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chromium / chromium / deps / nss / ccb083050bac653bd6b98c38237fdf93c5d64a7a / . / nss / lib / freebl / mpi / mpmontg.c
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/* This file implements moduluar exponentiation using Montgomery's
* method for modular reduction. This file implements the method
* described as "Improvement 2" in the paper "A Cryptogrpahic Library for
* the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
* published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
* "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
* published by Springer Verlag.
*/
#define MP_USING_CACHE_SAFE_MOD_EXP 1
#include <string.h>
#include "mpi-priv.h"
#include "mplogic.h"
#include "mpprime.h"
#ifdef MP_USING_MONT_MULF
#include "montmulf.h"
#endif
#include <stddef.h> /* ptrdiff_t */
/* if MP_CHAR_STORE_SLOW is defined, we */
/* need to know endianness of this platform. */
#ifdef MP_CHAR_STORE_SLOW
#if !defined(MP_IS_BIG_ENDIAN) && !defined(MP_IS_LITTLE_ENDIAN)
#error "You must define MP_IS_BIG_ENDIAN or MP_IS_LITTLE_ENDIAN\n" \
" if you define MP_CHAR_STORE_SLOW."
#endif
#endif
#define STATIC
#define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */
/*! computes T = REDC(T), 2^b == R
\param T < RN
*/
mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
{
mp_err res;
mp_size i;
i = (MP_USED(&mmm->N) << 1) + 1;
MP_CHECKOK( s_mp_pad(T, i) );
for (i = 0; i < MP_USED(&mmm->N); ++i ) {
mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
/* T += N * m_i * (MP_RADIX ** i); */
s_mp_mul_d_add_offset(&mmm->N, m_i, T, i);
}
s_mp_clamp(T);
/* T /= R */
s_mp_rshd( T, MP_USED(&mmm->N) );
if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
/* T = T - N */
MP_CHECKOK( s_mp_sub(T, &mmm->N) );
#ifdef DEBUG
if ((res = mp_cmp(T, &mmm->N)) >= 0) {
res = MP_UNDEF;
goto CLEANUP;
}
#endif
}
res = MP_OKAY;
CLEANUP:
return res;
}
#if !defined(MP_MONT_USE_MP_MUL)
/*! c <- REDC( a * b ) mod N
\param a < N i.e. "reduced"
\param b < N i.e. "reduced"
\param mmm modulus N and n0' of N
*/
mp_err s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
mp_mont_modulus *mmm)
{
mp_digit *pb;
mp_digit m_i;
mp_err res;
mp_size ib; /* "index b": index of current digit of B */
mp_size useda, usedb;
ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
if (MP_USED(a) < MP_USED(b)) {
const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
b = a;
a = xch;
}
MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
ib = (MP_USED(&mmm->N) << 1) + 1;
if((res = s_mp_pad(c, ib)) != MP_OKAY)
goto CLEANUP;
useda = MP_USED(a);
pb = MP_DIGITS(b);
s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
m_i = MP_DIGIT(c, 0) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);
/* Outer loop: Digits of b */
usedb = MP_USED(b);
for (ib = 1; ib < usedb; ib++) {
mp_digit b_i = *pb++;
/* Inner product: Digits of a */
if (b_i)
s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
m_i = MP_DIGIT(c, ib) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
}
if (usedb < MP_USED(&mmm->N)) {
for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib ) {
m_i = MP_DIGIT(c, ib) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
}
}
s_mp_clamp(c);
s_mp_rshd( c, MP_USED(&mmm->N) ); /* c /= R */
if (s_mp_cmp(c, &mmm->N) >= 0) {
MP_CHECKOK( s_mp_sub(c, &mmm->N) );
}
res = MP_OKAY;
CLEANUP:
return res;
}
#endif
STATIC
mp_err s_mp_to_mont(const mp_int *x, mp_mont_modulus *mmm, mp_int *xMont)
{
mp_err res;
/* xMont = x * R mod N where N is modulus */
MP_CHECKOK( mp_copy( x, xMont ) );
MP_CHECKOK( s_mp_lshd( xMont, MP_USED(&mmm->N) ) ); /* xMont = x << b */
MP_CHECKOK( mp_div(xMont, &mmm->N, 0, xMont) ); /* mod N */
CLEANUP:
return res;
}
#ifdef MP_USING_MONT_MULF
/* the floating point multiply is already cache safe,
* don't turn on cache safe unless we specifically
* force it */
#ifndef MP_FORCE_CACHE_SAFE
#undef MP_USING_CACHE_SAFE_MOD_EXP
