = 0;
}
/*
h = 1
*/
void fe_1(fe h)
{
h[0] = 1;
h[1] = 0;
h[2] = 0;
h[3] = 0;
h[4] = 0;
h[5] = 0;
h[6] = 0;
h[7] = 0;
h[8] = 0;
h[9] = 0;
}
/*
h = f + g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
void fe_add(fe h,const fe f,const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t h0 = f0 + g0;
int32_t h1 = f1 + g1;
int32_t h2 = f2 + g2;
int32_t h3 = f3 + g3;
int32_t h4 = f4 + g4;
int32_t h5 = f5 + g5;
int32_t h6 = f6 + g6;
int32_t h7 = f7 + g7;
int32_t h8 = f8 + g8;
int32_t h9 = f9 + g9;
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;
}
/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
void fe_cmov(fe f,const fe g,unsigned int b)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t x0 = f0 ^ g0;
int32_t x1 = f1 ^ g1;
int32_t x2 = f2 ^ g2;
int32_t x3 = f3 ^ g3;
int32_t x4 = f4 ^ g4;
int32_t x5 = f5 ^ g5;
int32_t x6 = f6 ^ g6;
int32_t x7 = f7 ^ g7;
int32_t x8 = f8 ^ g8;
int32_t x9 = f9 ^ g9;
b = -b;
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
f[0] = f0 ^ x0;
f[1] = f1 ^ x1;
f[2] = f2 ^ x2;
f[3] = f3 ^ x3;
f[4] = f4 ^ x4;
f[5] = f5 ^ x5;
f[6] = f6 ^ x6;
f[7] = f7 ^ x7;
f[8] = f8 ^ x8;
f[9] = f9 ^ x9;
}
/*
h = f
*/
void fe_copy(fe h,const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
h[0] = f0;
h[1] = f1;
h[2] = f2;
h[3] = f3;
h[4] = f4;
h[5] = f5;
h[6] = f6;
h[7] = f7;
h[8] = f8;
h[9] = f9;
}
static uint64_t load_3(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
return result;
}
static uint64_t load_4(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
result |= ((uint64_t) in[3]) << 24;
return result;
}
/*
Ignores top bit of h.
*/
void fe_frombytes(fe h,const unsigned char *s)
{
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = (load_3(s + 29) & 8388607) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
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;
}
void fe_invert(fe out,const fe z)
{
fe t0;
fe t1;
fe t2;
fe t3;
int i;
fe_sq(t0,z);
for (i = 1; i < 1; ++i) fe_sq(t0,t0);
fe_sq(t1,t0);
for (i = 1; i < 2; ++i) fe_sq(t1,t1);
fe_mul(t1,z,t1);
fe_mul(t0,t0,t1);
fe_sq(t2,t0);
for (i = 1; i < 1; ++i) fe_sq(t2,t2);
fe_mul(t1,t1,t2);
fe_sq(t2,t1);
for (i = 1; i < 5; ++i) fe_sq(t2,t2);
fe_mul(t1,t2,t1);
fe_sq(t2,t1);
for (i = 1; i < 10; ++i) fe_sq(t2,t2);
fe_mul(t2,t2,t1);
fe_sq(t3,t2);
for (i = 1; i < 20; ++i) fe_sq(t3,t3);
fe_mul(t2,t3,t2);
fe_sq(t2,t2);
for (i = 1; i < 10; ++i) fe_sq(t2,t2);
fe_mul(t1,t2,t1);
fe_sq(t2,t1);
for (i = 1; i < 50; ++i) fe_sq(t2,t2);
fe_mul(t2,t2,t1);
fe_sq(t3,t2);
for (i = 1; i < 100; ++i) fe_sq(t3,t3);
fe_mul(t2,t3,t2);
fe_sq(t2,t2);
for (i = 1; i < 50; ++i) fe_sq(t2,t2);
fe_mul(t1,t2,t1);
fe_sq(t1,t1);
for (i = 1; i < 5; ++i) fe_sq(t1,t1);
fe_mul(out,t1,t0);
return;
}
/*
return 1 if f is in {1,3,5,...,q-2}
return 0 if f is in {0,2,4,...,q-1}
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
int fe_isnegative(const fe f)
{
unsigned char s[32];
fe_tobytes(s,f);
return s[0] & 1;
}
/*
h = f * g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
Notes on implementation strategy:
Using schoolbook multiplication.
Karatsuba would save a little in some cost models.
Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.
There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.
There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.
With tighter constraints on inputs can squeeze carries into int32.
