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MastersThesis/PQ_TIIGER_TLS/sal/miracl-ubuntu22-11-04-24/includes/big.cpp

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update tiigertls
2024-04-15 09:53:30 +00:00
/*
* Copyright (c) 2012-2020 MIRACL UK Ltd.
*
* This file is part of MIRACL Core
* (see https://github.com/miracl/core).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* CORE basic functions for BIG type */
/* SU=m, SU is Stack Usage */
#include "big_XXX.h"
//int XXX::BIGMULS=0;
//int XXX::BIGSQRS=0;
/* test a=0? */
int XXX::BIG_iszilch(BIG a)
{
int i;
chunk d=0;
for (i = 0; i < NLEN_XXX; i++)
d|=a[i];
return (1 & ((d-1)>>BASEBITS_XXX));
}
/* test a=1? */
int XXX::BIG_isunity(BIG a)
{
int i;
chunk d=0;
for (i = 1; i < NLEN_XXX; i++)
d|=a[i];
return (1 & ((d-1)>>BASEBITS_XXX) & (((a[0]^1)-1)>>BASEBITS_XXX));
}
/* test a=0? */
int XXX::BIG_diszilch(DBIG a)
{
int i;
chunk d=0;
for (i = 0; i < DNLEN_XXX; i++)
d|=a[i];
return (1 & ((d-1)>>BASEBITS_XXX));
}
/* SU= 56 */
/* output a */
void XXX::BIG_output(BIG a)
{
BIG b;
int i, len;
len = BIG_nbits(a);
if (len % 4 == 0) len /= 4;
else
{
len /= 4;
len++;
}
if (len < MODBYTES_XXX * 2) len = MODBYTES_XXX * 2;
for (i = len - 1; i >= 0; i--)
{
BIG_copy(b, a);
BIG_shr(b, i * 4);
printf("%01x", (unsigned int) b[0] & 15);
}
}
/* SU= 16 */
void XXX::BIG_rawoutput(BIG a)
{
int i;
printf("(");
for (i = 0; i < NLEN_XXX - 1; i++)
#if CHUNK==64
printf("%jx,", (uintmax_t) a[i]);
printf("%jx)", (uintmax_t) a[NLEN_XXX - 1]);
#else
printf("%x,", (unsigned int) a[i]);
printf("%x)", (unsigned int) a[NLEN_XXX - 1]);
#endif
}
// modified to prevent Nonce@Once side channel attack
// Two tricks to thwart compiler optimization
// 1. Prevent mask removal by performing transformation that might change the mask, but in fact does not
// 2. Force the code to calculate an intermediate value, by making it part of (an unused) return value
// problem is XORing with all zeros or XORing with "random" shows up in side-channel, and reveals d
/* Swap a and b if d=1 */
chunk XXX::BIG_cswap(BIG a, BIG b, int d)
{
int i;
chunk e, r, ra, w, t, c = (chunk) - d;
w=0;
r=a[0]^b[1]; // sort of random
ra=r+r; ra>>=1; // I know this doesn't change r, but the compiler doesn't!
#ifdef DEBUG_NORM
for (i = 0; i < NLEN_XXX + 2; i++)
#else
for (i = 0; i < NLEN_XXX; i++)
#endif
{
t = c & (a[i] ^ b[i]);
t^=r;
e=a[i]^t; w^=e; // to force calculation of e
a[i]=e^ra;
e=b[i]^t; w^=e;
b[i]=e^ra;
}
return w; // to bewilder optimizer
}
/* Move g to f if d=1 */
chunk XXX::BIG_cmove(BIG f, BIG g, int d)
{
int i;
chunk e,w,r,ra,t,b = (chunk) - d;
w=0;
r=f[0]^g[1];
ra=r+r; ra>>=1; // I know this doesn't change r, but the compiler doesn't!
#ifdef DEBUG_NORM
for (i = 0; i < NLEN_XXX + 2; i++)
#else
for (i = 0; i < NLEN_XXX; i++)
#endif
{
t=(f[i]^g[i])&b;
t^=r;
e=f[i]^t; w^=e; // to force calculation of e
f[i]=e^ra;
}
return w; // to bewilder optimizer
}
/* Move g to f if d=1 */
chunk XXX::BIG_dcmove(DBIG f, DBIG g, int d)
{
int i;
chunk e,w,r,ra,t,b = (chunk) - d;
w=0;
r=f[0]^g[1];
ra=r+r; ra>>=1; // I know this doesn't change r, but the compiler doesn't!
#ifdef DEBUG_NORM
for (i = 0; i < DNLEN_XXX + 2; i++)
#else
for (i = 0; i < DNLEN_XXX; i++)
#endif
{
t=(f[i]^g[i])&b;
t^=r;
e=f[i]^t; w^=e;
f[i]=e^ra;
}
return w;
}
/* convert BIG to/from bytes */
/* SU= 64 */
void XXX::BIG_toBytes(char *b, BIG a)
{
int i;
BIG c;
BIG_copy(c, a);
BIG_norm(c);
for (i = MODBYTES_XXX - 1; i >= 0; i--)
{
b[i] = c[0] & 0xff;
BIG_fshr(c, 8);
}
}
/* SU= 16 */
void XXX::BIG_fromBytes(BIG a, char *b)
{
int i;
BIG_zero(a);
for (i = 0; i < MODBYTES_XXX; i++)
{
BIG_fshl(a, 8);
a[0] += (int)(unsigned char)b[i];
}
#ifdef DEBUG_NORM
a[MPV_XXX] = 1; a[MNV_XXX] = 0;
#endif
}
void XXX::BIG_fromBytesLen(BIG a, char *b, int s)
{
int i, len = s;
BIG_zero(a);
if (len > MODBYTES_XXX) len = MODBYTES_XXX;
for (i = 0; i < len; i++)
{
BIG_fshl(a, 8);
a[0] += (int)(unsigned char)b[i];
}
#ifdef DEBUG_NORM
a[MPV_XXX] = 1; a[MNV_XXX] = 0;
#endif
}
/* SU= 88 */
void XXX::BIG_doutput(DBIG a)
{
DBIG b;
int i, len;
BIG_dnorm(a);
len = BIG_dnbits(a);
if (len % 4 == 0) len /= 4;