#endif
unsigned int mp_using_mont_mulf = 1;
/* computes montgomery square of the integer in mResult */
#define SQR \
conv_i32_to_d32_and_d16(dm1, d16Tmp, mResult, nLen); \
mont_mulf_noconv(mResult, dm1, d16Tmp, \
dTmp, dn, MP_DIGITS(modulus), nLen, dn0)
/* computes montgomery product of x and the integer in mResult */
#define MUL(x) \
conv_i32_to_d32(dm1, mResult, nLen); \
mont_mulf_noconv(mResult, dm1, oddPowers[x], \
dTmp, dn, MP_DIGITS(modulus), nLen, dn0)
/* Do modular exponentiation using floating point multiply code. */
mp_err mp_exptmod_f(const mp_int * montBase,
const mp_int * exponent,
const mp_int * modulus,
mp_int * result,
mp_mont_modulus *mmm,
int nLen,
mp_size bits_in_exponent,
mp_size window_bits,
mp_size odd_ints)
{
mp_digit *mResult;
double *dBuf = 0, *dm1, *dn, *dSqr, *d16Tmp, *dTmp;
double dn0;
mp_size i;
mp_err res;
int expOff;
int dSize = 0, oddPowSize, dTmpSize;
mp_int accum1;
double *oddPowers[MAX_ODD_INTS];
/* function for computing n0prime only works if n0 is odd */
MP_DIGITS(&accum1) = 0;
for (i = 0; i < MAX_ODD_INTS; ++i)
oddPowers[i] = 0;
MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
mp_set(&accum1, 1);
MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
MP_CHECKOK( s_mp_pad(&accum1, nLen) );
oddPowSize = 2 * nLen + 1;
dTmpSize = 2 * oddPowSize;
dSize = sizeof(double) * (nLen * 4 + 1 +
((odd_ints + 1) * oddPowSize) + dTmpSize);
dBuf = (double *)malloc(dSize);
dm1 = dBuf; /* array of d32 */
dn = dBuf + nLen; /* array of d32 */
dSqr = dn + nLen; /* array of d32 */
d16Tmp = dSqr + nLen; /* array of d16 */
dTmp = d16Tmp + oddPowSize;
for (i = 0; i < odd_ints; ++i) {
oddPowers[i] = dTmp;
dTmp += oddPowSize;
}
mResult = (mp_digit *)(dTmp + dTmpSize); /* size is nLen + 1 */
/* Make dn and dn0 */
conv_i32_to_d32(dn, MP_DIGITS(modulus), nLen);
dn0 = (double)(mmm->n0prime & 0xffff);
/* Make dSqr */
conv_i32_to_d32_and_d16(dm1, oddPowers[0], MP_DIGITS(montBase), nLen);
mont_mulf_noconv(mResult, dm1, oddPowers[0],
dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
conv_i32_to_d32(dSqr, mResult, nLen);
for (i = 1; i < odd_ints; ++i) {
mont_mulf_noconv(mResult, dSqr, oddPowers[i - 1],
dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
conv_i32_to_d16(oddPowers[i], mResult, nLen);
}
s_mp_copy(MP_DIGITS(&accum1), mResult, nLen); /* from, to, len */
for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
mp_size smallExp;
MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
smallExp = (mp_size)res;
if (window_bits == 1) {
if (!smallExp) {
SQR;
} else if (smallExp & 1) {
SQR; MUL(0);
} else {
abort();
}
} else if (window_bits == 4) {
if (!smallExp) {
SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else {
abort();
}
} else if (window_bits == 5) {
if (!smallExp) {
SQR; SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else if (smallExp & 0x10) {
SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
} else {
abort();
}
} else if (window_bits == 6) {
if (!smallExp) {
SQR; SQR; SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else if (smallExp & 0x10) {
SQR; SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
} else if (smallExp & 0x20) {
SQR; MUL(smallExp/64); SQR; SQR; SQR; SQR; SQR;
} else {
abort();
}
} else {
abort();
}
}
s_mp_copy(mResult, MP_DIGITS(&accum1), nLen); /* from, to, len */
res = s_mp_redc(&accum1, mmm);
mp_exch(&accum1, result);
CLEANUP:
mp_clear(&accum1);
if (dBuf) {
if (dSize)
memset(dBuf, 0, dSize);
free(dBuf);
}
return res;
}
#undef SQR
#undef MUL
#endif
#define SQR(a,b) \
MP_CHECKOK( mp_sqr(a, b) );\
MP_CHECKOK( s_mp_redc(b, mmm) )
#if defined(MP_MONT_USE_MP_MUL)
#define MUL(x,a,b) \
MP_CHECKOK( mp_mul(a, oddPowers + (x), b) ); \
MP_CHECKOK( s_mp_redc(b, mmm) )
#else
#define MUL(x,a,b) \
MP_CHECKOK( s_mp_mul_mont(a, oddPowers + (x), b, mmm) )
#endif
#define SWAPPA ptmp = pa1; pa1 = pa2; pa2 = ptmp
/* Do modular exponentiation using integer multiply code. */
