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 */
28uint32_t
29br_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}
161