*/
void fe_mul(fe h,const fe f,const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int32_t g3_19 = 19 * g3;
int32_t g4_19 = 19 * g4;
int32_t g5_19 = 19 * g5;
int32_t g6_19 = 19 * g6;
int32_t g7_19 = 19 * g7;
int32_t g8_19 = 19 * g8;
int32_t g9_19 = 19 * g9;
int32_t f1_2 = 2 * f1;
int32_t f3_2 = 2 * f3;
int32_t f5_2 = 2 * f5;
int32_t f7_2 = 2 * f7;
int32_t f9_2 = 2 * f9;
int64_t f0g0 = f0 * (int64_t) g0;
int64_t f0g1 = f0 * (int64_t) g1;
int64_t f0g2 = f0 * (int64_t) g2;
int64_t f0g3 = f0 * (int64_t) g3;
int64_t f0g4 = f0 * (int64_t) g4;
int64_t f0g5 = f0 * (int64_t) g5;
int64_t f0g6 = f0 * (int64_t) g6;
int64_t f0g7 = f0 * (int64_t) g7;
int64_t f0g8 = f0 * (int64_t) g8;
int64_t f0g9 = f0 * (int64_t) g9;
int64_t f1g0 = f1 * (int64_t) g0;
int64_t f1g1_2 = f1_2 * (int64_t) g1;
int64_t f1g2 = f1 * (int64_t) g2;
int64_t f1g3_2 = f1_2 * (int64_t) g3;
int64_t f1g4 = f1 * (int64_t) g4;
int64_t f1g5_2 = f1_2 * (int64_t) g5;
int64_t f1g6 = f1 * (int64_t) g6;
int64_t f1g7_2 = f1_2 * (int64_t) g7;
int64_t f1g8 = f1 * (int64_t) g8;
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
int64_t f2g0 = f2 * (int64_t) g0;
int64_t f2g1 = f2 * (int64_t) g1;
int64_t f2g2 = f2 * (int64_t) g2;
int64_t f2g3 = f2 * (int64_t) g3;
int64_t f2g4 = f2 * (int64_t) g4;
int64_t f2g5 = f2 * (int64_t) g5;
int64_t f2g6 = f2 * (int64_t) g6;
int64_t f2g7 = f2 * (int64_t) g7;
int64_t f2g8_19 = f2 * (int64_t) g8_19;
int64_t f2g9_19 = f2 * (int64_t) g9_19;
int64_t f3g0 = f3 * (int64_t) g0;
int64_t f3g1_2 = f3_2 * (int64_t) g1;
int64_t f3g2 = f3 * (int64_t) g2;
int64_t f3g3_2 = f3_2 * (int64_t) g3;
int64_t f3g4 = f3 * (int64_t) g4;
int64_t f3g5_2 = f3_2 * (int64_t) g5;
int64_t f3g6 = f3 * (int64_t) g6;
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
int64_t f3g8_19 = f3 * (int64_t) g8_19;
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
int64_t f4g0 = f4 * (int64_t) g0;
int64_t f4g1 = f4 * (int64_t) g1;
int64_t f4g2 = f4 * (int64_t) g2;
int64_t f4g3 = f4 * (int64_t) g3;
int64_t f4g4 = f4 * (int64_t) g4;
int64_t f4g5 = f4 * (int64_t) g5;
int64_t f4g6_19 = f4 * (int64_t) g6_19;
int64_t f4g7_19 = f4 * (int64_t) g7_19;
int64_t f4g8_19 = f4 * (int64_t) g8_19;
int64_t f4g9_19 = f4 * (int64_t) g9_19;
int64_t f5g0 = f5 * (int64_t) g0;
int64_t f5g1_2 = f5_2 * (int64_t) g1;
int64_t f5g2 = f5 * (int64_t) g2;
int64_t f5g3_2 = f5_2 * (int64_t) g3;
int64_t f5g4 = f5 * (int64_t) g4;
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
int64_t f5g6_19 = f5 * (int64_t) g6_19;
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
int64_t f5g8_19 = f5 * (int64_t) g8_19;
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
int64_t f6g0 = f6 * (int64_t) g0;
int64_t f6g1 = f6 * (int64_t) g1;
int64_t f6g2 = f6 * (int64_t) g2;
int64_t f6g3 = f6 * (int64_t) g3;
int64_t f6g4_19 = f6 * (int64_t) g4_19;
int64_t f6g5_19 = f6 * (int64_t) g5_19;
int64_t f6g6_19 = f6 * (int64_t) g6_19;
int64_t f6g7_19 = f6 * (int64_t) g7_19;
int64_t f6g8_19 = f6 * (int64_t) g8_19;
int64_t f6g9_19 = f6 * (int64_t) g9_19;
int64_t f7g0 = f7 * (int64_t) g0;
int64_t f7g1_2 = f7_2 * (int64_t) g1;
int64_t f7g2 = f7 * (int64_t) g2;
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
int64_t f7g4_19 = f7 * (int64_t) g4_19;
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
int64_t f7g6_19 = f7 * (int64_t) g6_19;
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
int64_t f7g8_19 = f7 * (int64_t) g8_19;
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
int64_t f8g0 = f8 * (int64_t) g0;
int64_t f8g1 = f8 * (int64_t) g1;
int64_t f8g2_19 = f8 * (int64_t) g2_19;
int64_t f8g3_19 = f8 * (int64_t) g3_19;
int64_t f8g4_19 = f8 * (int64_t) g4_19;
int64_t f8g5_19 = f8 * (int64_t) g5_19;
int64_t f8g6_19 = f8 * (int64_t) g6_19;
int64_t f8g7_19 = f8 * (int64_t) g7_19;
int64_t f8g8_19 = f8 * (int64_t) g8_19;
int64_t f8g9_19 = f8 * (int64_t) g9_19;
int64_t f9g0 = f9 * (int64_t) g0;
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
int64_t f9g2_19 = f9 * (int64_t) g2_19;
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
int64_t f9g4_19 = f9 * (int64_t) g4_19;
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
int64_t f9g6_19 = f9 * (int64_t) g6_19;
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
int64_t f9g8_19 = f9 * (int64_t) g8_19;
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
/*
|h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
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;
}
/*
h = -f
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
void fe_neg(fe h,const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t h0 = -f0;
int32_t h1 = -f1;
int32_t h2 = -f2;
int32_t h3 = -f3;
int32_t h4 = -f4;
int32_t h5 = -f5;
int32_t h6 = -f6;
int32_t h7 = -f7;
int32_t h8 = -f8;
int32_t h9 = -f9;
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;
}
void fe_pow22523(fe out,const fe z)
{
fe t0;
fe t1;
fe t2;
int i;
fe_sq(t0,z);
for (i = 1; i < 1; ++i) fe_sq(t0,t0);
fe_sq(t1,t0);
for (i = 1; i < 2; ++i) fe_sq(t1,t1);
fe_mul(t1,z,t1);
fe_mul(t0,t0,t1);
fe_sq(t0,t0);
for (i = 1; i < 1; ++i) fe_sq(t0,t0);
fe_mul(t0,t1,t0);
fe_sq(t1,t0);
for (i = 1; i < 5; ++i) fe_sq(t1,t1);
fe_mul(t0,t1,t0);
fe_sq(t1,t0);
for (i = 1; i < 10; ++i) fe_sq(t1,t1);
fe_mul(t1,t1,t0);
fe_sq(t2,t1);
for (i = 1; i < 20; ++i) fe_sq(t2,t2);
fe_mul(t1,t2,t1);
fe_sq(t1,t1);
for (i = 1; i < 10; ++i) fe_sq(t1,t1);
fe_mul(t0,t1,t0);
fe_sq(t1,t0);
for (i = 1; i < 50; ++i) fe_sq(t1,t1);
fe_mul(t1,t1,t0);
fe_sq(t2,t1);
for (i = 1; i < 100; ++i) fe_sq(t2,t2);
fe_mul(t1,t2,t1);
fe_sq(t1,t1);
for (i = 1; i < 50; ++i) fe_sq(t1,t1);
fe_mul(t0,t1,t0);
fe_sq(t0,t0);
for (i = 1; i < 2; ++i) fe_sq(t0,t0);
fe_mul(out,t0,z);
return;
}
/*
h = f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
void fe_sq(fe h,const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
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;
}
/*
h = 2 * f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
void fe_sq2(fe h,const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
h0 += h0;
h1 += h1;
h2 += h2;
h3 += h3;
h4 += h4;
h5 += h5;
h6 += h6;
h7 += h7;
h8 += h8;
h9 += h9;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
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;
}
/*
h = f - g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
void fe_sub(fe h,const fe f,const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t h0 = f0 - g0;
int32_t h1 = f1 - g1;
int32_t h2 = f2 - g2;
int32_t h3 = f3 - g3;
int32_t h4 = f4 - g4;
int32_t h5 = f5 - g5;
int32_t h6 = f6 - g6;
int32_t h7 = f7 - g7;
int32_t h8 = f8 - g8;
int32_t h9 = f9 - g9;
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;
}
/*
Preconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
Proof:
Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
Then 0<y<1.