else
{
len /= 4;
len++;
}
for (i = len - 1; i >= 0; i--)
{
BIG_dcopy(b, a);
BIG_dshr(b, i * 4);
printf("%01x", (unsigned int) b[0] & 15);
}
}
void XXX::BIG_drawoutput(DBIG a)
{
int i;
printf("(");
for (i = 0; i < DNLEN_XXX - 1; i++)
#if CHUNK==64
printf("%jx,", (uintmax_t) a[i]);
printf("%jx)", (uintmax_t) a[DNLEN_XXX - 1]);
#else
printf("%x,", (unsigned int) a[i]);
printf("%x)", (unsigned int) a[DNLEN_XXX - 1]);
#endif
}
/* Copy b=a */
void XXX::BIG_copy(BIG b, BIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
b[i] = a[i];
#ifdef DEBUG_NORM
b[MPV_XXX] = a[MPV_XXX];
b[MNV_XXX] = a[MNV_XXX];
#endif
}
/* Copy from ROM b=a */
void XXX::BIG_rcopy(BIG b, const BIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
b[i] = a[i];
#ifdef DEBUG_NORM
b[MPV_XXX] = 1; b[MNV_XXX] = 0;
#endif
}
/* double length DBIG copy b=a */
void XXX::BIG_dcopy(DBIG b, DBIG a)
{
int i;
for (i = 0; i < DNLEN_XXX; i++)
b[i] = a[i];
#ifdef DEBUG_NORM
b[DMPV_XXX] = a[DMPV_XXX];
b[DMNV_XXX] = a[DMNV_XXX];
#endif
}
/* Copy BIG to bottom half of DBIG */
void XXX::BIG_dscopy(DBIG b, BIG a)
{
int i;
for (i = 0; i < NLEN_XXX - 1; i++)
b[i] = a[i];
b[NLEN_XXX - 1] = a[NLEN_XXX - 1] & BMASK_XXX; /* top word normalized */
b[NLEN_XXX] = a[NLEN_XXX - 1] >> BASEBITS_XXX;
for (i = NLEN_XXX + 1; i < DNLEN_XXX; i++) b[i] = 0;
#ifdef DEBUG_NORM
b[DMPV_XXX] = a[MPV_XXX];
b[DMNV_XXX] = a[MNV_XXX];
#endif
}
/* Copy BIG to top half of DBIG */
void XXX::BIG_dsucopy(DBIG b, BIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
b[i] = 0;
for (i = NLEN_XXX; i < DNLEN_XXX; i++)
b[i] = a[i - NLEN_XXX];
#ifdef DEBUG_NORM
b[DMPV_XXX] = a[MPV_XXX];
b[DMNV_XXX] = a[MNV_XXX];
#endif
}
/* Copy bottom half of DBIG to BIG */
void XXX::BIG_sdcopy(BIG b, DBIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
b[i] = a[i];
#ifdef DEBUG_NORM
b[MPV_XXX] = a[DMPV_XXX];
b[MNV_XXX] = a[DMNV_XXX];
#endif
}
/* Copy top half of DBIG to BIG */
void XXX::BIG_sducopy(BIG b, DBIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
b[i] = a[i + NLEN_XXX];
#ifdef DEBUG_NORM
b[MPV_XXX] = a[DMPV_XXX];
b[MNV_XXX] = a[DMNV_XXX];
#endif
}
/* Set a=0 */
void XXX::BIG_zero(BIG a)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
a[i] = 0;
#ifdef DEBUG_NORM
a[MPV_XXX] = a[MNV_XXX] = 0;
#endif
}
void XXX::BIG_dzero(DBIG a)
{
int i;
for (i = 0; i < DNLEN_XXX; i++)
a[i] = 0;
#ifdef DEBUG_NORM
a[DMPV_XXX] = a[DMNV_XXX] = 0;
#endif
}
/* set a=1 */
void XXX::BIG_one(BIG a)
{
int i;
a[0] = 1;
for (i = 1; i < NLEN_XXX; i++)
a[i] = 0;
#ifdef DEBUG_NORM
a[MPV_XXX] = 1;
a[MNV_XXX] = 0;
#endif
}
/* Set c=a+b */
/* SU= 8 */
void XXX::BIG_add(BIG c, BIG a, BIG b)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
c[i] = a[i] + b[i];
#ifdef DEBUG_NORM
c[MPV_XXX] = a[MPV_XXX] + b[MPV_XXX];
c[MNV_XXX] = a[MNV_XXX] + b[MNV_XXX];
if (c[MPV_XXX] > NEXCESS_XXX) printf("add problem - positive digit overflow %d\n", (int)c[MPV_XXX]);
if (c[MNV_XXX] > NEXCESS_XXX) printf("add problem - negative digit overflow %d\n", (int)c[MNV_XXX]);
#endif
}
/* Set c=a or b */
/* SU= 8 */
void XXX::BIG_or(BIG c, BIG a, BIG b)
{
int i;
BIG_norm(a);
BIG_norm(b);
for (i = 0; i < NLEN_XXX; i++)
c[i] = a[i] | b[i];
#ifdef DEBUG_NORM
c[MPV_XXX] = 1;
c[MNV_XXX] = 0;
#endif
}
/* Set c=c+d */
void XXX::BIG_inc(BIG c, int d)
{
BIG_norm(c);
c[0] += (chunk)d;
#ifdef DEBUG_NORM
c[MPV_XXX] += 1;
#endif
}
/* Set c=a-b */
/* SU= 8 */
void XXX::BIG_sub(BIG c, BIG a, BIG b)
{
int i;
for (i = 0; i < NLEN_XXX; i++)
c[i] = a[i] - b[i];
#ifdef DEBUG_NORM
c[MPV_XXX] = a[MPV_XXX] + b[MNV_XXX];
c[MNV_XXX] = a[MNV_XXX] + b[MPV_XXX];
if (c[MPV_XXX] > NEXCESS_XXX) printf("sub problem - positive digit overflow %d\n", (int)c[MPV_XXX]);
if (c[MNV_XXX] > NEXCESS_XXX) printf("sub problem - negative digit overflow %d\n", (int)c[MNV_XXX]);
#endif
}
/* SU= 8 */
void XXX::BIG_dsub(DBIG c, DBIG a, DBIG b)
{
int i;
for (i = 0; i < DNLEN_XXX; i++)
c[i] = a[i] - b[i];
#ifdef DEBUG_NORM
c[DMPV_XXX] = a[DMPV_XXX] + b[DMNV_XXX];
c[DMNV_XXX] = a[DMNV_XXX] + b[DMPV_XXX];
if (c[DMPV_XXX] > NEXCESS_XXX) printf("double sub problem - positive digit overflow %d\n", (int)c[DMPV_XXX]);