mp_err mp_exptmod_i(const mp_int * montBase,
const mp_int * exponent,
const mp_int * modulus,
mp_int * result,
mp_mont_modulus *mmm,
int nLen,
mp_size bits_in_exponent,
mp_size window_bits,
mp_size odd_ints)
{
mp_int *pa1, *pa2, *ptmp;
mp_size i;
mp_err res;
int expOff;
mp_int accum1, accum2, power2, oddPowers[MAX_ODD_INTS];
/* power2 = base ** 2; oddPowers[i] = base ** (2*i + 1); */
/* oddPowers[i] = base ** (2*i + 1); */
MP_DIGITS(&accum1) = 0;
MP_DIGITS(&accum2) = 0;
MP_DIGITS(&power2) = 0;
for (i = 0; i < MAX_ODD_INTS; ++i) {
MP_DIGITS(oddPowers + i) = 0;
}
MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
MP_CHECKOK( mp_init_copy(&oddPowers[0], montBase) );
MP_CHECKOK( mp_init_size(&power2, nLen + 2 * MP_USED(montBase) + 2) );
MP_CHECKOK( mp_sqr(montBase, &power2) ); /* power2 = montBase ** 2 */
MP_CHECKOK( s_mp_redc(&power2, mmm) );
for (i = 1; i < odd_ints; ++i) {
MP_CHECKOK( mp_init_size(oddPowers + i, nLen + 2 * MP_USED(&power2) + 2) );
MP_CHECKOK( mp_mul(oddPowers + (i - 1), &power2, oddPowers + i) );
MP_CHECKOK( s_mp_redc(oddPowers + i, mmm) );
}
/* set accumulator to montgomery residue of 1 */
mp_set(&accum1, 1);
MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
pa1 = &accum1;
pa2 = &accum2;
for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
mp_size smallExp;
MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
smallExp = (mp_size)res;
if (window_bits == 1) {
if (!smallExp) {
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 1) {
SQR(pa1,pa2); MUL(0,pa2,pa1);
} else {
abort();
}
} else if (window_bits == 4) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/2, pa1,pa2); SWAPPA;
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/8,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 8) {
SQR(pa1,pa2); MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else {
abort();
}
} else if (window_bits == 5) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); MUL(smallExp/2,pa2,pa1);
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/4,pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/8,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 8) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/16,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 0x10) {
SQR(pa1,pa2); MUL(smallExp/32,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else {
abort();
}
} else if (window_bits == 6) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/2,pa1,pa2); SWAPPA;
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/8,pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 8) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 0x10) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/32,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 0x20) {
SQR(pa1,pa2); MUL(smallExp/64,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else {
abort();
}
} else {
abort();
}
}
res = s_mp_redc(pa1, mmm);
mp_exch(pa1, result);
CLEANUP:
mp_clear(&accum1);
mp_clear(&accum2);
mp_clear(&power2);
for (i = 0; i < odd_ints; ++i) {
mp_clear(oddPowers + i);
}
return res;
}
#undef SQR
#undef MUL
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
unsigned int mp_using_cache_safe_exp = 1;
#endif
mp_err mp_set_safe_modexp(int value)
{
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
mp_using_cache_safe_exp = value;
return MP_OKAY;
#else
if (value == 0) {
return MP_OKAY;
}
return MP_BADARG;
#endif
}
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
#define WEAVE_WORD_SIZE 4
#ifndef MP_CHAR_STORE_SLOW
/*
* mpi_to_weave takes an array of bignums, a matrix in which each bignum
* occupies all the columns of a row, and transposes it into a matrix in
* which each bignum occupies a column of every row. The first row of the
* input matrix becomes the first column of the output matrix. The n'th
* row of input becomes the n'th column of output. The input data is said
* to be "interleaved" or "woven" into the output matrix.