Write r=h-pq.
Have 0<=r<=p-1=2^255-20.
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
Write x=r+19(2^-255)r+y.
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/
void fe_tobytes(unsigned char *s,const fe h)
{
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
int32_t h3 = h[3];
int32_t h4 = h[4];
int32_t h5 = h[5];
int32_t h6 = h[6];
int32_t h7 = h[7];
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
int32_t carry0;
int32_t carry1;
int32_t carry2;
int32_t carry3;
int32_t carry4;
int32_t carry5;
int32_t carry6;
int32_t carry7;
int32_t carry8;
int32_t carry9;
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
carry0 = h0 >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry1 = h1 >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry2 = h2 >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry3 = h3 >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry4 = h4 >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry5 = h5 >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry6 = h6 >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry7 = h7 >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry8 = h8 >> 26;
h9 += carry8;
h8 -= carry8 << 26;
carry9 = h9 >> 25;
h9 -= carry9 << 25;
/* h10 = carry9 */
/*
Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
Have h0+...+2^230 h9 between 0 and 2^255-1;
evidently 2^255 h10-2^255 q = 0.
Goal: Output h0+...+2^230 h9.
*/
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
s[3] = (h0 >> 24) | (h1 << 2);
s[4] = h1 >> 6;
s[5] = h1 >> 14;
s[6] = (h1 >> 22) | (h2 << 3);
s[7] = h2 >> 5;
s[8] = h2 >> 13;
s[9] = (h2 >> 21) | (h3 << 5);
s[10] = h3 >> 3;
s[11] = h3 >> 11;
s[12] = (h3 >> 19) | (h4 << 6);
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
s[19] = (h5 >> 24) | (h6 << 1);
s[20] = h6 >> 7;
s[21] = h6 >> 15;
s[22] = (h6 >> 23) | (h7 << 3);
s[23] = h7 >> 5;
s[24] = h7 >> 13;
s[25] = (h7 >> 21) | (h8 << 4);
s[26] = h8 >> 4;
s[27] = h8 >> 12;
s[28] = (h8 >> 20) | (h9 << 6);
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
}
/*
*
* sc code
*
*
The set of scalars is \Z/l
where l = 2^252 + 27742317777372353535851937790883648493.
This is the order of the curve ed25519.
The point is that if a is a scalar and P is a point,
and b is congruent to a mod l, then aP = bP.
Thus, reducing mod l can possibly give you a smaller scalar,
so your elliptic curve operations take less time
*/
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c)
{
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t c0 = 2097151 & load_3(c);
int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
int64_t c8 = 2097151 & load_3(c + 21);
int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
int64_t c11 = (load_4(c + 28) >> 7);
int64_t s0;
int64_t s1;
int64_t s2;
int64_t s3;
int64_t s4;
int64_t s5;
int64_t s6;
int64_t s7;
int64_t s8;
int64_t s9;
int64_t s10;
int64_t s11;
int64_t s12;
int64_t s13;
int64_t s14;
int64_t s15;
int64_t s16;
int64_t s17;
int64_t s18;
int64_t s19;
int64_t s20;
int64_t s21;
int64_t s22;
int64_t s23;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
int64_t carry17;
int64_t carry18;
int64_t carry19;
int64_t carry20;
int64_t carry21;
int64_t carry22;
s0 = c0 + a0*b0;
s1 = c1 + a0*b1 + a1*b0;
s2 = c2 + a0*b2 + a1*b1 + a2*b0;
s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
s20 = a9*b11 + a10*b10 + a11*b9;
s21 = a10*b11 + a11*b10;
s22 = a11*b11;
s23 = 0;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21;
s13 += carry12;
s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21;
s15 += carry14;
s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21;
s17 += carry16;
s16 -= carry16 << 21;
carry18 = (s18 + (1<<20)) >> 21;
s19 += carry18;
s18 -= carry18 << 21;
carry20 = (s20 + (1<<20)) >> 21;
s21 += carry20;
s20 -= carry20 << 21;
carry22 = (s22 + (1<<20)) >> 21;
s23 += carry22;
s22 -= carry22 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21;
s14 += carry13;
s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21;
s16 += carry15;
s15 -= carry15 << 21;
carry17 = (s17 + (1<<20)) >> 21;
s18 += carry17;
s17 -= carry17 << 21;
carry19 = (s19 + (1<<20)) >> 21;
s20 += carry19;
s19 -= carry19 << 21;
carry21 = (s21 + (1<<20)) >> 21;
s22 += carry21;
s21 -= carry21 << 21;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21;
s13 += carry12;
s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21;
s15 += carry14;
s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21;
s17 += carry16;
s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21;
s14 += carry13;
s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21;
s16 += carry15;
s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/*
Input:
s[0]+256*s[1]+...+256^63*s[63] = s
Output:
s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
void sc_reduce(unsigned char *s)
{
int64_t s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
int64_t s16 = 2097151 & load_3(s + 42);
int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
int64_t s23 = (load_4(s + 60) >> 3);
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21;
s13 += carry12;
s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21;
s15 += carry14;
s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21;
s17 += carry16;
s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21;
s14 += carry13;
s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21;
s16 += carry15;
s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) {
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t s0 = a0 - b0;
int64_t s1 = a1 - b1;
int64_t s2 = a2 - b2;
int64_t s3 = a3 - b3;
int64_t s4 = a4 - b4;
int64_t s5 = a5 - b5;
int64_t s6 = a6 - b6;
int64_t s7 = a7 - b7;
int64_t s8 = a8 - b8;
int64_t s9 = a9 - b9;
int64_t s10 = a10 - b10;
int64_t s11 = a11 - b11;
int64_t s12 = 0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
Output:
s[0]+256*s[1]+...+256^31*s[31] = (c-ab) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
//x
void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t c0 = 2097151 & load_3(c);
int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
int64_t c8 = 2097151 & load_3(c + 21);
int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
int64_t c11 = (load_4(c + 28) >> 7);
int64_t s0;
int64_t s1;
int64_t s2;
int64_t s3;
int64_t s4;
int64_t s5;
int64_t s6;
int64_t s7;
int64_t s8;
int64_t s9;
int64_t s10;
int64_t s11;
int64_t s12;
int64_t s13;
int64_t s14;
int64_t s15;
int64_t s16;
int64_t s17;
int64_t s18;
int64_t s19;
int64_t s20;
int64_t s21;
int64_t s22;
int64_t s23;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
int64_t carry17;
int64_t carry18;
int64_t carry19;
int64_t carry20;
int64_t carry21;
int64_t carry22;
s0 = c0 - a0*b0;
s1 = c1 - (a0*b1 + a1*b0);
s2 = c2 - (a0*b2 + a1*b1 + a2*b0);
s3 = c3 - (a0*b3 + a1*b2 + a2*b1 + a3*b0);
