summaryrefslogtreecommitdiff
path: root/lib/mpi/mpi-pow.c
blob: edf345b7f06b6fed6769872038a25a5487cee462 (plain)
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
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
/* mpi-pow.c  -  MPI functions
 *	Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * GnuPG is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */

#include <linux/sched.h>
#include <linux/string.h>
#include "mpi-internal.h"
#include "longlong.h"

/****************
 * RES = BASE ^ EXP mod MOD
 */
int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
{
	mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
	struct karatsuba_ctx karactx = {};
	mpi_ptr_t xp_marker = NULL;
	mpi_ptr_t tspace = NULL;
	mpi_ptr_t rp, ep, mp, bp;
	mpi_size_t esize, msize, bsize, rsize;
	int esign, msign, bsign, rsign;
	mpi_size_t size;
	int mod_shift_cnt;
	int negative_result;
	int assign_rp = 0;
	mpi_size_t tsize = 0;	/* to avoid compiler warning */
	/* fixme: we should check that the warning is void */
	int rc = -ENOMEM;

	esize = exp->nlimbs;
	msize = mod->nlimbs;
	size = 2 * msize;
	esign = exp->sign;
	msign = mod->sign;

	rp = res->d;
	ep = exp->d;

	if (!msize)
		return -EINVAL;

	if (!esize) {
		/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
		 * depending on if MOD equals 1.  */
		res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
		if (res->nlimbs) {
			if (mpi_resize(res, 1) < 0)
				goto enomem;
			rp = res->d;
			rp[0] = 1;
		}
		res->sign = 0;
		goto leave;
	}

	/* Normalize MOD (i.e. make its most significant bit set) as required by
	 * mpn_divrem.  This will make the intermediate values in the calculation
	 * slightly larger, but the correct result is obtained after a final
	 * reduction using the original MOD value.  */
	mp = mp_marker = mpi_alloc_limb_space(msize);
	if (!mp)
		goto enomem;
	mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
	if (mod_shift_cnt)
		mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
	else
		MPN_COPY(mp, mod->d, msize);

	bsize = base->nlimbs;
	bsign = base->sign;
	if (bsize > msize) {	/* The base is larger than the module. Reduce it. */
		/* Allocate (BSIZE + 1) with space for remainder and quotient.
		 * (The quotient is (bsize - msize + 1) limbs.)  */
		bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
		if (!bp)
			goto enomem;
		MPN_COPY(bp, base->d, bsize);
		/* We don't care about the quotient, store it above the remainder,
		 * at BP + MSIZE.  */
		mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
		bsize = msize;
		/* Canonicalize the base, since we are going to multiply with it
		 * quite a few times.  */
		MPN_NORMALIZE(bp, bsize);
	} else
		bp = base->d;

	if (!bsize) {
		res->nlimbs = 0;
		res->sign = 0;
		goto leave;
	}

	if (res->alloced < size) {
		/* We have to allocate more space for RES.  If any of the input
		 * parameters are identical to RES, defer deallocation of the old
		 * space.  */
		if (rp == ep || rp == mp || rp == bp) {
			rp = mpi_alloc_limb_space(size);
			if (!rp)
				goto enomem;
			assign_rp = 1;
		} else {
			if (mpi_resize(res, size) < 0)
				goto enomem;
			rp = res->d;
		}
	} else {		/* Make BASE, EXP and MOD not overlap with RES.  */
		if (rp == bp) {
			/* RES and BASE are identical.  Allocate temp. space for BASE.  */
			BUG_ON(bp_marker);
			bp = bp_marker = mpi_alloc_limb_space(bsize);
			if (!bp)
				goto enomem;
			MPN_COPY(bp, rp, bsize);
		}
		if (rp == ep) {
			/* RES and EXP are identical.  Allocate temp. space for EXP.  */
			ep = ep_marker = mpi_alloc_limb_space(esize);
			if (!ep)
				goto enomem;
			MPN_COPY(ep, rp, esize);
		}
		if (rp == mp) {
			/* RES and MOD are identical.  Allocate temporary space for MOD. */
			BUG_ON(mp_marker);
			mp = mp_marker = mpi_alloc_limb_space(msize);
			if (!mp)
				goto enomem;
			MPN_COPY(mp, rp, msize);
		}
	}

	MPN_COPY(rp, bp, bsize);
	rsize = bsize;
	rsign = bsign;