*
* The array of bignums is left in this woven form. Each time a single
* bignum value is needed, it is recreated by fetching the n'th column,
* forming a single row which is the new bignum.
*
* The purpose of this interleaving is make it impossible to determine which
* of the bignums is being used in any one operation by examining the pattern
* of cache misses.
*
* The weaving function does not transpose the entire input matrix in one call.
* It transposes 4 rows of mp_ints into their respective columns of output.
*
* There are two different implementations of the weaving and unweaving code
* in this file. One uses byte loads and stores. The second uses loads and
* stores of mp_weave_word size values. The weaved forms of these two
* implementations differ. Consequently, each one has its own explanation.
*
* Here is the explanation for the byte-at-a-time implementation.
*
* This implementation treats each mp_int bignum as an array of bytes,
* rather than as an array of mp_digits. It stores those bytes as a
* column of bytes in the output matrix. It doesn't care if the machine
* uses big-endian or little-endian byte ordering within mp_digits.
* The first byte of the mp_digit array becomes the first byte in the output
* column, regardless of whether that byte is the MSB or LSB of the mp_digit.
*
* "bignums" is an array of mp_ints.
* It points to four rows, four mp_ints, a subset of a larger array of mp_ints.
*
* "weaved" is the weaved output matrix.
* The first byte of bignums[0] is stored in weaved[0].
*
* "nBignums" is the total number of bignums in the array of which "bignums"
* is a part.
*
* "nDigits" is the size in mp_digits of each mp_int in the "bignums" array.
* mp_ints that use less than nDigits digits are logically padded with zeros
* while being stored in the weaved array.
*/
mp_err mpi_to_weave(const mp_int *bignums,
unsigned char *weaved,
mp_size nDigits, /* in each mp_int of input */
mp_size nBignums) /* in the entire source array */
{
mp_size i;
unsigned char * endDest = weaved + (nDigits * nBignums * sizeof(mp_digit));
for (i=0; i < WEAVE_WORD_SIZE; i++) {
mp_size used = MP_USED(&bignums[i]);
unsigned char *pSrc = (unsigned char *)MP_DIGITS(&bignums[i]);
unsigned char *endSrc = pSrc + (used * sizeof(mp_digit));
unsigned char *pDest = weaved + i;
ARGCHK(MP_SIGN(&bignums[i]) == MP_ZPOS, MP_BADARG);
ARGCHK(used <= nDigits, MP_BADARG);
for (; pSrc < endSrc; pSrc++) {
*pDest = *pSrc;
pDest += nBignums;
}
while (pDest < endDest) {
*pDest = 0;
pDest += nBignums;
}
}
return MP_OKAY;
}
/* Reverse the operation above for one mp_int.
* Reconstruct one mp_int from its column in the weaved array.
* "pSrc" points to the offset into the weave array of the bignum we
* are going to reconstruct.
*/
mp_err weave_to_mpi(mp_int *a, /* output, result */
const unsigned char *pSrc, /* input, byte matrix */
mp_size nDigits, /* per mp_int output */
mp_size nBignums) /* bignums in weaved matrix */
{
unsigned char *pDest = (unsigned char *)MP_DIGITS(a);
unsigned char *endDest = pDest + (nDigits * sizeof(mp_digit));
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = nDigits;
for (; pDest < endDest; pSrc += nBignums, pDest++) {
*pDest = *pSrc;
}
s_mp_clamp(a);
return MP_OKAY;
}
#else
/* Need a primitive that we know is 32 bits long... */
/* this is true on all modern processors we know of today*/
typedef unsigned int mp_weave_word;
/*
* on some platforms character stores into memory is very expensive since they
* generate a read/modify/write operation on the bus. On those platforms
* we need to do integer writes to the bus. Because of some unrolled code,
* in this current code the size of mp_weave_word must be four. The code that
* makes this assumption explicity is called out. (on some platforms a write
* of 4 bytes still requires a single read-modify-write operation.
*
* This function is takes the identical parameters as the function above,
* however it lays out the final array differently. Where the previous function
* treats the mpi_int as an byte array, this function treats it as an array of
* mp_digits where each digit is stored in big endian order.
*
* since we need to interleave on a byte by byte basis, we need to collect
* several mpi structures together into a single PRUint32 before we write. We
* also need to make sure the PRUint32 is arranged so that the first value of
* the first array winds up in b[0]. This means construction of that PRUint32
* is endian specific (even though the layout of the mp_digits in the array
* is always big endian).
