1*0957b409SSimon J. Gerraty /*
2*0957b409SSimon J. Gerraty * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3*0957b409SSimon J. Gerraty *
4*0957b409SSimon J. Gerraty * Permission is hereby granted, free of charge, to any person obtaining
5*0957b409SSimon J. Gerraty * a copy of this software and associated documentation files (the
6*0957b409SSimon J. Gerraty * "Software"), to deal in the Software without restriction, including
7*0957b409SSimon J. Gerraty * without limitation the rights to use, copy, modify, merge, publish,
8*0957b409SSimon J. Gerraty * distribute, sublicense, and/or sell copies of the Software, and to
9*0957b409SSimon J. Gerraty * permit persons to whom the Software is furnished to do so, subject to
10*0957b409SSimon J. Gerraty * the following conditions:
11*0957b409SSimon J. Gerraty *
12*0957b409SSimon J. Gerraty * The above copyright notice and this permission notice shall be
13*0957b409SSimon J. Gerraty * included in all copies or substantial portions of the Software.
14*0957b409SSimon J. Gerraty *
15*0957b409SSimon J. Gerraty * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16*0957b409SSimon J. Gerraty * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17*0957b409SSimon J. Gerraty * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18*0957b409SSimon J. Gerraty * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19*0957b409SSimon J. Gerraty * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20*0957b409SSimon J. Gerraty * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21*0957b409SSimon J. Gerraty * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22*0957b409SSimon J. Gerraty * SOFTWARE.
23*0957b409SSimon J. Gerraty */
24*0957b409SSimon J. Gerraty
25*0957b409SSimon J. Gerraty #include "inner.h"
26*0957b409SSimon J. Gerraty
27*0957b409SSimon J. Gerraty /* see inner.h */
28*0957b409SSimon J. Gerraty 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)29*0957b409SSimon J. Gerraty br_i15_modpow_opt(uint16_t *x,
30*0957b409SSimon J. Gerraty const unsigned char *e, size_t elen,
31*0957b409SSimon J. Gerraty const uint16_t *m, uint16_t m0i, uint16_t *tmp, size_t twlen)
32*0957b409SSimon J. Gerraty {
33*0957b409SSimon J. Gerraty size_t mlen, mwlen;
34*0957b409SSimon J. Gerraty uint16_t *t1, *t2, *base;
35*0957b409SSimon J. Gerraty size_t u, v;
36*0957b409SSimon J. Gerraty uint32_t acc;
37*0957b409SSimon J. Gerraty int acc_len, win_len;
38*0957b409SSimon J. Gerraty
39*0957b409SSimon J. Gerraty /*
40*0957b409SSimon J. Gerraty * Get modulus size.
41*0957b409SSimon J. Gerraty */
42*0957b409SSimon J. Gerraty mwlen = (m[0] + 31) >> 4;
43*0957b409SSimon J. Gerraty mlen = mwlen * sizeof m[0];
44*0957b409SSimon J. Gerraty mwlen += (mwlen & 1);
45*0957b409SSimon J. Gerraty t1 = tmp;
46*0957b409SSimon J. Gerraty t2 = tmp + mwlen;
47*0957b409SSimon J. Gerraty
48*0957b409SSimon J. Gerraty /*
49*0957b409SSimon J. Gerraty * Compute possible window size, with a maximum of 5 bits.
50*0957b409SSimon J. Gerraty * When the window has size 1 bit, we use a specific code
51*0957b409SSimon J. Gerraty * that requires only two temporaries. Otherwise, for a
52*0957b409SSimon J. Gerraty * window of k bits, we need 2^k+1 temporaries.
53*0957b409SSimon J. Gerraty */
54*0957b409SSimon J. Gerraty if (twlen < (mwlen << 1)) {
55*0957b409SSimon J. Gerraty return 0;
56*0957b409SSimon J. Gerraty }
57*0957b409SSimon J. Gerraty for (win_len = 5; win_len > 1; win_len --) {
58*0957b409SSimon J. Gerraty if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
59*0957b409SSimon J. Gerraty break;
60*0957b409SSimon J. Gerraty }
61*0957b409SSimon J. Gerraty }
62*0957b409SSimon J. Gerraty
63*0957b409SSimon J. Gerraty /*
64*0957b409SSimon J. Gerraty * Everything is done in Montgomery representation.
65*0957b409SSimon J. Gerraty */
66*0957b409SSimon J. Gerraty br_i15_to_monty(x, m);
67*0957b409SSimon J. Gerraty
68*0957b409SSimon J. Gerraty /*
69*0957b409SSimon J. Gerraty * Compute window contents. If the window has size one bit only,
70*0957b409SSimon J. Gerraty * then t2 is set to x; otherwise, t2[0] is left untouched, and
71*0957b409SSimon J. Gerraty * t2[k] is set to x^k (for k >= 1).
72*0957b409SSimon J. Gerraty */
73*0957b409SSimon J. Gerraty if (win_len == 1) {
74*0957b409SSimon J. Gerraty memcpy(t2, x, mlen);
75*0957b409SSimon J. Gerraty } else {
76*0957b409SSimon J. Gerraty memcpy(t2 + mwlen, x, mlen);
77*0957b409SSimon J. Gerraty base = t2 + mwlen;
78*0957b409SSimon J. Gerraty for (u = 2; u < ((unsigned)1 << win_len); u ++) {
79*0957b409SSimon J. Gerraty br_i15_montymul(base + mwlen, base, x, m, m0i);
80*0957b409SSimon J. Gerraty base += mwlen;
81*0957b409SSimon J. Gerraty }
82*0957b409SSimon J. Gerraty }
83*0957b409SSimon J. Gerraty
84*0957b409SSimon J. Gerraty /*
85*0957b409SSimon J. Gerraty * We need to set x to 1, in Montgomery representation. This can
86*0957b409SSimon J. Gerraty * be done efficiently by setting the high word to 1, then doing
87*0957b409SSimon J. Gerraty * one word-sized shift.