if (c[DMNV_XXX] > NEXCESS_XXX) printf("double sub problem - negative digit overflow %d\n", (int)c[DMNV_XXX]);
#endif
}
void XXX::BIG_dadd(DBIG c, DBIG a, DBIG b)
{
int i;
for (i = 0; i < DNLEN_XXX; i++)
c[i] = a[i] + b[i];
#ifdef DEBUG_NORM
c[DMPV_XXX] = a[DMPV_XXX] + b[DMNV_XXX];
c[DMNV_XXX] = a[DMNV_XXX] + b[DMPV_XXX];
if (c[DMPV_XXX] > NEXCESS_XXX) printf("double add problem - positive digit overflow %d\n", (int)c[DMPV_XXX]);
if (c[DMNV_XXX] > NEXCESS_XXX) printf("double add problem - negative digit overflow %d\n", (int)c[DMNV_XXX]);
#endif
}
/* Set c=c-1 */
void XXX::BIG_dec(BIG c, int d)
{
BIG_norm(c);
c[0] -= (chunk)d;
#ifdef DEBUG_NORM
c[MNV_XXX] += 1;
#endif
}
/* multiplication r=a*c by c<=NEXCESS_XXX */
void XXX::BIG_imul(BIG r, BIG a, int c)
{
int i;
for (i = 0; i < NLEN_XXX; i++) r[i] = a[i] * c;
#ifdef DEBUG_NORM
r[MPV_XXX] = a[MPV_XXX] * c;
r[MNV_XXX] = a[MNV_XXX] * c;
if (r[MPV_XXX] > NEXCESS_XXX) printf("int mul problem - positive digit overflow %d\n", (int)r[MPV_XXX]);
if (r[MNV_XXX] > NEXCESS_XXX) printf("int mul problem - negative digit overflow %d\n", (int)r[MNV_XXX]);
#endif
}
/* multiplication r=a*c by larger integer - c<=FEXCESS */
/* SU= 24 */
chunk XXX::BIG_pmul(BIG r, BIG a, int c)
{
int i;
chunk ak, carry = 0;
for (i = 0; i < NLEN_XXX; i++)
{
ak = a[i];
r[i] = 0;
carry = muladd(ak, (chunk)c, carry, &r[i]);
}
#ifdef DEBUG_NORM
r[MPV_XXX] = 1;
r[MNV_XXX] = 0;
#endif
return carry;
}
/* r/=3 */
/* SU= 16 */
/*
int XXX::BIG_div3(BIG r)
{
int i;
chunk ak,base,carry=0;
BIG_norm(r);
base=((chunk)1<<BASEBITS_XXX);
for (i=NLEN_XXX-1; i>=0; i--)
{
ak=(carry*base+r[i]);
r[i]=ak/3;
carry=ak%3;
}
return (int)carry;
}
*/
/* multiplication c=a*b by even larger integer b>FEXCESS, resulting in DBIG */
/* SU= 24 */
void XXX::BIG_pxmul(DBIG c, BIG a, int b)
{
int j;
chunk carry;
BIG_dzero(c);
carry = 0;
for (j = 0; j < NLEN_XXX; j++)
carry = muladd(a[j], (chunk)b, carry, &c[j]);
c[NLEN_XXX] = carry;
#ifdef DEBUG_NORM
c[DMPV_XXX] = 1;
c[DMNV_XXX] = 0;
#endif
}
/* .. if you know the result will fit in a BIG, c must be distinct from a and b */
/* SU= 40 */
void XXX::BIG_smul(BIG c, BIG a, BIG b)
{
int i, j;
chunk carry;
BIG_zero(c);
for (i = 0; i < NLEN_XXX; i++)
{
carry = 0;
for (j = 0; j < NLEN_XXX; j++)
{
if (i + j < NLEN_XXX)
carry = muladd(a[i], b[j], carry, &c[i + j]);
}
}
#ifdef DEBUG_NORM
c[MPV_XXX] = 1;
c[MNV_XXX] = 0;
#endif
}
/* Set c=a*b */
/* SU= 72 */
void XXX::BIG_mul(DBIG c, BIG a, BIG b)
{
int i,k;
#ifdef dchunk
dchunk co,t;
dchunk s;
dchunk d[NLEN_XXX];
int m;
#endif
//XXX::BIGMULS++;
#ifdef DEBUG_NORM
if ((a[MPV_XXX] != 1 && a[MPV_XXX] != 0) || a[MNV_XXX] != 0) printf("First input to mul not normed\n");
if ((b[MPV_XXX] != 1 && b[MPV_XXX] != 0) || b[MNV_XXX] != 0) printf("Second input to mul not normed\n");
#endif
/* Faster to Combafy it.. Let the compiler unroll the loops! */
#ifdef COMBA
/* faster psuedo-Karatsuba method */
#ifdef UNWOUND
#ifdef USE_KARATSUBA
INLINE_MUL2
#else
INLINE_MUL1
#endif
#else
#ifndef USE_KARATSUBA
t=(dchunk)a[0]*b[0];
c[0]=(chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
for (i=1;i<NLEN_XXX;i++)
{
k=0;
while (k<=i) {t+=(dchunk)a[k]*b[i-k]; k++;}
c[i]=(chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
}
for (i=NLEN_XXX;i<2*NLEN_XXX-1;i++)
{
k=i-(NLEN_XXX-1);
while (k<=NLEN_XXX-1) {t+=(dchunk)a[k]*b[i-k]; k++;}
c[i]=(chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
}
c[2 * NLEN_XXX - 1] = (chunk)t;
#else
for (i = 0; i < NLEN_XXX; i++)
d[i] = (dchunk)a[i] * b[i];
s = d[0];
t = s;
c[0] = (chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
for (k = 1; k < NLEN_XXX; k++)
{
s += d[k];
t += s;
/*for (i = k; i >= 1 + k / 2; i--) This causes a huge slow down! gcc/g++ optimizer problem (I think) */
for (i=1+k/2;i<=k;i++) t += (dchunk)(a[i] - a[k - i]) * (b[k - i] - b[i]);
c[k] = (chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
}
for (k = NLEN_XXX; k < 2 * NLEN_XXX - 1; k++)
{
s -= d[k - NLEN_XXX];
t += s;
for (i=1+k/2;i<NLEN_XXX;i++) t += (dchunk)(a[i] - a[k - i]) * (b[k - i] - b[i]);
c[k] = (chunk)t & BMASK_XXX;
