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-rw-r--r--security/nss/lib/freebl/mpi/mpmontg.c1151
1 files changed, 1151 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/mpmontg.c b/security/nss/lib/freebl/mpi/mpmontg.c
new file mode 100644
index 0000000000..36ae51b352
--- /dev/null
+++ b/security/nss/lib/freebl/mpi/mpmontg.c
@@ -0,0 +1,1151 @@
+/* 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 ((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 = 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(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
+
+/*
+ * 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(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 = (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(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);
+ /* 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);
+
+ 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;
+}
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