s4 = c4 - (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0);
s5 = c5 - (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0);
s6 = c6 - (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0);
s7 = c7 - (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0);
s8 = c8 - (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0);
s9 = c9 - (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0);
s10 = c10 - (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0);
s11 = c11 - (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0);
s12 = -(a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1);
s13 = -(a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2);
s14 = -(a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3);
s15 = -(a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4);
s16 = -(a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5);
s17 = -(a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6);
s18 = -(a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7);
s19 = -(a8*b11 + a9*b10 + a10*b9 + a11*b8);
s20 = -(a9*b11 + a10*b10 + a11*b9);
s21 = -(a10*b11 + a11*b10);
s22 = -a11*b11;
s23 = 0;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21;
s13 += carry12;
s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21;
s15 += carry14;
s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21;
s17 += carry16;
s16 -= carry16 << 21;
carry18 = (s18 + (1<<20)) >> 21;
s19 += carry18;
s18 -= carry18 << 21;
carry20 = (s20 + (1<<20)) >> 21;
s21 += carry20;
s20 -= carry20 << 21;
carry22 = (s22 + (1<<20)) >> 21;
s23 += carry22;
s22 -= carry22 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21;
s14 += carry13;
s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21;
s16 += carry15;
s15 -= carry15 << 21;
carry17 = (s17 + (1<<20)) >> 21;
s18 += carry17;
s17 -= carry17 << 21;
carry19 = (s19 + (1<<20)) >> 21;
s20 += carry19;
s19 -= carry19 << 21;
carry21 = (s21 + (1<<20)) >> 21;
s22 += carry21;
s21 -= carry21 << 21;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21;
s13 += carry12;
s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21;
s15 += carry14;
s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21;
s17 += carry16;
s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21;
s14 += carry13;
s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21;
s16 += carry15;
s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/*
*
* ge code
*
*
ge means group element.
Here the group is the set of pairs (x,y) of field elements (see fe.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.
Representations:
ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
ge_precomp (Duif): (y+x,y-x,2dxy)
*/
/*
r = p + q
*/
void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
fe t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->YplusX);
fe_mul(r->Y,r->Y,q->YminusX);
fe_mul(r->T,q->T2d,p->T);
fe_mul(r->X,p->Z,q->Z);
fe_add(t0,r->X,r->X);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_add(r->Z,t0,r->T);
fe_sub(r->T,t0,r->T);
}
static void slide(signed char *r,const unsigned char *a)
{
int i;
int b;
int k;
for (i = 0; i < 256; ++i)
r[i] = 1 & (a[i >> 3] >> (i & 7));
for (i = 0; i < 256; ++i)
if (r[i]) {
for (b = 1; b <= 6 && i + b < 256; ++b) {
if (r[i + b]) {
if (r[i] + (r[i + b] << b) <= 15) {
r[i] += r[i + b] << b;
r[i + b] = 0;
} else if (r[i] - (r[i + b] << b) >= -15) {
r[i] -= r[i + b] << b;
for (k = i + b; k < 256; ++k) {
if (!r[k]) {
r[k] = 1;
break;
}
r[k] = 0;
}
} else
break;
}
}
}
}
static ge_precomp Bi[8] = {
{
{ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
{ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
{ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
{ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
{ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
{ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
{ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
{ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
{ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
{ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
{ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
{ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
{ -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
{ -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
{ 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
},
{
{ -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
{ 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
{ 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
},
{
{ -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
{ -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
{ -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
},
{
{ -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
{ -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
{ -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
},
} ;
/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/
void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b)
{
signed char aslide[256];
signed char bslide[256];
ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
slide(aslide,a);
slide(bslide,b);
ge_p3_to_cached(&Ai[0],A);
ge_p3_dbl(&t,A);
ge_p1p1_to_p3(&A2,&t);
ge_add(&t,&A2,&Ai[0]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[1],&u);
ge_add(&t,&A2,&Ai[1]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[2],&u);
ge_add(&t,&A2,&Ai[2]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[3],&u);
ge_add(&t,&A2,&Ai[3]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[4],&u);
ge_add(&t,&A2,&Ai[4]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[5],&u);
ge_add(&t,&A2,&Ai[5]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[6],&u);
ge_add(&t,&A2,&Ai[6]);
ge_p1p1_to_p3(&u,&t);
ge_p3_to_cached(&Ai[7],&u);
ge_p2_0(r);
for (i = 255; i >= 0; --i) {
if (aslide[i] || bslide[i]) break;
}
for (; i >= 0; --i) {
ge_p2_dbl(&t,r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u,&t);
ge_add(&t,&u,&Ai[aslide[i]/2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u,&t);
ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
}
if (bslide[i] > 0) {
ge_p1p1_to_p3(&u,&t);
ge_madd(&t,&u,&Bi[bslide[i]/2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u,&t);
ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
}
ge_p1p1_to_p2(r,&t);
}
}
static const fe d = {
-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116
} ;
static const fe sqrtm1 = {
-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482
} ;
int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
{
fe u;
fe v;
fe v3;
fe vxx;
fe check;
fe_frombytes(h->Y,s);
fe_1(h->Z);
fe_sq(u,h->Y);
fe_mul(v,u,d);
fe_sub(u,u,h->Z); /* u = y^2-1 */
fe_add(v,v,h->Z); /* v = dy^2+1 */
fe_sq(v3,v);