t = t >> BASEBITS_XXX;
}
c[2 * NLEN_XXX - 1] = (chunk)t;
#endif
#endif
#else
int j;
chunk carry;
BIG_dzero(c);
for (i = 0; i < NLEN_XXX; i++)
{
carry = 0;
for (j = 0; j < NLEN_XXX; j++)
carry = muladd(a[i], b[j], carry, &c[i + j]);
c[NLEN_XXX + i] = carry;
}
#endif
#ifdef DEBUG_NORM
c[DMPV_XXX] = 1;
c[DMNV_XXX] = 0;
#endif
}
/* Set c=a*a */
/* SU= 80 */
void XXX::BIG_sqr(DBIG c, BIG a)
{
int i, j;
#ifdef dchunk
dchunk t, co;
#endif
//XXX::BIGSQRS++;
#ifdef DEBUG_NORM
if ((a[MPV_XXX] != 1 && a[MPV_XXX] != 0) || a[MNV_XXX] != 0) printf("Input to sqr not normed\n");
#endif
/* Note 2*a[i] in loop below and extra addition */
#ifdef COMBA
#ifdef UNWOUND
INLINE_SQR
#else
t = (dchunk)a[0] * a[0];
c[0] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
for (j = 1; j < NLEN_XXX - 1; )
{
t = (dchunk)a[j] * a[0];
for (i = 1; i < (j + 1) / 2; i++) {t += (dchunk)a[j - i] * a[i]; }
t += t; t += co;
c[j] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
j++;
t = (dchunk)a[j] * a[0];
for (i = 1; i < (j + 1) / 2; i++) {t += (dchunk)a[j - i] * a[i]; }
t += t; t += co;
t += (dchunk)a[j / 2] * a[j / 2];
c[j] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
j++;
}
for (j = NLEN_XXX - 1 + NLEN_XXX % 2; j < DNLEN_XXX - 3; )
{
t = (dchunk)a[NLEN_XXX - 1] * a[j - NLEN_XXX + 1];
for (i = j - NLEN_XXX + 2; i < (j + 1) / 2; i++) {t += (dchunk)a[j - i] * a[i]; }
t += t; t += co;
c[j] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
j++;
t = (dchunk)a[NLEN_XXX - 1] * a[j - NLEN_XXX + 1];
for (i = j - NLEN_XXX + 2; i < (j + 1) / 2; i++) {t += (dchunk)a[j - i] * a[i]; }
t += t; t += co;
t += (dchunk)a[j / 2] * a[j / 2];
c[j] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
j++;
}
t = (dchunk)a[NLEN_XXX - 2] * a[NLEN_XXX - 1];
t += t; t += co;
c[DNLEN_XXX - 3] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
t = (dchunk)a[NLEN_XXX - 1] * a[NLEN_XXX - 1] + co;
c[DNLEN_XXX - 2] = (chunk)t & BMASK_XXX;
co = t >> BASEBITS_XXX;
c[DNLEN_XXX - 1] = (chunk)co;
#endif
#else
chunk carry;
BIG_dzero(c);
for (i = 0; i < NLEN_XXX; i++)
{
carry = 0;
for (j = i + 1; j < NLEN_XXX; j++)
carry = muladd(a[i], a[j], carry, &c[i + j]);
c[NLEN_XXX + i] = carry;
}
for (i = 0; i < DNLEN_XXX; i++) c[i] *= 2;
for (i = 0; i < NLEN_XXX; i++)
c[2 * i + 1] += muladd(a[i], a[i], 0, &c[2 * i]);
BIG_dnorm(c);
#endif
#ifdef DEBUG_NORM
c[DMPV_XXX] = 1;
c[DMNV_XXX] = 0;
#endif
}
/* Montgomery reduction */
void XXX::BIG_monty(BIG a, BIG md, chunk MC, DBIG d)
{
int i, k;
#ifdef dchunk
dchunk c,t,s;
dchunk dd[NLEN_XXX];
chunk v[NLEN_XXX];
#endif
#ifdef DEBUG_NORM
if ((d[DMPV_XXX] != 1 && d[DMPV_XXX] != 0) || d[DMNV_XXX] != 0) printf("Input to redc not normed\n");
#endif
#ifdef COMBA
#ifdef UNWOUND
#ifdef USE_KARATSUBA
INLINE_REDC2
#else
INLINE_REDC1
#endif
#else
#ifndef USE_KARATSUBA
t = d[0];
v[0] = ((chunk)t * MC)&BMASK_XXX;
t += (dchunk)v[0] * md[0];
t = (t >> BASEBITS_XXX) + d[1];
for (i = 1; i < NLEN_XXX; i++)
{
k=1;
t += (dchunk)v[0] * md[i];
while (k<i) {t += (dchunk)v[k]*md[i-k]; k++;}
v[i] = ((chunk)t * MC)&BMASK_XXX;
t += (dchunk)v[i] * md[0];
t = (t >> BASEBITS_XXX) + d[i + 1];
}
for (i = NLEN_XXX; i < 2 * NLEN_XXX - 1; i++)
{
k=i-(NLEN_XXX-1);
while (k<=NLEN_XXX-1) {t += (dchunk)v[k]*md[i-k]; k++;}
a[i - NLEN_XXX] = (chunk)t & BMASK_XXX;
t = (t >> BASEBITS_XXX) + d[i + 1];
}
a[NLEN_XXX - 1] = (chunk)t & BMASK_XXX;
#else
t = d[0];
v[0] = ((chunk)t * MC)&BMASK_XXX;
t += (dchunk)v[0] * md[0];
t = (t >> BASEBITS_XXX) + d[1];
s = 0;
for (k = 1; k < NLEN_XXX; k++)
{
t = t + s + (dchunk)v[0] * md[k];
for (i=1+k/2;i<k;i++) t += (dchunk)(v[k - i] - v[i]) * (md[i] - md[k - i]);
v[k] = ((chunk)t * MC)&BMASK_XXX;
t += (dchunk)v[k] * md[0];
t = (t >> BASEBITS_XXX) + d[k + 1];
dd[k] = (dchunk)v[k] * md[k];
s += dd[k];
}
for (k = NLEN_XXX; k < 2 * NLEN_XXX - 1; k++)
{
t = t + s;
for (i=1+k/2;i<NLEN_XXX;i++) t += (dchunk)(v[k - i] - v[i]) * (md[i] - md[k - i]);
a[k - NLEN_XXX] = (chunk)t & BMASK_XXX;
t = (t >> BASEBITS_XXX) + d[k + 1];
s -= dd[k - NLEN_XXX + 1];
}
a[NLEN_XXX - 1] = (chunk)t & BMASK_XXX;
#endif
#endif
#else
int j;
chunk m, carry;
for (i = 0; i < NLEN_XXX; i++)
{