	{
		mpi_size_t i;
		mpi_ptr_t xp;
		int c;
		mpi_limb_t e;
		mpi_limb_t carry_limb;

		xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
		if (!xp)
			goto enomem;

		negative_result = (ep[0] & 1) && base->sign;

		i = esize - 1;
		e = ep[i];
		c = count_leading_zeros(e);
		e = (e << c) << 1;	/* shift the exp bits to the left, lose msb */
		c = BITS_PER_MPI_LIMB - 1 - c;

		/* Main loop.
		 *
		 * Make the result be pointed to alternately by XP and RP.  This
		 * helps us avoid block copying, which would otherwise be necessary
		 * with the overlap restrictions of mpihelp_divmod. With 50% probability
		 * the result after this loop will be in the area originally pointed
		 * by RP (==RES->d), and with 50% probability in the area originally
		 * pointed to by XP.
		 */

		for (;;) {
			while (c) {
				mpi_ptr_t tp;
				mpi_size_t xsize;

				/*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
				if (rsize < KARATSUBA_THRESHOLD)
					mpih_sqr_n_basecase(xp, rp, rsize);
				else {
					if (!tspace) {
						tsize = 2 * rsize;
						tspace =
						    mpi_alloc_limb_space(tsize);
						if (!tspace)
							goto enomem;
					} else if (tsize < (2 * rsize)) {
						mpi_free_limb_space(tspace);
						tsize = 2 * rsize;
						tspace =
						    mpi_alloc_limb_space(tsize);
						if (!tspace)
							goto enomem;
					}
					mpih_sqr_n(xp, rp, rsize, tspace);
				}

				xsize = 2 * rsize;
				if (xsize > msize) {
					mpihelp_divrem(xp + msize, 0, xp, xsize,
						       mp, msize);
					xsize = msize;
				}

				tp = rp;
				rp = xp;
				xp = tp;
				rsize = xsize;

				if ((mpi_limb_signed_t) e < 0) {
					/*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
					if (bsize < KARATSUBA_THRESHOLD) {
						mpi_limb_t tmp;
						if (mpihelp_mul
						    (xp, rp, rsize, bp, bsize,
						     &tmp) < 0)
							goto enomem;
					} else {
						if (mpihelp_mul_karatsuba_case
						    (xp, rp, rsize, bp, bsize,
						     &karactx) < 0)
							goto enomem;
					}

					xsize = rsize + bsize;
					if (xsize > msize) {
						mpihelp_divrem(xp + msize, 0,
							       xp, xsize, mp,
							       msize);
						xsize = msize;
					}

					tp = rp;
					rp = xp;
					xp = tp;
					rsize = xsize;
				}
				e <<= 1;
				c--;
				cond_resched();
			}

			i--;
			if (i < 0)
				break;
			e = ep[i];
			c = BITS_PER_MPI_LIMB;
		}

		/* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
		 * steps.  Adjust the result by reducing it with the original MOD.
		 *
		 * Also make sure the result is put in RES->d (where it already
		 * might be, see above).
		 */
		if (mod_shift_cnt) {
			carry_limb =
			    mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
			rp = res->d;
			if (carry_limb) {
				rp[rsize] = carry_limb;
				rsize++;
			}
		} else {
			MPN_COPY(res->d, rp, rsize);
			rp = res->d;
		}

		if (rsize >= msize) {
			mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
			rsize = msize;
		}

		/* Remove any leading zero words from the result.  */
		if (mod_shift_cnt)
			mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
		MPN_NORMALIZE(rp, rsize);
	}

	if (negative_result && rsize) {
		if (mod_shift_cnt)
			mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
		mpihelp_sub(rp, mp, msize, rp, rsize);
		rsize = msize;
		rsign = msign;
		MPN_NORMALIZE(rp, rsize);
	}
	res->nlimbs = rsize;
	res->sign = rsign;

leave:
	rc = 0;
enomem:
	mpihelp_release_karatsuba_ctx(&karactx);
	if (assign_rp)
		mpi_assign_limb_space(res, rp, size);
	if (mp_marker)
		mpi_free_limb_space(mp_marker);
	if (bp_marker)
		mpi_free_limb_space(bp_marker);
	if (ep_marker)
		mpi_free_limb_space(ep_marker);
	if (xp_marker)
		mpi_free_limb_space(xp_marker);
	if (tspace)
		mpi_free_limb_space(tspace);
	return rc;
}
EXPORT_SYMBOL_GPL(mpi_powm);