*
* The final data is stored as follows :
*
* Our same logical array p array, m is sizeof(mp_digit),
* N is still count and n is now b_size. If we define p[i].digit[j]0 as the
* most significant byte of the word p[i].digit[j], p[i].digit[j]1 as
* the next most significant byte of p[i].digit[j], ... and p[i].digit[j]m-1
* is the least significant byte.
* Our array would look like:
* p[0].digit[0]0 p[1].digit[0]0 ... p[N-2].digit[0]0 p[N-1].digit[0]0
* p[0].digit[0]1 p[1].digit[0]1 ... p[N-2].digit[0]1 p[N-1].digit[0]1
* . .
* p[0].digit[0]m-1 p[1].digit[0]m-1 ... p[N-2].digit[0]m-1 p[N-1].digit[0]m-1
* p[0].digit[1]0 p[1].digit[1]0 ... p[N-2].digit[1]0 p[N-1].digit[1]0
* . .
* . .
* p[0].digit[n-1]m-2 p[1].digit[n-1]m-2 ... p[N-2].digit[n-1]m-2 p[N-1].digit[n-1]m-2
* p[0].digit[n-1]m-1 p[1].digit[n-1]m-1 ... p[N-2].digit[n-1]m-1 p[N-1].digit[n-1]m-1
*
*/
mp_err mpi_to_weave(const mp_int *a, unsigned char *b,
mp_size b_size, mp_size count)
{
mp_size i;
mp_digit *digitsa0;
mp_digit *digitsa1;
mp_digit *digitsa2;
mp_digit *digitsa3;
mp_size useda0;
mp_size useda1;
mp_size useda2;
mp_size useda3;
mp_weave_word *weaved = (mp_weave_word *)b;
count = count/sizeof(mp_weave_word);
/* this code pretty much depends on this ! */
#if MP_ARGCHK == 2
assert(WEAVE_WORD_SIZE == 4);
assert(sizeof(mp_weave_word) == 4);
#endif
digitsa0 = MP_DIGITS(&a[0]);
digitsa1 = MP_DIGITS(&a[1]);
digitsa2 = MP_DIGITS(&a[2]);
digitsa3 = MP_DIGITS(&a[3]);
useda0 = MP_USED(&a[0]);
useda1 = MP_USED(&a[1]);
useda2 = MP_USED(&a[2]);
useda3 = MP_USED(&a[3]);
ARGCHK(MP_SIGN(&a[0]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[1]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[2]) == MP_ZPOS, MP_BADARG);
ARGCHK(MP_SIGN(&a[3]) == MP_ZPOS, MP_BADARG);
ARGCHK(useda0 <= b_size, MP_BADARG);
ARGCHK(useda1 <= b_size, MP_BADARG);
ARGCHK(useda2 <= b_size, MP_BADARG);
ARGCHK(useda3 <= b_size, MP_BADARG);
#define SAFE_FETCH(digit, used, word) ((word) < (used) ? (digit[word]) : 0)
for (i=0; i < b_size; i++) {
mp_digit d0 = SAFE_FETCH(digitsa0,useda0,i);
mp_digit d1 = SAFE_FETCH(digitsa1,useda1,i);
mp_digit d2 = SAFE_FETCH(digitsa2,useda2,i);
mp_digit d3 = SAFE_FETCH(digitsa3,useda3,i);
register mp_weave_word acc;
/*
* ONE_STEP takes the MSB of each of our current digits and places that
* byte in the appropriate position for writing to the weaved array.
* On little endian:
* b3 b2 b1 b0
* On big endian:
* b0 b1 b2 b3
* When the data is written it would always wind up:
* b[0] = b0
* b[1] = b1
* b[2] = b2
* b[3] = b3
*
* Once we've written the MSB, we shift the whole digit up left one
* byte, putting the Next Most Significant Byte in the MSB position,
* so we we repeat the next one step that byte will be written.
* NOTE: This code assumes sizeof(mp_weave_word) and MP_WEAVE_WORD_SIZE
* is 4.