if (MC == -1) m = (-d[i])&BMASK_XXX;
else
{
if (MC == 1) m = d[i];
else m = (MC * d[i])&BMASK_XXX;
}
carry = 0;
for (j = 0; j < NLEN_XXX; j++)
carry = muladd(m, md[j], carry, &d[i + j]);
d[NLEN_XXX + i] += carry;
}
BIG_sducopy(a, d);
BIG_norm(a);
#endif
#ifdef DEBUG_NORM
a[MPV_XXX] = 1; a[MNV_XXX] = 0;
#endif
}
/* General shift left of a by n bits */
/* a MUST be normalised */
/* SU= 32 */
void XXX::BIG_shl(BIG a, int k)
{
int i;
int n = k % BASEBITS_XXX;
int m = k / BASEBITS_XXX;
a[NLEN_XXX - 1] = ((a[NLEN_XXX - 1 - m] << n));
if (NLEN_XXX >= m + 2) a[NLEN_XXX - 1] |= (a[NLEN_XXX - m - 2] >> (BASEBITS_XXX - n));
for (i = NLEN_XXX - 2; i > m; i--)
a[i] = ((a[i - m] << n)&BMASK_XXX) | (a[i - m - 1] >> (BASEBITS_XXX - n));
a[m] = (a[0] << n)&BMASK_XXX;
for (i = 0; i < m; i++) a[i] = 0;
}
/* Fast shift left of a by n bits, where n less than a word, Return excess (but store it as well) */
/* a MUST be normalised */
/* SU= 16 */
int XXX::BIG_fshl(BIG a, int n)
{
int i;
a[NLEN_XXX - 1] = ((a[NLEN_XXX - 1] << n)) | (a[NLEN_XXX - 2] >> (BASEBITS_XXX - n)); /* top word not masked */
for (i = NLEN_XXX - 2; i > 0; i--)
a[i] = ((a[i] << n)&BMASK_XXX) | (a[i - 1] >> (BASEBITS_XXX - n));
a[0] = (a[0] << n)&BMASK_XXX;
return (int)(a[NLEN_XXX - 1] >> ((8 * MODBYTES_XXX) % BASEBITS_XXX)); /* return excess - only used in ff.c */
}
/* double length left shift of a by k bits - k can be > BASEBITS_XXX , a MUST be normalised */
/* SU= 32 */
void XXX::BIG_dshl(DBIG a, int k)
{
int i;
int n = k % BASEBITS_XXX;
int m = k / BASEBITS_XXX;
a[DNLEN_XXX - 1] = ((a[DNLEN_XXX - 1 - m] << n)) | (a[DNLEN_XXX - m - 2] >> (BASEBITS_XXX - n));
for (i = DNLEN_XXX - 2; i > m; i--)
a[i] = ((a[i - m] << n)&BMASK_XXX) | (a[i - m - 1] >> (BASEBITS_XXX - n));
a[m] = (a[0] << n)&BMASK_XXX;
for (i = 0; i < m; i++) a[i] = 0;
}
/* General shift right of a by k bits */
/* a MUST be normalised */
/* SU= 32 */
void XXX::BIG_shr(BIG a, int k)
{
int i;
int n = k % BASEBITS_XXX;
int m = k / BASEBITS_XXX;
for (i = 0; i < NLEN_XXX - m - 1; i++)
a[i] = (a[m + i] >> n) | ((a[m + i + 1] << (BASEBITS_XXX - n))&BMASK_XXX);
if (NLEN_XXX > m) a[NLEN_XXX - m - 1] = a[NLEN_XXX - 1] >> n;
for (i = NLEN_XXX - m; i < NLEN_XXX; i++) a[i] = 0;
}
/* Fast combined shift, subtract and norm. Return sign of result */
int XXX::BIG_ssn(BIG r, BIG a, BIG m)
{
int i, n = NLEN_XXX - 1;
chunk carry;
m[0] = (m[0] >> 1) | ((m[1] << (BASEBITS_XXX - 1))&BMASK_XXX);
r[0] = a[0] - m[0];
carry = r[0] >> BASEBITS_XXX;
r[0] &= BMASK_XXX;
for (i = 1; i < n; i++)
{
m[i] = (m[i] >> 1) | ((m[i + 1] << (BASEBITS_XXX - 1))&BMASK_XXX);
r[i] = a[i] - m[i] + carry;
carry = r[i] >> BASEBITS_XXX;
r[i] &= BMASK_XXX;
}
m[n] >>= 1;
r[n] = a[n] - m[n] + carry;
#ifdef DEBUG_NORM
r[MPV_XXX] = 1; r[MNV_XXX] = 0;
#endif
return ((r[n] >> (CHUNK - 1)) & 1);
}
/* Faster shift right of a by k bits. Return shifted out part */
/* a MUST be normalised */
/* SU= 16 */
int XXX::BIG_fshr(BIG a, int k)
{
int i;
chunk r = a[0] & (((chunk)1 << k) - 1); /* shifted out part */
for (i = 0; i < NLEN_XXX - 1; i++)
a[i] = (a[i] >> k) | ((a[i + 1] << (BASEBITS_XXX - k))&BMASK_XXX);
a[NLEN_XXX - 1] = a[NLEN_XXX - 1] >> k;
return (int)r;
}
/* double length right shift of a by k bits - can be > BASEBITS_XXX */
/* SU= 32 */
void XXX::BIG_dshr(DBIG a, int k)
{
int i;
int n = k % BASEBITS_XXX;
int m = k / BASEBITS_XXX;
for (i = 0; i < DNLEN_XXX - m - 1; i++)
a[i] = (a[m + i] >> n) | ((a[m + i + 1] << (BASEBITS_XXX - n))&BMASK_XXX);
a[DNLEN_XXX - m - 1] = a[DNLEN_XXX - 1] >> n;
for (i = DNLEN_XXX - m; i < DNLEN_XXX; i++ ) a[i] = 0;
}
/* Split DBIG d into two BIGs t|b. Split happens at n bits, where n falls into NLEN_XXX word */
/* d MUST be normalised */
/* SU= 24 */
chunk XXX::BIG_split(BIG t, BIG b, DBIG d, int n)
{
int i;
chunk nw, carry = 0;
int m = n % BASEBITS_XXX;
if (m == 0)
{
for (i = 0; i < NLEN_XXX; i++) b[i] = d[i];
if (t != b)
{
for (i = NLEN_XXX; i < 2 * NLEN_XXX; i++) t[i - NLEN_XXX] = d[i];
carry = t[NLEN_XXX - 1] >> BASEBITS_XXX;
t[NLEN_XXX - 1] = t[NLEN_XXX - 1] & BMASK_XXX; /* top word normalized */
}
return carry;
}
