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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 */
#include <assert.h>
#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 (s_mp_cmp(T, &mmm->N) >= 0) {
/* T = T - N */
MP_CHECKOK(s_mp_sub(T, &mmm->N));
#ifdef DEBUG
if (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
mp_err
mp_to_mont(const mp_int *x, const mp_int *N, mp_int *xMont)
{
mp_err res;
/* xMont = x * R mod N where N is modulus */
if (x != xMont) {
MP_CHECKOK(mp_copy(x, xMont));
}
MP_CHECKOK(s_mp_lshd(xMont, MP_USED(N))); /* xMont = x << b */
MP_CHECKOK(mp_div(xMont, N, 0, xMont)); /* mod N */
CLEANUP:
return res;
}
mp_digit
mp_calculate_mont_n0i(const mp_int *N)
{
return 0 - s_mp_invmod_radix(MP_DIGIT(N, 0));
}
#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(mp_to_mont(&accum1, &(mmm->N), &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 = malloc(dSize);
if (!dBuf) {
res = MP_MEM;
goto CLEANUP;
}
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(mp_to_mont(&accum1, &(mmm->N), &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
/*
* 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.
*
* This implementation treats each mp_int bignum as an array of mp_digits,
* It stores those bytes as a column of mp_digits in the output matrix. It
* doesn't care if the machine uses big-endian or little-endian byte ordering
* within mp_digits.
*
* "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,
mp_digit *weaved,
mp_size nDigits, /* in each mp_int of input */
mp_size nBignums) /* in the entire source array */
{
mp_size i;
mp_digit *endDest = weaved + (nDigits * nBignums);
for (i = 0; i < WEAVE_WORD_SIZE; i++) {
mp_size used = MP_USED(&bignums[i]);
mp_digit *pSrc = MP_DIGITS(&bignums[i]);
mp_digit *endSrc = pSrc + used;
mp_digit *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;
}
/*
* These functions return 0xffffffff if the output is true, and 0 otherwise.
*/
#define CONST_TIME_MSB(x) (0L - ((x) >> (8 * sizeof(x) - 1)))
#define CONST_TIME_EQ_Z(x) CONST_TIME_MSB(~(x) & ((x)-1))
#define CONST_TIME_EQ(a, b) CONST_TIME_EQ_Z((a) ^ (b))
/* Reverse the operation above for one mp_int.
* Reconstruct one mp_int from its column in the weaved array.
* Every read accesses every element of the weaved array, in order to
* avoid timing attacks based on patterns of memory accesses.
*/
mp_err
weave_to_mpi(mp_int *a, /* out, result */
const mp_digit *weaved, /* in, byte matrix */
mp_size index, /* which column to read */
mp_size nDigits, /* number of mp_digits in each bignum */
mp_size nBignums) /* width of the matrix */
{
/* these are indices, but need to be the same size as mp_digit
* because of the CONST_TIME operations */
mp_digit i, j;
mp_digit d;
mp_digit *pDest = MP_DIGITS(a);
MP_SIGN(a) = MP_ZPOS;
MP_USED(a) = nDigits;
assert(weaved != NULL);
/* Fetch the proper column in constant time, indexing over the whole array */
for (i = 0; i < nDigits; ++i) {
d = 0;
for (j = 0; j < nBignums; ++j) {
d |= weaved[i * nBignums + j] & CONST_TIME_EQ(j, index);
}
pDest[i] = d;
}
s_mp_clamp(a);
return MP_OKAY;
}
#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;
mp_digit *powersArray = NULL;
mp_digit *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(mp_to_mont(&accum[0], &(mmm->N), &accum[0]));
MP_CHECKOK(mp_copy(montBase, &accum[1]));
SQR(montBase, &accum[2]);
MUL_NOWEAVE(montBase, &accum[2], &accum[3]);
powersArray = (mp_digit *)malloc(num_powers * (nLen * sizeof(mp_digit) + 1));
if (!powersArray) {
res = MP_MEM;
goto CLEANUP;
}
/* powers[i] = base ** (i); */
powers = (mp_digit *)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(mp_to_mont(&accum1, &(mmm->N), &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);
/* zero required by FIPS here, can't use PORT_ZFree
* because mpi doesn't link with util */
if (powers) {
PORT_Memset(powers, 0, num_powers * 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);
if (mp_cmp_z(inBase) == MP_LT)
return MP_RANGE;
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 = mp_calculate_mont_n0i(modulus);
MP_CHECKOK(mp_to_mont(base, modulus, &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;
}