fe_mul(v3,v3,v); /* v3 = v^3 */
fe_sq(h->X,v3);
fe_mul(h->X,h->X,v);
fe_mul(h->X,h->X,u); /* x = uv^7 */
fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
fe_mul(h->X,h->X,v3);
fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */
fe_sq(vxx,h->X);
fe_mul(vxx,vxx,v);
fe_sub(check,vxx,u); /* vx^2-u */
if (fe_isnonzero(check)) {
fe_add(check,vxx,u); /* vx^2+u */
if (fe_isnonzero(check)) return -1;
fe_mul(h->X,h->X,sqrtm1);
}
if (fe_isnegative(h->X) == (s[31] >> 7))
fe_neg(h->X,h->X);
fe_mul(h->T,h->X,h->Y);
return 0;
}
/*
r = p + q
*/
void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
fe t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->yplusx);
fe_mul(r->Y,r->Y,q->yminusx);
fe_mul(r->T,q->xy2d,p->T);
fe_add(t0,p->Z,p->Z);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_add(r->Z,t0,r->T);
fe_sub(r->T,t0,r->T);
}
/*
r = p - q
*/
void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
fe t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->yminusx);
fe_mul(r->Y,r->Y,q->yplusx);
fe_mul(r->T,q->xy2d,p->T);
fe_add(t0,p->Z,p->Z);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_sub(r->Z,t0,r->T);
fe_add(r->T,t0,r->T);
}
/*
r = p
*/
extern void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
{
fe_mul(r->X,p->X,p->T);
fe_mul(r->Y,p->Y,p->Z);
fe_mul(r->Z,p->Z,p->T);
}
/*
r = p
*/
extern void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
{
fe_mul(r->X,p->X,p->T);
fe_mul(r->Y,p->Y,p->Z);
fe_mul(r->Z,p->Z,p->T);
fe_mul(r->T,p->X,p->Y);
}
void ge_p2_0(ge_p2 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
}
/*
r = 2 * p
*/
void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
{
fe t0;
fe_sq(r->X,p->X);
fe_sq(r->Z,p->Y);
fe_sq2(r->T,p->Z);
fe_add(r->Y,p->X,p->Y);
fe_sq(t0,r->Y);
fe_add(r->Y,r->Z,r->X);
fe_sub(r->Z,r->Z,r->X);
fe_sub(r->X,t0,r->Y);
fe_sub(r->T,r->T,r->Z);
}
void ge_p3_0(ge_p3 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
fe_0(h->T);
}
/*
r = 2 * p
*/
void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p)
{
ge_p2 q;
ge_p3_to_p2(&q,p);
ge_p2_dbl(r,&q);
}
/*
r = p
*/
static const fe d2 = {
-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199
} ;
extern void ge_p3_to_cached(ge_cached *r,const ge_p3 *p)
{
fe_add(r->YplusX,p->Y,p->X);
fe_sub(r->YminusX,p->Y,p->X);
fe_copy(r->Z,p->Z);
fe_mul(r->T2d,p->T,d2);
}
/*
r = p
*/
extern void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p)
{
fe_copy(r->X,p->X);
fe_copy(r->Y,p->Y);
fe_copy(r->Z,p->Z);
}
void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
{
fe recip;
fe x;
fe y;
fe_invert(recip,h->Z);
fe_mul(x,h->X,recip);
fe_mul(y,h->Y,recip);
fe_tobytes(s,y);
s[31] ^= fe_isnegative(x) << 7;
}
void ge_precomp_0(ge_precomp *h)
{
fe_1(h->yplusx);
fe_1(h->yminusx);
fe_0(h->xy2d);
}
static unsigned char equal(signed char b,signed char c)
{
unsigned char ub = b;
unsigned char uc = c;
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
uint32_t y = x; /* 0: yes; 1..255: no */
y -= 1; /* 4294967295: yes; 0..254: no */
y >>= 31; /* 1: yes; 0: no */
return y;
}
static unsigned char negative(signed char b)
{
unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
x >>= 63; /* 1: yes; 0: no */
return x;
}
static void ge_precomp_cmov(ge_precomp *t,ge_precomp *u,unsigned char b)
{
fe_cmov(t->yplusx,u->yplusx,b);
fe_cmov(t->yminusx,u->yminusx,b);
fe_cmov(t->xy2d,u->xy2d,b);
}
/* base[i][j] = (j+1)*256^i*B */
static ge_precomp base[32][8] = {
{
{
{ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
{ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
{ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
{ -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 },
{ -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 },
{ 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 },
},
{
{ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
{ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
{ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
{ -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 },
{ 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 },
{ 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 },
},
{
{ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
{ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
{ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
{ -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 },
{ -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 },
{ -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 },
},
{
{ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
{ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
{ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
{ 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 },
{ -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 },
{ 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 },
},
},
{
{
{ -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 },
{ 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 },
{ 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 },
},
{
{ -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 },
{ 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 },
{ 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 },
},
{
{ -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 },
{ 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 },
{ 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 },
},
{
{ -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 },
{ -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 },
{ -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 },
},
{
{ 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 },
{ 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 },
{ 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 },
},
{
{ -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 },
{ -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 },
{ -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 },
},
{
{ 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 },
{ -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 },
{ -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 },
},
{
{ 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 },
{ 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 },
{ 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 },
},
},
{
{
{ 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 },
{ 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 },
{ -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 },
},
{
{ 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 },
{ -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 },
{ -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 },
},
{
{ -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 },
{ 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 },