for (i = 0; i < NLEN_XXX - 1; i++) b[i] = d[i];
b[NLEN_XXX - 1] = d[NLEN_XXX - 1] & (((chunk)1 << m) - 1);
if (t != b)
{
carry = (d[DNLEN_XXX - 1] << (BASEBITS_XXX - m));
for (i = DNLEN_XXX - 2; i >= NLEN_XXX - 1; i--)
{
nw = (d[i] >> m) | carry;
carry = (d[i] << (BASEBITS_XXX - m))&BMASK_XXX;
t[i - NLEN_XXX + 1] = nw;
}
}
#ifdef DEBUG_NORM
t[MPV_XXX] = 1; t[MNV_XXX] = 0;
b[MPV_XXX] = 1; b[MNV_XXX] = 0;
#endif
return carry;
}
/* you gotta keep the sign of carry! Look - no branching! */
/* Note that sign bit is needed to disambiguate between +ve and -ve values */
/* normalise BIG - force all digits < 2^BASEBITS_XXX */
chunk XXX::BIG_norm(BIG a)
{
int i;
chunk d, carry;
carry=a[0]>>BASEBITS_XXX;
a[0]&=BMASK_XXX;
for (i = 1; i < NLEN_XXX - 1; i++)
{
d = a[i] + carry;
a[i] = d & BMASK_XXX;
carry = d >> BASEBITS_XXX;
}
a[NLEN_XXX - 1] = (a[NLEN_XXX - 1] + carry);
#ifdef DEBUG_NORM
a[MPV_XXX] = 1; a[MNV_XXX] = 0;
#endif
return (a[NLEN_XXX - 1] >> ((8 * MODBYTES_XXX) % BASEBITS_XXX)); /* only used in ff.c */
}
void XXX::BIG_dnorm(DBIG a)
{
int i;
chunk d, carry;
carry=a[0]>>BASEBITS_XXX;
a[0]&=BMASK_XXX;
for (i = 1; i < DNLEN_XXX - 1; i++)
{
d = a[i] + carry;
a[i] = d & BMASK_XXX;
carry = d >> BASEBITS_XXX;
}
a[DNLEN_XXX - 1] = (a[DNLEN_XXX - 1] + carry);
#ifdef DEBUG_NORM
a[DMPV_XXX] = 1; a[DMNV_XXX] = 0;
#endif
}
/* Compare a and b. Return 1 for a>b, -1 for a<b, 0 for a==b */
/* a and b MUST be normalised before call */
/* sodium constant time implementation */
int XXX::BIG_comp(BIG a, BIG b)
{
int i;
chunk gt=0; chunk eq=1;
for (i = NLEN_XXX-1; i>=0; i--)
{
gt |= ((b[i]-a[i]) >> BASEBITS_XXX) & eq;
eq &= ((b[i]^a[i])-1) >> BASEBITS_XXX;
}
return (int)(gt+gt+eq-1);
}
int XXX::BIG_dcomp(DBIG a, DBIG b)
{
int i;
chunk gt=0; chunk eq=1;
for (i = DNLEN_XXX-1; i>=0; i--)
{
gt |= ((b[i]-a[i]) >> BASEBITS_XXX) & eq;
eq &= ((b[i]^a[i])-1) >> BASEBITS_XXX;
}
return (int)(gt+gt+eq-1);
}
/* return number of bits in a */
/* SU= 8 */
int XXX::BIG_nbits(BIG a)
{
int bts, k = NLEN_XXX - 1;
BIG t;
chunk c;
BIG_copy(t, a);
BIG_norm(t);
while (k >= 0 && t[k] == 0) k--;
if (k < 0) return 0;
bts = BASEBITS_XXX * k;
c = t[k];
while (c != 0)
{
c /= 2;
bts++;
}
return bts;
}
/* SU= 8, Calculate number of bits in a DBIG - output normalised */
int XXX::BIG_dnbits(DBIG a)
{
int bts, k = DNLEN_XXX - 1;
DBIG t;
chunk c;
BIG_dcopy(t, a);
BIG_dnorm(t);
while (k >= 0 && t[k] == 0) k--;
if (k < 0) return 0;
bts = BASEBITS_XXX * k;
c = t[k];
while (c != 0)
{
c /= 2;
bts++;
}
return bts;
}
// Set b=b mod m in constant time (if bd is known at compile time)
// bd is Max number of bits in b - Actual number of bits in m
void XXX::BIG_ctmod(BIG b, BIG m, int bd)
{
int k=bd;
BIG r,c;
BIG_copy(c,m);
BIG_norm(b);
BIG_shl(c,k);
while (k>=0)
{
BIG_sub(r, b, c);
BIG_norm(r);
BIG_cmove(b, r, 1 - ((r[NLEN_XXX - 1] >> (CHUNK - 1)) & 1));
BIG_fshr(c, 1);
k--;
}
}
/* Set b=b mod m */
/* SU= 16 */
void XXX::BIG_mod(BIG b, BIG m)
{
int k=BIG_nbits(b)-BIG_nbits(m);
if (k<0) k=0;
BIG_ctmod(b,m,k);
/*
int k = 0;
BIG r;
BIG c;
BIG_copy(c, m);
BIG_norm(b);
if (BIG_comp(b, c) < 0)
return;
do
{
BIG_fshl(c, 1);
k++;
}
while (BIG_comp(b, c) >= 0);
while (k > 0)
{
BIG_fshr(c, 1);
// constant time...
BIG_sub(r, b, c);
BIG_norm(r);
BIG_cmove(b, r, 1 - ((r[NLEN_XXX - 1] >> (CHUNK - 1)) & 1));
k--;
} */
}
// Set a=b mod m in constant time (if bd is known at compile time)
// bd is Max number of bits in b - Actual number of bits in m
void XXX::BIG_ctdmod(BIG a, DBIG b, BIG m, int bd)
{
int k=bd;
DBIG c,r;
BIG_dscopy(c,m);
BIG_dnorm(b);
BIG_dshl(c,k);
while (k>=0)
{
BIG_dsub(r, b, c);
BIG_dnorm(r);
BIG_dcmove(b, r, 1 - ((r[DNLEN_XXX - 1] >> (CHUNK - 1)) & 1));
BIG_dshr(c, 1);
k--;
}
BIG_sdcopy(a,b);
}
/* Set a=b mod c, b is destroyed. Slow but rarely used. */
/* SU= 96 */
void XXX::BIG_dmod(BIG a, DBIG b, BIG m)
{
int k=BIG_dnbits(b)-BIG_nbits(m);
if (k<0) k=0;
BIG_ctdmod(a,b,m,k);
/*
int k = 0;
DBIG c, r;
BIG_dnorm(b);
BIG_dscopy(c,m);
if (BIG_dcomp(b, c) < 0)
{
BIG_sdcopy(a, b);
return;
}
do
{
BIG_dshl(c, 1);
k++;
}
while (BIG_dcomp(b, c) >= 0);
while (k > 0)
{
BIG_dshr(c, 1);
// constant time...
