1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
|
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*/
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, res, digs;
mp_digit mu;
/* can the fast reduction [comba] method be used?
*
* Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
digs = (n->used * 2) + 1;
if ((digs < (int)MP_WARRAY) &&
(x->used <= (int)MP_WARRAY) &&
(n->used <
(int)(1u << (((size_t)CHAR_BIT * sizeof(mp_word)) - (2u * (size_t)DIGIT_BIT))))) {
return fast_mp_montgomery_reduce(x, n, rho);
}
/* grow the input as required */
if (x->alloc < digs) {
if ((res = mp_grow(x, digs)) != MP_OKAY) {
return res;
}
}
x->used = digs;
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
* montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
/* a = a + mu * m * b**i */
{
int iy;
mp_digit *tmpn, *tmpx, u;
mp_word r;
/* alias for digits of the modulus */
tmpn = n->dp;
/* alias for the digits of x [the input] */
tmpx = x->dp + ix;
/* set the carry to zero */
u = 0;
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
/* compute product and sum */
r = ((mp_word)mu * (mp_word)*tmpn++) +
(mp_word)u + (mp_word)*tmpx;
/* get carry */
u = (mp_digit)(r >> (mp_word)DIGIT_BIT);
/* fix digit */
*tmpx++ = (mp_digit)(r & (mp_word)MP_MASK);
}
/* At this point the ix'th digit of x should be zero */
/* propagate carries upwards as required*/
while (u != 0u) {
*tmpx += u;
u = *tmpx >> DIGIT_BIT;
*tmpx++ &= MP_MASK;
}
}
}
/* at this point the n.used'th least
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/
/* x = x/b**n.used */
mp_clamp(x);
mp_rshd(x, n->used);
/* if x >= n then x = x - n */
if (mp_cmp_mag(x, n) != MP_LT) {
return s_mp_sub(x, n, x);
}
return MP_OKAY;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */
|