*/
#ifdef MP_IS_LITTLE_ENDIAN
#define MPI_WEAVE_ONE_STEP \
acc = (d0 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d0 <<= 8; /*b0*/ \
acc |= (d1 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d1 <<= 8; /*b1*/ \
acc |= (d2 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d2 <<= 8; /*b2*/ \
acc |= (d3 >> (MP_DIGIT_BIT-32)) & 0xff000000; d3 <<= 8; /*b3*/ \
*weaved = acc; weaved += count;
#else
#define MPI_WEAVE_ONE_STEP \
acc = (d0 >> (MP_DIGIT_BIT-32)) & 0xff000000; d0 <<= 8; /*b0*/ \
acc |= (d1 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d1 <<= 8; /*b1*/ \
acc |= (d2 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d2 <<= 8; /*b2*/ \
acc |= (d3 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d3 <<= 8; /*b3*/ \
*weaved = acc; weaved += count;
#endif
switch (sizeof(mp_digit)) {
case 32:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 16:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 8:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 4:
MPI_WEAVE_ONE_STEP
MPI_WEAVE_ONE_STEP
case 2:
MPI_WEAVE_ONE_STEP
case 1:
MPI_WEAVE_ONE_STEP
break;
}
}
return MP_OKAY;
}
/* reverse the operation above for one entry.
* b points to the offset into the weave array of the power we are
* calculating */
mp_err weave_to_mpi(mp_int *a, const unsigned char *b,
mp_size b_size, mp_size count)
{
mp_digit *pb = MP_DIGITS(a);
mp_digit *end = &pb[b_size];
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = b_size;
for (; pb < end; pb++) {
register mp_digit digit;
digit = *b << 8; b += count;
#define MPI_UNWEAVE_ONE_STEP digit |= *b; b += count; digit = digit << 8;
switch (sizeof(mp_digit)) {
case 32:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 16:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 8:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 4:
MPI_UNWEAVE_ONE_STEP
MPI_UNWEAVE_ONE_STEP
case 2:
break;
}
digit |= *b; b += count;
*pb = digit;
}
s_mp_clamp(a);
return MP_OKAY;
}
#endif
#define SQR(a,b) \
MP_CHECKOK( mp_sqr(a, b) );\
MP_CHECKOK( s_mp_redc(b, mmm) )
#if defined(MP_MONT_USE_MP_MUL)
#define MUL_NOWEAVE(x,a,b) \
MP_CHECKOK( mp_mul(a, x, b) ); \
MP_CHECKOK( s_mp_redc(b, mmm) )
#else
#define MUL_NOWEAVE(x,a,b) \
MP_CHECKOK( s_mp_mul_mont(a, x, b, mmm) )
#endif
#define MUL(x,a,b) \
MP_CHECKOK( weave_to_mpi(&tmp, powers + (x), nLen, num_powers) ); \
MUL_NOWEAVE(&tmp,a,b)
#define SWAPPA ptmp = pa1; pa1 = pa2; pa2 = ptmp
#define MP_ALIGN(x,y) ((((ptrdiff_t)(x))+((y)-1))&(((ptrdiff_t)0)-(y)))
/* Do modular exponentiation using integer multiply code. */
mp_err mp_exptmod_safe_i(const mp_int * montBase,
const mp_int * exponent,
const mp_int * modulus,
mp_int * result,
mp_mont_modulus *mmm,
int nLen,
mp_size bits_in_exponent,
mp_size window_bits,
mp_size num_powers)
{
mp_int *pa1, *pa2, *ptmp;
mp_size i;
mp_size first_window;
mp_err res;
int expOff;
mp_int accum1, accum2, accum[WEAVE_WORD_SIZE];
mp_int tmp;
unsigned char *powersArray = NULL;
unsigned char *powers = NULL;
MP_DIGITS(&accum1) = 0;
MP_DIGITS(&accum2) = 0;
MP_DIGITS(&accum[0]) = 0;
MP_DIGITS(&accum[1]) = 0;
MP_DIGITS(&accum[2]) = 0;
MP_DIGITS(&accum[3]) = 0;
MP_DIGITS(&tmp) = 0;
/* grab the first window value. This allows us to preload accumulator1
* and save a conversion, some squares and a multiple*/
MP_CHECKOK( mpl_get_bits(exponent,
bits_in_exponent-window_bits, window_bits) );
first_window = (mp_size)res;
MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
/* build the first WEAVE_WORD powers inline */
/* if WEAVE_WORD_SIZE is not 4, this code will have to change */
if (num_powers > 2) {
MP_CHECKOK( mp_init_size(&accum[0], 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum[1], 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum[2], 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum[3], 3 * nLen + 2) );
mp_set(&accum[0], 1);
MP_CHECKOK( s_mp_to_mont(&accum[0], mmm, &accum[0]) );
MP_CHECKOK( mp_copy(montBase, &accum[1]) );
SQR(montBase, &accum[2]);
MUL_NOWEAVE(montBase, &accum[2], &accum[3]);
powersArray = (unsigned char *)malloc(num_powers*(nLen*sizeof(mp_digit)+1));
if (!powersArray) {
res = MP_MEM;
goto CLEANUP;
}
/* powers[i] = base ** (i); */ \
powers = (unsigned char *)MP_ALIGN(powersArray,num_powers); \
MP_CHECKOK( mpi_to_weave(accum, powers, nLen, num_powers) );
if (first_window < 4) {
MP_CHECKOK( mp_copy(&accum[first_window], &accum1) );
first_window = num_powers;
}
} else {
if (first_window == 0) {
mp_set(&accum1, 1);
MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
} else {
/* assert first_window == 1? */
MP_CHECKOK( mp_copy(montBase, &accum1) );
}
}
/*
* calculate all the powers in the powers array.