{ 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 },
},
{
{ -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 },
{ 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 },
{ 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 },
},
{
{ -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 },
{ 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 },
{ -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 },
},
{
{ -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 },
{ -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 },
{ 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 },
},
{
{ 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 },
{ -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 },
{ -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 },
},
{
{ 31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060 },
{ 11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608 },
{ -20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606 },
},
},
{
{
{ 7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389 },
{ -19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016 },
{ -11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341 },
},
{
{ -22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505 },
{ 14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553 },
{ -28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655 },
},
{
{ 15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220 },
{ 12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631 },
{ -4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099 },
},
{
{ 26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556 },
{ 14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749 },
{ 236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930 },
},
{
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{ -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
{ -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
{ -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
},
{
{ -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 },
{ 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 },
{ -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
},
},
} ;
static void select(ge_precomp *t,int pos,signed char b)
{
ge_precomp minust;
unsigned char bnegative = negative(b);
unsigned char babs = b - (((-bnegative) & b) << 1);
ge_precomp_0(t);
ge_precomp_cmov(t,&base[pos][0],equal(babs,1));
ge_precomp_cmov(t,&base[pos][1],equal(babs,2));
ge_precomp_cmov(t,&base[pos][2],equal(babs,3));
ge_precomp_cmov(t,&base[pos][3],equal(babs,4));
ge_precomp_cmov(t,&base[pos][4],equal(babs,5));
ge_precomp_cmov(t,&base[pos][5],equal(babs,6));
ge_precomp_cmov(t,&base[pos][6],equal(babs,7));
ge_precomp_cmov(t,&base[pos][7],equal(babs,8));
fe_copy(minust.yplusx,t->yminusx);
fe_copy(minust.yminusx,t->yplusx);
fe_neg(minust.xy2d,t->xy2d);
ge_precomp_cmov(t,&minust,bnegative);
}
/*
h = a * B
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.
Preconditions:
a[31] <= 127
*/
void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
{
signed char e[64];
signed char carry;
ge_p1p1 r;
ge_p2 s;
ge_precomp t;
int i;
for (i = 0; i < 32; ++i) {
e[2 * i + 0] = (a[i] >> 0) & 15;
e[2 * i + 1] = (a[i] >> 4) & 15;
}
/* each e[i] is between 0 and 15 */
/* e[63] is between 0 and 7 */
carry = 0;
for (i = 0; i < 63; ++i) {
e[i] += carry;
carry = e[i] + 8;
carry >>= 4;
e[i] -= carry << 4;
}
e[63] += carry;
/* each e[i] is between -8 and 8 */
ge_p3_0(h);
for (i = 1; i < 64; i += 2) {
select(&t,i / 2,e[i]);
ge_madd(&r,h,&t);
ge_p1p1_to_p3(h,&r);
}
ge_p3_dbl(&r,h);
ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s);
ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s);
ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s);
ge_p1p1_to_p3(h,&r);
for (i = 0; i < 64; i += 2) {
select(&t,i / 2,e[i]);
ge_madd(&r,h,&t);
ge_p1p1_to_p3(h,&r);
}
}
/*
r = p - q
*/
void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
fe t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->YminusX);
fe_mul(r->Y,r->Y,q->YplusX);
fe_mul(r->T,q->T2d,p->T);
fe_mul(r->X,p->Z,q->Z);
fe_add(t0,r->X,r->X);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_sub(r->Z,t0,r->T);
fe_add(r->T,t0,r->T);
}
void ge_tobytes(unsigned char *s,const ge_p2 *h)
{
fe recip;
fe x;
fe y;
fe_invert(recip,h->Z);
fe_mul(x,h->X,recip);
fe_mul(y,h->Y,recip);
fe_tobytes(s,y);
s[31] ^= fe_isnegative(x) << 7;
}
/*
*
* xmr specific code
*
*
This code is from the original CryptoNote.
Some additional functions were needed to compute ring signatures
which are not needed for signing.
Note that sc_sub and sc_mulsub have been given their own file
since these have been rewritten
*/
/*Code inherited from the original cryptonote (I didn't write these) */
/*These functions either don't exist in, or are modified from ref10*/
/* From fe_isnonzero.c, modified */
//x
static int fe_isnonzero(const fe f) {
unsigned char s[32];
fe_tobytes(s, f);
return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
}
//double scalar mult precomp
void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) {
ge_p1p1 t;
ge_p3 s2, u;
ge_p3_to_cached(&r[0], s);
ge_p3_dbl(&t, s);
ge_p1p1_to_p3(&s2, &t);
ge_add(&t, &s2, &r[0]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[1], &u);
ge_add(&t, &s2, &r[1]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[2], &u);
ge_add(&t, &s2, &r[2]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[3], &u);
ge_add(&t, &s2, &r[3]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[4], &u);
ge_add(&t, &s2, &r[4]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[5], &u);
ge_add(&t, &s2, &r[5]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[6], &u);
ge_add(&t, &s2, &r[6]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&r[7], &u);
}
/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/
void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
signed char aslide[256];
signed char bslide[256];
ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */
ge_p1p1 t;
ge_p3 u;
int i;
slide(aslide, a);
slide(bslide, b);
ge_dsm_precomp(Ai, A);/* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */
ge_p2_0(r);
for (i = 255; i >= 0; --i) {
//so this gets us to the highest i such that both have a nonzero
if (aslide[i] || bslide[i]) break;
}
for (; i >= 0; --i) {
ge_p2_dbl(&t, r);//simple double and add
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Ai[aslide[i]/2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
}
if (bslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_madd(&t, &u, &ge_Bi[bslide[i]/2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]);
}
ge_p1p1_to_p2(r, &t);
}
}
/* From ge_frombytes.c, modified */
//this is like xrecover ..