BIG_dsub(r, b, c);
BIG_dnorm(r);
BIG_dcmove(b, r, 1 - ((r[DNLEN_XXX - 1] >> (CHUNK - 1)) & 1));
k--;
}
BIG_sdcopy(a, b); */
}
// a=b/m in constant time (if bd is known at compile time)
// bd is Max number of bits in b - Actual number of bits in m
void XXX::BIG_ctddiv(BIG a,DBIG b,BIG m,int bd)
{
int d,k=bd;
DBIG c,dr;
BIG e,r;
BIG_dscopy(c,m);
BIG_dnorm(b);
BIG_zero(a);
BIG_zero(e);
BIG_inc(e, 1);
BIG_shl(e,k);
BIG_dshl(c,k);
while (k >= 0)
{
BIG_dsub(dr, b, c);
BIG_dnorm(dr);
d = 1 - ((dr[DNLEN_XXX - 1] >> (CHUNK - 1)) & 1);
BIG_dcmove(b, dr, d);
BIG_add(r, a, e);
BIG_norm(r);
BIG_cmove(a, r, d);
BIG_dshr(c, 1);
BIG_fshr(e, 1);
k--;
}
}
/* Set a=b/c, b is destroyed. Slow but rarely used. */
/* SU= 136 */
void XXX::BIG_ddiv(BIG a, DBIG b, BIG m)
{
int k=BIG_dnbits(b)-BIG_nbits(m);
if (k<0) k=0;
BIG_ctddiv(a,b,m,k);
/*
int d, k = 0;
DBIG c, dr;
BIG e, r;
BIG_dnorm(b);
BIG_dscopy(c,m);
BIG_zero(a);
BIG_zero(e);
BIG_inc(e, 1);
while (BIG_dcomp(b, c) >= 0)
{
BIG_fshl(e, 1);
BIG_dshl(c, 1);
k++;
}
while (k > 0)
{
BIG_dshr(c, 1);
BIG_fshr(e, 1);
BIG_dsub(dr, b, c);
BIG_dnorm(dr);
d = 1 - ((dr[DNLEN_XXX - 1] >> (CHUNK - 1)) & 1);
BIG_dcmove(b, dr, d);
BIG_add(r, a, e);
BIG_norm(r);
BIG_cmove(a, r, d);
k--;
} */
}
// a=a/m in constant time (if bd is known at compile time)
// bd is Max number of bits in b - Actual number of bits in m
void XXX::BIG_ctsdiv(BIG b,BIG m,int bd)
{
int d, k=bd;
BIG e,a,r,c;
BIG_norm(b);
BIG_copy(a,b);
BIG_copy(c,m);
BIG_zero(b);
BIG_zero(e);
BIG_inc(e, 1);
BIG_shl(c,k);
BIG_shl(e,k);
while (k >= 0)
{
BIG_sub(r, a, c);
BIG_norm(r);
d = 1 - ((r[NLEN_XXX - 1] >> (CHUNK - 1)) & 1);
BIG_cmove(a, r, d);
BIG_add(r, b, e);
BIG_norm(r);
BIG_cmove(b, r, d);
BIG_fshr(c, 1);
BIG_fshr(e, 1);
k--;
}
}
void XXX::BIG_sdiv(BIG b, BIG m)
{
int k=BIG_nbits(b)-BIG_nbits(m);
if (k<0) k=0;
BIG_ctsdiv(b,m,k);
/*
int d, k = 0;
BIG c, e, a, r;
BIG_norm(b);
BIG_copy(a,b);
BIG_copy(c, m);
BIG_zero(b);
BIG_zero(e);
BIG_inc(e, 1);
while (BIG_comp(a, c) >= 0)
{
BIG_fshl(e, 1);
BIG_fshl(c, 1);
k++;
}
while (k > 0)
{
BIG_fshr(c, 1);
BIG_fshr(e, 1);
BIG_sub(r, a, c);
BIG_norm(r);
d = 1 - ((r[NLEN_XXX - 1] >> (CHUNK - 1)) & 1);
BIG_cmove(a, r, d);
BIG_add(r, b, e);
BIG_norm(r);
BIG_cmove(b, r, d);
k--;
} */
}
/* return LSB of a */
int XXX::BIG_parity(BIG a)
{
return a[0] % 2;
}
/* return n-th bit of a */
/* SU= 16 */
int XXX::BIG_bit(BIG a, int n)
{
return (int)((a[n / BASEBITS_XXX] & ((chunk)1 << (n % BASEBITS_XXX))) >> (n%BASEBITS_XXX));
}
/* return last n bits of a, where n is small < BASEBITS_XXX */
/* SU= 16 */
int XXX::BIG_lastbits(BIG a, int n)
{
int msk = (1 << n) - 1;
BIG_norm(a);
return ((int)a[0])&msk;
}
/* get 8*MODBYTES_XXX size random number */
void XXX::BIG_random(BIG m, csprng *rng)
{
int i, b, j = 0, r = 0;
int len = 8 * MODBYTES_XXX;
BIG_zero(m);
/* generate random BIG */
for (i = 0; i < len; i++)
{
if (j == 0) r = RAND_byte(rng);
else r >>= 1;
b = r & 1;
BIG_shl(m, 1);
m[0] += b;
j++;
j &= 7;
}
#ifdef DEBUG_NORM
m[MPV_XXX] = 1; m[MNV_XXX] = 0;
#endif
}
/* get random BIG from rng, modulo q. Done one bit at a time, so its portable */
extern int NFILLPOOL;
void XXX::BIG_randomnum(BIG m, BIG q, csprng *rng)
{
int i, b, j = 0, r = 0;
int n=2 * BIG_nbits(q);
DBIG d;
BIG_dzero(d);
/* generate random DBIG */
for (i = 0; i < n; i++)
{
if (j == 0) r = RAND_byte(rng);
else r >>= 1;
b = r & 1;
BIG_dshl(d, 1);
d[0] += b;
j++;
j &= 7;
}
/* reduce modulo a BIG. Removes bias */
BIG_dmod(m, d, q);
#ifdef DEBUG_NORM
m[MPV_XXX] = 1; m[MNV_XXX] = 0;
#endif
}
/* create randum BIG less than r and less than trunc bits */
void XXX::BIG_randtrunc(BIG s, BIG r, int trunc, csprng *rng)
{
BIG_randomnum(s, r, rng);
if (BIG_nbits(r) > trunc)
BIG_mod2m(s, trunc);
}
/* Set r=a*b mod m */
/* SU= 96 */
void XXX::BIG_modmul(BIG r, BIG a1, BIG b1, BIG m)
{
DBIG d;
BIG a, b;
BIG_copy(a, a1);
BIG_copy(b, b1);
BIG_mod(a, m);
BIG_mod(b, m);
BIG_mul(d, a, b);
BIG_ctdmod(r, d, m,BIG_nbits(m));
}
/* Set a=a*a mod m */
/* SU= 88 */
void XXX::BIG_modsqr(BIG r, BIG a1, BIG m)
{
DBIG d;
BIG a;
BIG_copy(a, a1);
BIG_mod(a, m);
BIG_sqr(d, a);
BIG_ctdmod(r, d, m, BIG_nbits(m));
}
/* Set r=-a mod m */
/* SU= 16 */
void XXX::BIG_modneg(BIG r, BIG a1, BIG m)
{
BIG a;
BIG_copy(a, a1);
BIG_mod(a, m);
BIG_sub(r, m, a); BIG_norm(r);
}
/* Set r=a+b mod m */