* this adds 2**(k-1)-2 square operations over just calculating the
* odd powers where k is the window size in the two other mp_modexpt
* implementations in this file. We will get some of that
* back by not needing the first 'k' squares and one multiply for the
* first window.
* Given the value of 4 for WEAVE_WORD_SIZE, this loop will only execute if
* num_powers > 2, in which case powers will have been allocated.
*/
for (i = WEAVE_WORD_SIZE; i < num_powers; i++) {
int acc_index = i & (WEAVE_WORD_SIZE-1); /* i % WEAVE_WORD_SIZE */
if ( i & 1 ) {
MUL_NOWEAVE(montBase, &accum[acc_index-1] , &accum[acc_index]);
/* we've filled the array do our 'per array' processing */
if (acc_index == (WEAVE_WORD_SIZE-1)) {
MP_CHECKOK( mpi_to_weave(accum, powers + i - (WEAVE_WORD_SIZE-1),
nLen, num_powers) );
if (first_window <= i) {
MP_CHECKOK( mp_copy(&accum[first_window & (WEAVE_WORD_SIZE-1)],
&accum1) );
first_window = num_powers;
}
}
} else {
/* up to 8 we can find 2^i-1 in the accum array, but at 8 we our source
* and target are the same so we need to copy.. After that, the
* value is overwritten, so we need to fetch it from the stored
* weave array */
if (i > 2* WEAVE_WORD_SIZE) {
MP_CHECKOK(weave_to_mpi(&accum2, powers+i/2, nLen, num_powers));
SQR(&accum2, &accum[acc_index]);
} else {
int half_power_index = (i/2) & (WEAVE_WORD_SIZE-1);
if (half_power_index == acc_index) {
/* copy is cheaper than weave_to_mpi */
MP_CHECKOK(mp_copy(&accum[half_power_index], &accum2));
SQR(&accum2,&accum[acc_index]);
} else {
SQR(&accum[half_power_index],&accum[acc_index]);
}
}
}
}
/* if the accum1 isn't set, Then there is something wrong with our logic
* above and is an internal programming error.
