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/*
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "inner.h"
/* see inner.h */
uint32_t
br_i15_modpow_opt(uint16_t *x,
const unsigned char *e, size_t elen,
const uint16_t *m, uint16_t m0i, uint16_t *tmp, size_t twlen)
{
size_t mlen, mwlen;
uint16_t *t1, *t2, *base;
size_t u, v;
uint32_t acc;
int acc_len, win_len;
/*
* Get modulus size.
*/
mwlen = (m[0] + 31) >> 4;
mlen = mwlen * sizeof m[0];
mwlen += (mwlen & 1);
t1 = tmp;
t2 = tmp + mwlen;
/*
* Compute possible window size, with a maximum of 5 bits.
* When the window has size 1 bit, we use a specific code
* that requires only two temporaries. Otherwise, for a
* window of k bits, we need 2^k+1 temporaries.
*/
if (twlen < (mwlen << 1)) {
return 0;
}
for (win_len = 5; win_len > 1; win_len --) {
if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
break;
}
}
/*
* Everything is done in Montgomery representation.
*/
br_i15_to_monty(x, m);
/*
* Compute window contents. If the window has size one bit only,
* then t2 is set to x; otherwise, t2[0] is left untouched, and
* t2[k] is set to x^k (for k >= 1).
*/
if (win_len == 1) {
memcpy(t2, x, mlen);
} else {
memcpy(t2 + mwlen, x, mlen);
base = t2 + mwlen;
for (u = 2; u < ((unsigned)1 << win_len); u ++) {
br_i15_montymul(base + mwlen, base, x, m, m0i);
base += mwlen;
}
}
/*
* We need to set x to 1, in Montgomery representation. This can
* be done efficiently by setting the high word to 1, then doing
* one word-sized shift.
*/
br_i15_zero(x, m[0]);
x[(m[0] + 15) >> 4] = 1;
br_i15_muladd_small(x, 0, m);
/*
* We process bits from most to least significant. At each
* loop iteration, we have acc_len bits in acc.
*/
acc = 0;
acc_len = 0;
while (acc_len > 0 || elen > 0) {
int i, k;
uint32_t bits;
/*
* Get the next bits.
*/
k = win_len;
if (acc_len < win_len) {
if (elen > 0) {
acc = (acc << 8) | *e ++;
elen --;
acc_len += 8;
} else {
k = acc_len;
}
}
bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
acc_len -= k;
/*
* We could get exactly k bits. Compute k squarings.
*/
for (i = 0; i < k; i ++) {
br_i15_montymul(t1, x, x, m, m0i);
memcpy(x, t1, mlen);
}
/*
* Window lookup: we want to set t2 to the window
* lookup value, assuming the bits are non-zero. If
* the window length is 1 bit only, then t2 is
* already set; otherwise, we do a constant-time lookup.
*/
if (win_len > 1) {
br_i15_zero(t2, m[0]);
base = t2 + mwlen;
for (u = 1; u < ((uint32_t)1 << k); u ++) {
uint32_t mask;
mask = -EQ(u, bits);
for (v = 1; v < mwlen; v ++) {
t2[v] |= mask & base[v];
}
base += mwlen;
}
}
/*
* Multiply with the looked-up value. We keep the
* product only if the exponent bits are not all-zero.
*/
br_i15_montymul(t1, x, t2, m, m0i);
CCOPY(NEQ(bits, 0), x, t1, mlen);
}
/*
* Convert back from Montgomery representation, and exit.
*/
br_i15_from_monty(x, m, m0i);
return 1;
}
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