_ Git - BearSSL/blob - src/int/i15_modpow2.c

   1 /*
   2  * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining
   5  * a copy of this software and associated documentation files (the
   6  * "Software"), to deal in the Software without restriction, including
   7  * without limitation the rights to use, copy, modify, merge, publish,
   8  * distribute, sublicense, and/or sell copies of the Software, and to
   9  * permit persons to whom the Software is furnished to do so, subject to
  10  * the following conditions:
  11  *
  12  * The above copyright notice and this permission notice shall be
  13  * included in all copies or substantial portions of the Software.
  14  *
  15  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  16  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  17  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  18  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
  19  * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
  20  * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  21  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  22  * SOFTWARE.
  23  */
  24
  25 #include "inner.h"
  26
  27 /* see inner.h */
  28 uint32_t
  29 br_i15_modpow_opt(uint16_t *x,
  30         const unsigned char *e, size_t elen,
  31         const uint16_t *m, uint16_t m0i, uint16_t *tmp, size_t twlen)
  32 {
  33         size_t mlen, mwlen;
  34         uint16_t *t1, *t2, *base;
  35         size_t u, v;
  36         uint32_t acc;
  37         int acc_len, win_len;
  38
  39         /*
  40          * Get modulus size.
  41          */
  42         mwlen = (m[0] + 31) >> 4;
  43         mlen = mwlen * sizeof m[0];
  44         t1 = tmp;
  45         t2 = tmp + mwlen;
  46
  47         /*
  48          * Compute possible window size, with a maximum of 5 bits.
  49          * When the window has size 1 bit, we use a specific code
  50          * that requires only two temporaries. Otherwise, for a
  51          * window of k bits, we need 2^k+1 temporaries.
  52          */
  53         if (twlen < (mwlen << 1)) {
  54                 return 0;
  55         }
  56         for (win_len = 5; win_len > 1; win_len --) {
  57                 if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
  58                         break;
  59                 }
  60         }
  61
  62         /*
  63          * Everything is done in Montgomery representation.
  64          */
  65         br_i15_to_monty(x, m);
  66
  67         /*
  68          * Compute window contents. If the window has size one bit only,
  69          * then t2 is set to x; otherwise, t2[0] is left untouched, and
  70          * t2[k] is set to x^k (for k >= 1).
  71          */
  72         if (win_len == 1) {
  73                 memcpy(t2, x, mlen);
  74         } else {
  75                 memcpy(t2 + mwlen, x, mlen);
  76                 base = t2 + mwlen;
  77                 for (u = 2; u < ((unsigned)1 << win_len); u ++) {
  78                         br_i15_montymul(base + mwlen, base, x, m, m0i);
  79                         base += mwlen;
  80                 }
  81         }
  82
  83         /*
  84          * We need to set x to 1, in Montgomery representation. This can
  85          * be done efficiently by setting the high word to 1, then doing
  86          * one word-sized shift.
  87          */
  88         br_i15_zero(x, m[0]);
  89         x[mwlen - 1] = 1;
  90         br_i15_muladd_small(x, 0, m);
  91
  92         /*
  93          * We process bits from most to least significant. At each
  94          * loop iteration, we have acc_len bits in acc.
  95          */
  96         acc = 0;
  97         acc_len = 0;
  98         while (acc_len > 0 || elen > 0) {
  99                 int i, k;
 100                 uint32_t bits;
 101
 102                 /*
 103                  * Get the next bits.
 104                  */
 105                 k = win_len;
 106                 if (acc_len < win_len) {
 107                         if (elen > 0) {
 108                                 acc = (acc << 8) | *e ++;
 109                                 elen --;
 110                                 acc_len += 8;
 111                         } else {
 112                                 k = acc_len;
 113                         }
 114                 }
 115                 bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
 116                 acc_len -= k;
 117
 118                 /*
 119                  * We could get exactly k bits. Compute k squarings.
 120                  */
 121                 for (i = 0; i < k; i ++) {
 122                         br_i15_montymul(t1, x, x, m, m0i);
 123                         memcpy(x, t1, mlen);
 124                 }
 125
 126                 /*
 127                  * Window lookup: we want to set t2 to the window
 128                  * lookup value, assuming the bits are non-zero. If
 129                  * the window length is 1 bit only, then t2 is
 130                  * already set; otherwise, we do a constant-time lookup.
 131                  */
 132                 if (win_len > 1) {
 133                         br_i15_zero(t2, m[0]);
 134                         base = t2 + mwlen;
 135                         for (u = 1; u < ((uint32_t)1 << k); u ++) {
 136                                 uint32_t m;
 137
 138                                 m = -EQ(u, bits);
 139                                 for (v = 1; v < mwlen; v ++) {
 140                                         t2[v] |= m & base[v];
 141                                 }
 142                                 base += mwlen;
 143                         }
 144                 }
 145
 146                 /*
 147                  * Multiply with the looked-up value. We keep the
 148                  * product only if the exponent bits are not all-zero.
 149                  */
 150                 br_i15_montymul(t1, x, t2, m, m0i);
 151                 CCOPY(NEQ(bits, 0), x, t1, mlen);
 152         }
 153
 154         /*
 155          * Convert back from Montgomery representation, and exit.
 156          */
 157         br_i15_from_monty(x, m, m0i);
 158         return 1;
 159 }