*/
#if MP_ARGCHK == 2
assert(MP_USED(&accum1) != 0);
#endif
/* set accumulator to montgomery residue of 1 */
pa1 = &accum1;
pa2 = &accum2;
/* tmp is not used if window_bits == 1. */
if (window_bits != 1) {
MP_CHECKOK( mp_init_size(&tmp, 3 * nLen + 2) );
}
for (expOff = bits_in_exponent - window_bits*2; expOff >= 0; expOff -= window_bits) {
mp_size smallExp;
MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
smallExp = (mp_size)res;
/* handle unroll the loops */
switch (window_bits) {
case 1:
if (!smallExp) {
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 1) {
SQR(pa1,pa2); MUL_NOWEAVE(montBase,pa2,pa1);
} else {
abort();
}
break;
case 6:
SQR(pa1,pa2); SQR(pa2,pa1);
/* fall through */
case 4:
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp, pa1,pa2); SWAPPA;
break;
case 5:
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); MUL(smallExp,pa2,pa1);
break;
default:
abort(); /* could do a loop? */
}
}
res = s_mp_redc(pa1, mmm);
mp_exch(pa1, result);
CLEANUP:
mp_clear(&accum1);
mp_clear(&accum2);
mp_clear(&accum[0]);
mp_clear(&accum[1]);
mp_clear(&accum[2]);
mp_clear(&accum[3]);
mp_clear(&tmp);
/* PORT_Memset(powers,0,num_powers*nLen*sizeof(mp_digit)); */
free(powersArray);
return res;
}
#undef SQR
#undef MUL
#endif
mp_err mp_exptmod(const mp_int *inBase, const mp_int *exponent,
const mp_int *modulus, mp_int *result)
{
const mp_int *base;
mp_size bits_in_exponent, i, window_bits, odd_ints;
mp_err res;
int nLen;
mp_int montBase, goodBase;
mp_mont_modulus mmm;
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
static unsigned int max_window_bits;
#endif
/* function for computing n0prime only works if n0 is odd */
if (!mp_isodd(modulus))
return s_mp_exptmod(inBase, exponent, modulus, result);
MP_DIGITS(&montBase) = 0;
MP_DIGITS(&goodBase) = 0;
if (mp_cmp(inBase, modulus) < 0) {
base = inBase;
} else {
MP_CHECKOK( mp_init(&goodBase) );
base = &goodBase;
MP_CHECKOK( mp_mod(inBase, modulus, &goodBase) );
}
nLen = MP_USED(modulus);
MP_CHECKOK( mp_init_size(&montBase, 2 * nLen + 2) );
mmm.N = *modulus; /* a copy of the mp_int struct */
/* compute n0', given n0, n0' = -(n0 ** -1) mod MP_RADIX
** where n0 = least significant mp_digit of N, the modulus.
*/
mmm.n0prime = 0 - s_mp_invmod_radix( MP_DIGIT(modulus, 0) );
MP_CHECKOK( s_mp_to_mont(base, &mmm, &montBase) );
bits_in_exponent = mpl_significant_bits(exponent);
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
if (mp_using_cache_safe_exp) {
if (bits_in_exponent > 780)
window_bits = 6;
else if (bits_in_exponent > 256)
window_bits = 5;
else if (bits_in_exponent > 20)
window_bits = 4;
/* RSA public key exponents are typically under 20 bits (common values
* are: 3, 17, 65537) and a 4-bit window is inefficient
*/
else
window_bits = 1;
} else
#endif
if (bits_in_exponent > 480)
window_bits = 6;
else if (bits_in_exponent > 160)
window_bits = 5;
else if (bits_in_exponent > 20)
window_bits = 4;
/* RSA public key exponents are typically under 20 bits (common values
* are: 3, 17, 65537) and a 4-bit window is inefficient
*/
else
window_bits = 1;
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
/*
* clamp the window size based on
* the cache line size.
*/
if (!max_window_bits) {
unsigned long cache_size = s_mpi_getProcessorLineSize();
/* processor has no cache, use 'fast' code always */
if (cache_size == 0) {
mp_using_cache_safe_exp = 0;
}
if ((cache_size == 0) || (cache_size >= 64)) {
max_window_bits = 6;
} else if (cache_size >= 32) {
max_window_bits = 5;
} else if (cache_size >= 16) {
max_window_bits = 4;
} else max_window_bits = 1; /* should this be an assert? */
}
/* clamp the window size down before we caclulate bits_in_exponent */
if (mp_using_cache_safe_exp) {
if (window_bits > max_window_bits) {
window_bits = max_window_bits;
}
}
#endif
odd_ints = 1 << (window_bits - 1);
i = bits_in_exponent % window_bits;
if (i != 0) {
bits_in_exponent += window_bits - i;
}
#ifdef MP_USING_MONT_MULF
if (mp_using_mont_mulf) {
MP_CHECKOK( s_mp_pad(&montBase, nLen) );
res = mp_exptmod_f(&montBase, exponent, modulus, result, &mmm, nLen,
bits_in_exponent, window_bits, odd_ints);
} else
#endif
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
if (mp_using_cache_safe_exp) {
res = mp_exptmod_safe_i(&montBase, exponent, modulus, result, &mmm, nLen,
bits_in_exponent, window_bits, 1 << window_bits);
} else
#endif
res = mp_exptmod_i(&montBase, exponent, modulus, result, &mmm, nLen,
bits_in_exponent, window_bits, odd_ints);
CLEANUP:
mp_clear(&montBase);
mp_clear(&goodBase);
/* Don't mp_clear mmm.N because it is merely a copy of modulus.
** Just zap it.
*/
memset(&mmm, 0, sizeof mmm);
return res;
}