void XXX::BIG_modadd(BIG r, BIG a1, BIG b1, BIG m)
{
BIG a, b;
BIG_copy(a, a1);
BIG_copy(b, b1);
BIG_mod(a, m);
BIG_mod(b, m);
BIG_add(r,a,b); BIG_norm(r);
BIG_ctmod(r,m,1);
}
/* Set a=a/b mod m */
/* SU= 136 */
void XXX::BIG_moddiv(BIG r, BIG a1, BIG b1, BIG m)
{
DBIG d;
BIG z;
BIG a, b;
BIG_copy(a, a1);
BIG_copy(b, b1);
BIG_mod(a, m);
BIG_invmodp(z, b, m);
BIG_mul(d, a, z);
BIG_ctdmod(r, d, m, BIG_nbits(m));
}
/* Get jacobi Symbol (a/p). Returns 0, 1 or -1 */
/* SU= 216 */
int XXX::BIG_jacobi(BIG a, BIG p)
{
int n8, k, m = 0;
BIG t, x, n, zilch, one;
BIG_one(one);
BIG_zero(zilch);
if (BIG_parity(p) == 0 || BIG_comp(a, zilch) == 0 || BIG_comp(p, one) <= 0) return 0;
BIG_norm(a);
BIG_copy(x, a);
BIG_copy(n, p);
BIG_mod(x, p);
while (BIG_comp(n, one) > 0)
{
if (BIG_comp(x, zilch) == 0) return 0;
n8 = BIG_lastbits(n, 3);
k = 0;
while (BIG_parity(x) == 0)
{
k++;
BIG_shr(x, 1);
}
if (k % 2 == 1) m += (n8 * n8 - 1) / 8;
m += (n8 - 1) * (BIG_lastbits(x, 2) - 1) / 4;
BIG_copy(t, n);
BIG_mod(t, x);
BIG_copy(n, x);
BIG_copy(x, t);
m %= 2;
}
if (m == 0) return 1;
else return -1;
}
/*
int XXX::step1(BIG u,BIG x,BIG p)
{
int k=0;
BIG t;
while (BIG_bit(u,k)==0)
{
BIG_add(t,x,p);
BIG_cmove(x,t,BIG_parity(x));
BIG_norm(x);
BIG_fshr(x,1);
k++;
}
return k;
}
void XXX::step2(BIG xf,BIG xs,BIG p)
{
BIG t;
BIG_add(t,xf,p);
BIG_cmove(xf,t,(BIG_comp(xf,xs)>>1)&1); // move if x1<x2
BIG_sub(xf,xf,xs);
BIG_norm(xf);
}
*/
/* Arazi and Qi inversion mod 256 */
static int invmod256(int a)
{
int U, t1, t2, b, c;
t1 = 0;
c = (a >> 1) & 1;
t1 += c;
t1 &= 1;
t1 = 2 - t1;
t1 <<= 1;
U = t1 + 1;
// i=2
b = a & 3;
t1 = U * b;
t1 >>= 2;
c = (a >> 2) & 3;
t2 = (U * c) & 3;
t1 += t2;
t1 *= U;
t1 &= 3;
t1 = 4 - t1;
t1 <<= 2;
U += t1;
// i=4
b = a & 15;
t1 = U * b;
t1 >>= 4;
c = (a >> 4) & 15;
t2 = (U * c) & 15;
t1 += t2;
t1 *= U;
t1 &= 15;
t1 = 16 - t1;
t1 <<= 4;
U += t1;
return U;
}
/* a=1/a mod 2^BIGBITS_XXX. This is very fast! */
void XXX::BIG_invmod2m(BIG a)
{
int i;
BIG U, t1, b, c;
BIG_zero(U);
BIG_inc(U, invmod256(BIG_lastbits(a, 8)));
for (i = 8; i < BIGBITS_XXX; i <<= 1)
{
BIG_norm(U);
BIG_copy(b, a);
BIG_mod2m(b, i); // bottom i bits of a
BIG_smul(t1, U, b);
BIG_shr(t1, i); // top i bits of U*b
BIG_copy(c, a);
BIG_shr(c, i);
BIG_mod2m(c, i); // top i bits of a
BIG_smul(b, U, c);
BIG_mod2m(b, i); // bottom i bits of U*c
BIG_add(t1, t1, b);
BIG_norm(t1);
BIG_smul(b, t1, U);
BIG_copy(t1, b); // (t1+b)*U
BIG_mod2m(t1, i); // bottom i bits of (t1+b)*U
BIG_one(b);
BIG_shl(b, i);
BIG_sub(t1, b, t1);
BIG_norm(t1);
BIG_shl(t1, i);
BIG_add(U, U, t1);
}
BIG_copy(a, U);
BIG_norm(a);
BIG_mod2m(a, BIGBITS_XXX);
}
// Set r=1/a mod p. Binary method
// NOTE: This function is NOT side-channel safe
// If a is a secret then ALWAYS calculate 1/a = m*(1/am) mod p
// where m is a random masking value
void XXX::BIG_invmodp(BIG r, BIG a, BIG p)
{
BIG u, v, x1, x2, t, one;
int par,s;
BIG_mod(a, p);
if (BIG_iszilch(a))
{
BIG_zero(r);
return;
}
BIG_copy(u, a);
BIG_copy(v, p);
BIG_one(one);
BIG_copy(x1, one);
BIG_zero(x2);
while (BIG_comp(u, one) != 0 && BIG_comp(v, one) != 0)
{
while (BIG_parity(u) == 0)
{
BIG_fshr(u, 1);
BIG_add(t,x1,p);
BIG_cmove(x1,t,BIG_parity(x1));
BIG_norm(x1);
BIG_fshr(x1,1);
}
while (BIG_parity(v) == 0)
{
BIG_fshr(v, 1);
BIG_add(t,x2,p);
BIG_cmove(x2,t,BIG_parity(x2));
BIG_norm(x2);
BIG_fshr(x2,1);
}
if (BIG_comp(u, v) >= 0)
{
BIG_sub(u, u, v);
BIG_norm(u);
BIG_add(t,x1,p);
BIG_cmove(x1,t,(BIG_comp(x1,x2)>>1)&1); // move if x1<x2
BIG_sub(x1,x1,x2);
BIG_norm(x1);
}
else
{
BIG_sub(v, v, u);
BIG_norm(v);
BIG_add(t,x2,p);
BIG_cmove(x2,t,(BIG_comp(x2,x1)>>1)&1); // move if x2<x1
BIG_sub(x2,x2,x1);
BIG_norm(x2);
}
}
BIG_copy(r,x1);
BIG_cmove(r,x2,BIG_comp(u,one)&1);
}
/* set x = x mod 2^m */
void XXX::BIG_mod2m(BIG x, int m)
{
int i, wd, bt;
chunk msk;
BIG_norm(x);
wd = m / BASEBITS_XXX;
bt = m % BASEBITS_XXX;
msk = ((chunk)1 << bt) - 1;
x[wd] &= msk;
for (i = wd + 1; i < NLEN_XXX; i++) x[i] = 0;
}
// new
/* Convert to DBIG number from byte array of given length */
void XXX::BIG_dfromBytesLen(DBIG a, char *b, int s)
{
int i, len = s;
BIG_dzero(a);
for (i = 0; i < len; i++)
{
BIG_dshl(a, 8);
a[0] += (int)(unsigned char)b[i];
}
#ifdef DEBUG_NORM
a[DMPV_XXX] = 1; a[DMNV_XXX] = 0;
#endif
}
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