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  	mwlen += (mwlen & 1);
 45  	t1 = tmp;
 46  	t2 = tmp + mwlen;
 47  
 48  	/*
 49  	 * Compute possible window size, with a maximum of 5 bits.
 50  	 * When the window has size 1 bit, we use a specific code
 51  	 * that requires only two temporaries. Otherwise, for a
 52  	 * window of k bits, we need 2^k+1 temporaries.
 53  	 */
 54  	if (twlen < (mwlen << 1)) {
 55  		return 0;
 56  	}
 57  	for (win_len = 5; win_len > 1; win_len --) {
 58  		if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
 59  			break;
 60  		}
 61  	}
 62  
 63  	/*
 64  	 * Everything is done in Montgomery representation.
 65  	 */
 66  	br_i15_to_monty(x, m);
 67  
 68  	/*
 69  	 * Compute window contents. If the window has size one bit only,
 70  	 * then t2 is set to x; otherwise, t2[0] is left untouched, and
 71  	 * t2[k] is set to x^k (for k >= 1).
 72  	 */
 73  	if (win_len == 1) {
 74  		memcpy(t2, x, mlen);
 75  	} else {
 76  		memcpy(t2 + mwlen, x, mlen);
 77  		base = t2 + mwlen;
 78  		for (u = 2; u < ((unsigned)1 << win_len); u ++) {
 79  			br_i15_montymul(base + mwlen, base, x, m, m0i);
 80  			base += mwlen;
 81  		}
 82  	}
 83  
 84  	/*
 85  	 * We need to set x to 1, in Montgomery representation. This can
 86  	 * be done efficiently by setting the high word to 1, then doing
 87  	 * one word-sized shift.
 88  	 */
 89  	br_i15_zero(x, m[0]);
 90  	x[(m[0] + 15) >> 4] = 1;
 91  	br_i15_muladd_small(x, 0, m);
 92  
 93  	/*
 94  	 * We process bits from most to least significant. At each
 95  	 * loop iteration, we have acc_len bits in acc.
 96  	 */
 97  	acc = 0;
 98  	acc_len = 0;
 99  	while (acc_len > 0 || elen > 0) {
100  		int i, k;
101  		uint32_t bits;
102  
103  		/*
104  		 * Get the next bits.
105  		 */
106  		k = win_len;
107  		if (acc_len < win_len) {
108  			if (elen > 0) {
109  				acc = (acc << 8) | *e ++;
110  				elen --;
111  				acc_len += 8;
112  			} else {
113  				k = acc_len;
114  			}
115  		}
116  		bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
117  		acc_len -= k;
118  
119  		/*
120  		 * We could get exactly k bits. Compute k squarings.
121  		 */
122  		for (i = 0; i < k; i ++) {
123  			br_i15_montymul(t1, x, x, m, m0i);
124  			memcpy(x, t1, mlen);
125  		}
126  
127  		/*
128  		 * Window lookup: we want to set t2 to the window
129  		 * lookup value, assuming the bits are non-zero. If
130  		 * the window length is 1 bit only, then t2 is
131  		 * already set; otherwise, we do a constant-time lookup.
132  		 */
133  		if (win_len > 1) {
134  			br_i15_zero(t2, m[0]);
135  			base = t2 + mwlen;
136  			for (u = 1; u < ((uint32_t)1 << k); u ++) {
137  				uint32_t mask;
138  
139  				mask = -EQ(u, bits);
140  				for (v = 1; v < mwlen; v ++) {
141  					t2[v] |= mask & base[v];
142  				}
143  				base += mwlen;
144  			}
145  		}
146  
147  		/*
148  		 * Multiply with the looked-up value. We keep the
149  		 * product only if the exponent bits are not all-zero.
150  		 */
151  		br_i15_montymul(t1, x, t2, m, m0i);
152  		CCOPY(NEQ(bits, 0), x, t1, mlen);
153  	}
154  
155  	/*
156  	 * Convert back from Montgomery representation, and exit.
157  	 */
158  	br_i15_from_monty(x, m, m0i);
159  	return 1;
160  }