2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
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:
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
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
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
)
34 uint16_t *t1
, *t2
, *base
;
42 mwlen
= (m
[0] + 31) >> 4;
43 mlen
= mwlen
* sizeof m
[0];
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.
54 if (twlen
< (mwlen
<< 1)) {
57 for (win_len
= 5; win_len
> 1; win_len
--) {
58 if ((((uint32_t)1 << win_len
) + 1) * mwlen
<= twlen
) {
64 * Everything is done in Montgomery representation.
66 br_i15_to_monty(x
, m
);
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).
76 memcpy(t2
+ mwlen
, x
, mlen
);
78 for (u
= 2; u
< ((unsigned)1 << win_len
); u
++) {
79 br_i15_montymul(base
+ mwlen
, base
, x
, m
, m0i
);
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.
90 x
[(m
[0] + 15) >> 4] = 1;
91 br_i15_muladd_small(x
, 0, m
);
94 * We process bits from most to least significant. At each
95 * loop iteration, we have acc_len bits in acc.
99 while (acc_len
> 0 || elen
> 0) {
107 if (acc_len
< win_len
) {
109 acc
= (acc
<< 8) | *e
++;
116 bits
= (acc
>> (acc_len
- k
)) & (((uint32_t)1 << k
) - 1);
120 * We could get exactly k bits. Compute k squarings.
122 for (i
= 0; i
< k
; i
++) {
123 br_i15_montymul(t1
, x
, x
, m
, m0i
);
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.
134 br_i15_zero(t2
, m
[0]);
136 for (u
= 1; u
< ((uint32_t)1 << k
); u
++) {
140 for (v
= 1; v
< mwlen
; v
++) {
141 t2
[v
] |= m
& base
[v
];
148 * Multiply with the looked-up value. We keep the
149 * product only if the exponent bits are not all-zero.
151 br_i15_montymul(t1
, x
, t2
, m
, m0i
);
152 CCOPY(NEQ(bits
, 0), x
, t1
, mlen
);
156 * Convert back from Montgomery representation, and exit.
158 br_i15_from_monty(x
, m
, m0i
);