88*0957b409SSimon J. Gerraty */
89*0957b409SSimon J. Gerraty br_i15_zero(x, m[0]);
90*0957b409SSimon J. Gerraty x[(m[0] + 15) >> 4] = 1;
91*0957b409SSimon J. Gerraty br_i15_muladd_small(x, 0, m);
92*0957b409SSimon J. Gerraty
93*0957b409SSimon J. Gerraty /*
94*0957b409SSimon J. Gerraty * We process bits from most to least significant. At each
95*0957b409SSimon J. Gerraty * loop iteration, we have acc_len bits in acc.
96*0957b409SSimon J. Gerraty */
97*0957b409SSimon J. Gerraty acc = 0;
98*0957b409SSimon J. Gerraty acc_len = 0;
99*0957b409SSimon J. Gerraty while (acc_len > 0 || elen > 0) {
100*0957b409SSimon J. Gerraty int i, k;
101*0957b409SSimon J. Gerraty uint32_t bits;
102*0957b409SSimon J. Gerraty
103*0957b409SSimon J. Gerraty /*
104*0957b409SSimon J. Gerraty * Get the next bits.
105*0957b409SSimon J. Gerraty */
106*0957b409SSimon J. Gerraty k = win_len;
107*0957b409SSimon J. Gerraty if (acc_len < win_len) {
108*0957b409SSimon J. Gerraty if (elen > 0) {
109*0957b409SSimon J. Gerraty acc = (acc << 8) | *e ++;
110*0957b409SSimon J. Gerraty elen --;
111*0957b409SSimon J. Gerraty acc_len += 8;
112*0957b409SSimon J. Gerraty } else {
113*0957b409SSimon J. Gerraty k = acc_len;
114*0957b409SSimon J. Gerraty }
115*0957b409SSimon J. Gerraty }
116*0957b409SSimon J. Gerraty bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
117*0957b409SSimon J. Gerraty acc_len -= k;
118*0957b409SSimon J. Gerraty
119*0957b409SSimon J. Gerraty /*
120*0957b409SSimon J. Gerraty * We could get exactly k bits. Compute k squarings.
121*0957b409SSimon J. Gerraty */
122*0957b409SSimon J. Gerraty for (i = 0; i < k; i ++) {
123*0957b409SSimon J. Gerraty br_i15_montymul(t1, x, x, m, m0i);
124*0957b409SSimon J. Gerraty memcpy(x, t1, mlen);
125*0957b409SSimon J. Gerraty }
126*0957b409SSimon J. Gerraty
127*0957b409SSimon J. Gerraty /*
128*0957b409SSimon J. Gerraty * Window lookup: we want to set t2 to the window
129*0957b409SSimon J. Gerraty * lookup value, assuming the bits are non-zero. If
130*0957b409SSimon J. Gerraty * the window length is 1 bit only, then t2 is
131*0957b409SSimon J. Gerraty * already set; otherwise, we do a constant-time lookup.
132*0957b409SSimon J. Gerraty */
133*0957b409SSimon J. Gerraty if (win_len > 1) {
134*0957b409SSimon J. Gerraty br_i15_zero(t2, m[0]);
135*0957b409SSimon J. Gerraty base = t2 + mwlen;
136*0957b409SSimon J. Gerraty for (u = 1; u < ((uint32_t)1 << k); u ++) {
137*0957b409SSimon J. Gerraty uint32_t mask;
138*0957b409SSimon J. Gerraty
139*0957b409SSimon J. Gerraty mask = -EQ(u, bits);
140*0957b409SSimon J. Gerraty for (v = 1; v < mwlen; v ++) {
141*0957b409SSimon J. Gerraty t2[v] |= mask & base[v];
142*0957b409SSimon J. Gerraty }
143*0957b409SSimon J. Gerraty base += mwlen;
144*0957b409SSimon J. Gerraty }
145*0957b409SSimon J. Gerraty }
146*0957b409SSimon J. Gerraty
147*0957b409SSimon J. Gerraty /*
148*0957b409SSimon J. Gerraty * Multiply with the looked-up value. We keep the
149*0957b409SSimon J. Gerraty * product only if the exponent bits are not all-zero.
150*0957b409SSimon J. Gerraty */
151*0957b409SSimon J. Gerraty br_i15_montymul(t1, x, t2, m, m0i);
152*0957b409SSimon J. Gerraty CCOPY(NEQ(bits, 0), x, t1, mlen);
153*0957b409SSimon J. Gerraty }
154*0957b409SSimon J. Gerraty
155*0957b409SSimon J. Gerraty /*
156*0957b409SSimon J. Gerraty * Convert back from Montgomery representation, and exit.
157*0957b409SSimon J. Gerraty */
158*0957b409SSimon J. Gerraty br_i15_from_monty(x, m, m0i);
159*0957b409SSimon J. Gerraty return 1;
160*0957b409SSimon J. Gerraty }
161