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comparison 3rdparty/libtommath/bn_s_mp_exptmod.c @ 0:2cf249471370

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author Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
date Tue, 08 May 2018 16:09:12 +0900
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-1:000000000000 0:2cf249471370
1 #include <tommath_private.h>
2 #ifdef BN_S_MP_EXPTMOD_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
16 */
17 #ifdef MP_LOW_MEM
18 #define TAB_SIZE 32
19 #else
20 #define TAB_SIZE 256
21 #endif
22
23 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
24 {
25 mp_int M[TAB_SIZE], res, mu;
26 mp_digit buf;
27 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
28 int (*redux)(mp_int*,mp_int*,mp_int*);
29
30 /* find window size */
31 x = mp_count_bits (X);
32 if (x <= 7) {
33 winsize = 2;
34 } else if (x <= 36) {
35 winsize = 3;
36 } else if (x <= 140) {
37 winsize = 4;
38 } else if (x <= 450) {
39 winsize = 5;
40 } else if (x <= 1303) {
41 winsize = 6;
42 } else if (x <= 3529) {
43 winsize = 7;
44 } else {
45 winsize = 8;
46 }
47
48 #ifdef MP_LOW_MEM
49 if (winsize > 5) {
50 winsize = 5;
51 }
52 #endif
53
54 /* init M array */
55 /* init first cell */
56 if ((err = mp_init(&M[1])) != MP_OKAY) {
57 return err;
58 }
59
60 /* now init the second half of the array */
61 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
62 if ((err = mp_init(&M[x])) != MP_OKAY) {
63 for (y = 1<<(winsize-1); y < x; y++) {
64 mp_clear (&M[y]);
65 }
66 mp_clear(&M[1]);
67 return err;
68 }
69 }
70
71 /* create mu, used for Barrett reduction */
72 if ((err = mp_init (&mu)) != MP_OKAY) {
73 goto LBL_M;
74 }
75
76 if (redmode == 0) {
77 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
78 goto LBL_MU;
79 }
80 redux = mp_reduce;
81 } else {
82 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
83 goto LBL_MU;
84 }
85 redux = mp_reduce_2k_l;
86 }
87
88 /* create M table
89 *
90 * The M table contains powers of the base,
91 * e.g. M[x] = G**x mod P
92 *
93 * The first half of the table is not
94 * computed though accept for M[0] and M[1]
95 */
96 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
97 goto LBL_MU;
98 }
99
100 /* compute the value at M[1<<(winsize-1)] by squaring
101 * M[1] (winsize-1) times
102 */
103 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
104 goto LBL_MU;
105 }
106
107 for (x = 0; x < (winsize - 1); x++) {
108 /* square it */
109 if ((err = mp_sqr (&M[1 << (winsize - 1)],
110 &M[1 << (winsize - 1)])) != MP_OKAY) {
111 goto LBL_MU;
112 }
113
114 /* reduce modulo P */
115 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
116 goto LBL_MU;
117 }
118 }
119
120 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
121 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
122 */
123 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
124 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
125 goto LBL_MU;
126 }
127 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
128 goto LBL_MU;
129 }
130 }
131
132 /* setup result */
133 if ((err = mp_init (&res)) != MP_OKAY) {
134 goto LBL_MU;
135 }
136 mp_set (&res, 1);
137
138 /* set initial mode and bit cnt */
139 mode = 0;
140 bitcnt = 1;
141 buf = 0;
142 digidx = X->used - 1;
143 bitcpy = 0;
144 bitbuf = 0;
145
146 for (;;) {
147 /* grab next digit as required */
148 if (--bitcnt == 0) {
149 /* if digidx == -1 we are out of digits */
150 if (digidx == -1) {
151 break;
152 }
153 /* read next digit and reset the bitcnt */
154 buf = X->dp[digidx--];
155 bitcnt = (int) DIGIT_BIT;
156 }
157
158 /* grab the next msb from the exponent */
159 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
160 buf <<= (mp_digit)1;
161
162 /* if the bit is zero and mode == 0 then we ignore it
163 * These represent the leading zero bits before the first 1 bit
164 * in the exponent. Technically this opt is not required but it
165 * does lower the # of trivial squaring/reductions used
166 */
167 if ((mode == 0) && (y == 0)) {
168 continue;
169 }
170
171 /* if the bit is zero and mode == 1 then we square */
172 if ((mode == 1) && (y == 0)) {
173 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
174 goto LBL_RES;
175 }
176 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
177 goto LBL_RES;
178 }
179 continue;
180 }
181
182 /* else we add it to the window */
183 bitbuf |= (y << (winsize - ++bitcpy));
184 mode = 2;
185
186 if (bitcpy == winsize) {
187 /* ok window is filled so square as required and multiply */
188 /* square first */
189 for (x = 0; x < winsize; x++) {
190 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
191 goto LBL_RES;
192 }
193 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
194 goto LBL_RES;
195 }
196 }
197
198 /* then multiply */
199 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
200 goto LBL_RES;
201 }
202 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
203 goto LBL_RES;
204 }
205
206 /* empty window and reset */
207 bitcpy = 0;
208 bitbuf = 0;
209 mode = 1;
210 }
211 }
212
213 /* if bits remain then square/multiply */
214 if ((mode == 2) && (bitcpy > 0)) {
215 /* square then multiply if the bit is set */
216 for (x = 0; x < bitcpy; x++) {
217 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
218 goto LBL_RES;
219 }
220 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
221 goto LBL_RES;
222 }
223
224 bitbuf <<= 1;
225 if ((bitbuf & (1 << winsize)) != 0) {
226 /* then multiply */
227 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
228 goto LBL_RES;
229 }
230 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
231 goto LBL_RES;
232 }
233 }
234 }
235 }
236
237 mp_exch (&res, Y);
238 err = MP_OKAY;
239 LBL_RES:mp_clear (&res);
240 LBL_MU:mp_clear (&mu);
241 LBL_M:
242 mp_clear(&M[1]);
243 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
244 mp_clear (&M[x]);
245 }
246 return err;
247 }
248 #endif
249
250 /* $Source$ */
251 /* $Revision$ */
252 /* $Date$ */