//x
int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) {
fe u;
fe v;
fe vxx;
fe check;
/* From fe_frombytes.c */
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = (load_3(s + 29) & 8388607) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
/* Validate the number to be canonical */
if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 &&
h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 &&
h1 == 1073741760 && h0 >= 4294967277) {
return -1;
}
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
h->Y[0] = h0;
h->Y[1] = h1;
h->Y[2] = h2;
h->Y[3] = h3;
h->Y[4] = h4;
h->Y[5] = h5;
h->Y[6] = h6;
h->Y[7] = h7;
h->Y[8] = h8;
h->Y[9] = h9;
/* End fe_frombytes.c */
fe_1(h->Z);
fe_sq(u, h->Y);
fe_mul(v, u, fe_d);
fe_sub(u, u, h->Z); /* u = y^2-1 */
fe_add(v, v, h->Z); /* v = dy^2+1 */
fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */
fe_sq(vxx, h->X);
fe_mul(vxx, vxx, v);
fe_sub(check, vxx, u); /* vx^2-u */
if (fe_isnonzero(check)) {
fe_add(check, vxx, u); /* vx^2+u */
if (fe_isnonzero(check)) {
return -1;
}
fe_mul(h->X, h->X, fe_sqrtm1); //this is mapping X to X * sqrt(-1) c.f. 3.1 in hisil, dong, etc.
}
if (fe_isnegative(h->X) != (s[31] >> 7)) {
/* If x = 0, the sign must be positive */
if (!fe_isnonzero(h->X)) {
return -1;
}
fe_neg(h->X, h->X);
}
fe_mul(h->T, h->X, h->Y);
return 0;
}
/* New code */
/* (u / v)^(m + 1) */
static void fe_divpowm1(fe r, const fe u, const fe v) {
fe v3, uv7, t0, t1, t2;
int i;
fe_sq(v3, v);
fe_mul(v3, v3, v); /* v3 = v^3 */
fe_sq(uv7, v3);
fe_mul(uv7, uv7, v);
fe_mul(uv7, uv7, u); /* uv7 = uv^7 */
/*fe_pow22523(uv7, uv7);*/
/* From fe_pow22523.c */
fe_sq(t0, uv7);
fe_sq(t1, t0);
fe_sq(t1, t1);
fe_mul(t1, uv7, t1);
fe_mul(t0, t0, t1);
fe_sq(t0, t0);
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 0; i < 4; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 0; i < 9; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, t1, t0);
fe_sq(t2, t1);
for (i = 0; i < 19; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
for (i = 0; i < 10; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 0; i < 49; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, t1, t0);
fe_sq(t2, t1);
for (i = 0; i < 99; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
for (i = 0; i < 50; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t0, t0);
fe_sq(t0, t0);
fe_mul(t0, t0, uv7);
/* End fe_pow22523.c */
/* t0 = (uv^7)^((q-5)/8) */
fe_mul(t0, t0, v3);
fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */
}
static void ge_cached_0(ge_cached *r) {
fe_1(r->YplusX);
fe_1(r->YminusX);
fe_1(r->Z);
fe_0(r->T2d);
}
static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char b) {
fe_cmov(t->YplusX, u->YplusX, b);
fe_cmov(t->YminusX, u->YminusX, b);
fe_cmov(t->Z, u->Z, b);
fe_cmov(t->T2d, u->T2d, b);
}
/* Assumes that a[31] <= 127 */
void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) {
signed char e[64];
int carry, carry2, i;
ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */
ge_p1p1 t;
ge_p3 u;
carry = 0; /* 0..1 */
for (i = 0; i < 31; i++) {
carry += a[i]; /* 0..256 */
carry2 = (carry + 8) >> 4; /* 0..16 */
e[2 * i] = carry - (carry2 << 4); /* -8..7 */
carry = (carry2 + 8) >> 4; /* 0..1 */
e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */
}
carry += a[31]; /* 0..128 */
carry2 = (carry + 8) >> 4; /* 0..8 */
e[62] = carry - (carry2 << 4); /* -8..7 */
e[63] = carry2; /* 0..8 */
ge_p3_to_cached(&Ai[0], A);
for (i = 0; i < 7; i++) {
ge_add(&t, A, &Ai[i]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[i + 1], &u);
}
ge_p2_0(r);
for (i = 63; i >= 0; i--) {
signed char b = e[i];
unsigned char bnegative = negative(b);
unsigned char babs = b - (((-bnegative) & b) << 1);
ge_cached cur, minuscur;
ge_p2_dbl(&t, r);
ge_p1p1_to_p2(r, &t);
ge_p2_dbl(&t, r);
ge_p1p1_to_p2(r, &t);
ge_p2_dbl(&t, r);
ge_p1p1_to_p2(r, &t);
ge_p2_dbl(&t, r);
ge_p1p1_to_p3(&u, &t);
ge_cached_0(&cur);
ge_cached_cmov(&cur, &Ai[0], equal(babs, 1));
ge_cached_cmov(&cur, &Ai[1], equal(babs, 2));
ge_cached_cmov(&cur, &Ai[2], equal(babs, 3));
ge_cached_cmov(&cur, &Ai[3], equal(babs, 4));
ge_cached_cmov(&cur, &Ai[4], equal(babs, 5));
ge_cached_cmov(&cur, &Ai[5], equal(babs, 6));
ge_cached_cmov(&cur, &Ai[6], equal(babs, 7));
ge_cached_cmov(&cur, &Ai[7], equal(babs, 8));
fe_copy(minuscur.YplusX, cur.YminusX);
fe_copy(minuscur.YminusX, cur.YplusX);
fe_copy(minuscur.Z, cur.Z);
fe_neg(minuscur.T2d, cur.T2d);
ge_cached_cmov(&cur, &minuscur, bnegative);
ge_add(&t, &u, &cur);
ge_p1p1_to_p2(r, &t);
}
}
//assume Bi has precomputed multiples
void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bii) {
signed char aslide[256];
signed char bslide[256];
ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ //precomps
ge_p1p1 t;
ge_p3 u;
int i;
slide(aslide, a);
slide(bslide, b);
ge_dsm_precomp(Ai, A);
ge_p2_0(r);
for (i = 255; i >= 0; --i) {
if (aslide[i] || bslide[i]) break;
}
for (; i >= 0; --i) {
ge_p2_dbl(&t, r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Ai[aslide[i]/2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
}
if (bslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Bii[bslide[i]/2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Bii[(-bslide[i])/2]);
}
ge_p1p1_to_p2(r, &t);
}
}
//x
void ge_mul8(ge_p1p1 *r, const ge_p2 *t) {
ge_p2 u;
ge_p2_dbl(r, t);
ge_p1p1_to_p2(&u, r);
ge_p2_dbl(r, &u);
ge_p1p1_to_p2(&u, r);
ge_p2_dbl(r, &u);
}
//x
void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) {
fe u, v, w, x, y, z;
unsigned char sign;
/* From fe_frombytes.c */
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = load_3(s + 29) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
u[0] = h0;
u[1] = h1;
u[2] = h2;
u[3] = h3;
u[4] = h4;
u[5] = h5;
u[6] = h6;
u[7] = h7;
u[8] = h8;
u[9] = h9;
/* End fe_frombytes.c */
fe_sq2(v, u); /* 2 * u^2 */
fe_1(w);
fe_add(w, v, w); /* w = 2 * u^2 + 1 */
fe_sq(x, w); /* w^2 */
fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */
fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */
fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */
fe_sq(y, r->X);
fe_mul(x, y, x);
fe_sub(y, w, x);
fe_copy(z, fe_ma);
if (fe_isnonzero(y)) {
fe_add(y, w, x);
if (fe_isnonzero(y)) {
goto negative;
} else {
fe_mul(r->X, r->X, fe_fffb1);
}
} else {
fe_mul(r->X, r->X, fe_fffb2);
}
fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */
fe_mul(z, z, v); /* -2 * A * u^2 */
sign = 0;
goto setsign;
negative:
fe_mul(x, x, fe_sqrtm1);
fe_sub(y, w, x);
if (fe_isnonzero(y)) {
assert((fe_add(y, w, x), !fe_isnonzero(y)));
fe_mul(r->X, r->X, fe_fffb3);
} else {
fe_mul(r->X, r->X, fe_fffb4);
}
/* r->X = sqrt(A * (A + 2) * w / x) */
/* z = -A */
sign = 1;
setsign:
if (fe_isnegative(r->X) != sign) {
assert(fe_isnonzero(r->X));
fe_neg(r->X, r->X);
}
fe_add(r->Z, z, w);
fe_sub(r->Y, z, w);
fe_mul(r->X, r->X, r->Z);
#if !defined(NDEBUG)
{
fe check_x, check_y, check_iz, check_v;
fe_invert(check_iz, r->Z);
fe_mul(check_x, r->X, check_iz);
fe_mul(check_y, r->Y, check_iz);
fe_sq(check_x, check_x);
fe_sq(check_y, check_y);
fe_mul(check_v, check_x, check_y);
fe_mul(check_v, fe_d, check_v);
fe_add(check_v, check_v, check_x);
fe_sub(check_v, check_v, check_y);
fe_1(check_x);
fe_add(check_v, check_v, check_x);
assert(!fe_isnonzero(check_v));
}
#endif
}
//x
void sc_0(unsigned char *s) {
int i;
for (i = 0; i < 32; i++) {
s[i] = 0;
}
}
//x
void sc_reduce32(unsigned char *s) {
int64_t s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = (load_4(s + 28) >> 7);
int64_t s12 = 0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
//x
void sc_reduce32copy(unsigned char * scopy, const unsigned char *s) {
int64_t s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = (load_4(s + 28) >> 7);
int64_t s12 = 0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
scopy[0] = s0 >> 0;
scopy[1] = s0 >> 8;
scopy[2] = (s0 >> 16) | (s1 << 5);
scopy[3] = s1 >> 3;
scopy[4] = s1 >> 11;
scopy[5] = (s1 >> 19) | (s2 << 2);
scopy[6] = s2 >> 6;
scopy[7] = (s2 >> 14) | (s3 << 7);
scopy[8] = s3 >> 1;
scopy[9] = s3 >> 9;
scopy[10] = (s3 >> 17) | (s4 << 4);
scopy[11] = s4 >> 4;
scopy[12] = s4 >> 12;
scopy[13] = (s4 >> 20) | (s5 << 1);
scopy[14] = s5 >> 7;
scopy[15] = (s5 >> 15) | (s6 << 6);
scopy[16] = s6 >> 2;
scopy[17] = s6 >> 10;
scopy[18] = (s6 >> 18) | (s7 << 3);
scopy[19] = s7 >> 5;
scopy[20] = s7 >> 13;
scopy[21] = s8 >> 0;
scopy[22] = s8 >> 8;
scopy[23] = (s8 >> 16) | (s9 << 5);
scopy[24] = s9 >> 3;
scopy[25] = s9 >> 11;
scopy[26] = (s9 >> 19) | (s10 << 2);
scopy[27] = s10 >> 6;
scopy[28] = (s10 >> 14) | (s11 << 7);
scopy[29] = s11 >> 1;
scopy[30] = s11 >> 9;
scopy[31] = s11 >> 17;
}
//x
void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) {
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t s0 = a0 + b0;
int64_t s1 = a1 + b1;
int64_t s2 = a2 + b2;
int64_t s3 = a3 + b3;
int64_t s4 = a4 + b4;
int64_t s5 = a5 + b5;
int64_t s6 = a6 + b6;
int64_t s7 = a7 + b7;
int64_t s8 = a8 + b8;
int64_t s9 = a9 + b9;
int64_t s10 = a10 + b10;
int64_t s11 = a11 + b11;
int64_t s12 = 0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 << 5);
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 << 2);
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 << 7);
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 << 4);
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 << 1);
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 << 6);
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 << 3);
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 << 5);
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 << 2);
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 << 7);
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/* Assumes that a != INT64_MIN */
//x c.f. lt in 32 bit ref
static int64_t signum(int64_t a) {
return (a >> 63) - ((-a) >> 63);
}
//x
int sc_check(const unsigned char *s) {
int64_t s0 = load_4(s);
int64_t s1 = load_4(s + 4);
int64_t s2 = load_4(s + 8);
int64_t s3 = load_4(s + 12);
int64_t s4 = load_4(s + 16);
int64_t s5 = load_4(s + 20);
int64_t s6 = load_4(s + 24);
int64_t s7 = load_4(s + 28);
return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8;
}
//x
int sc_isnonzero(const unsigned char *s) {
return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
}
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