1 // SPDX-License-Identifier: GPL-2.0-or-later
2 /* mpi-pow.c - MPI functions
3 * Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
4 *
5 * This file is part of GnuPG.
6 *
7 * Note: This code is heavily based on the GNU MP Library.
8 * Actually it's the same code with only minor changes in the
9 * way the data is stored; this is to support the abstraction
10 * of an optional secure memory allocation which may be used
11 * to avoid revealing of sensitive data due to paging etc.
12 * The GNU MP Library itself is published under the LGPL;
13 * however I decided to publish this code under the plain GPL.
14 */
15
16 #include <linux/sched.h>
17 #include <linux/string.h>
18 #include "mpi-internal.h"
19 #include "longlong.h"
20
21 /****************
22 * RES = BASE ^ EXP mod MOD
23 */
24 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
25 {
26 mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
27 struct karatsuba_ctx karactx = {};
28 mpi_ptr_t xp_marker = NULL;
29 mpi_ptr_t tspace = NULL;
30 mpi_ptr_t rp, ep, mp, bp;
31 mpi_size_t esize, msize, bsize, rsize;
32 int msign, bsign, rsign;
33 mpi_size_t size;
34 int mod_shift_cnt;
35 int negative_result;
36 int assign_rp = 0;
37 mpi_size_t tsize = 0; /* to avoid compiler warning */
38 /* fixme: we should check that the warning is void */
39 int rc = -ENOMEM;
40
41 esize = exp->nlimbs;
42 msize = mod->nlimbs;
43 size = 2 * msize;
44 msign = mod->sign;
45
46 rp = res->d;
47 ep = exp->d;
48
49 if (!msize)
50 return -EINVAL;
51
52 if (!esize) {
53 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
54 * depending on if MOD equals 1. */
55 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
56 if (res->nlimbs) {
57 if (mpi_resize(res, 1) < 0)
58 goto enomem;
59 rp = res->d;
60 rp[0] = 1;
61 }
62 res->sign = 0;
63 goto leave;
64 }
65
66 /* Normalize MOD (i.e. make its most significant bit set) as required by
67 * mpn_divrem. This will make the intermediate values in the calculation
68 * slightly larger, but the correct result is obtained after a final
69 * reduction using the original MOD value. */
70 mp = mp_marker = mpi_alloc_limb_space(msize);
71 if (!mp)
72 goto enomem;
73 mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
74 if (mod_shift_cnt)
75 mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
76 else
77 MPN_COPY(mp, mod->d, msize);
78
79 bsize = base->nlimbs;
80 bsign = base->sign;
81 if (bsize > msize) { /* The base is larger than the module. Reduce it. */
82 /* Allocate (BSIZE + 1) with space for remainder and quotient.
83 * (The quotient is (bsize - msize + 1) limbs.) */
84 bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
85 if (!bp)
86 goto enomem;
87 MPN_COPY(bp, base->d, bsize);
88 /* We don't care about the quotient, store it above the remainder,
89 * at BP + MSIZE. */
90 mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
91 bsize = msize;
92 /* Canonicalize the base, since we are going to multiply with it
93 * quite a few times. */
94 MPN_NORMALIZE(bp, bsize);
95 } else
96 bp = base->d;
97
98 if (!bsize) {
99 res->nlimbs = 0;
100 res->sign = 0;
101 goto leave;
102 }
103
104 if (res->alloced < size) {
105 /* We have to allocate more space for RES. If any of the input
106 * parameters are identical to RES, defer deallocation of the old
107 * space. */
108 if (rp == ep || rp == mp || rp == bp) {
109 rp = mpi_alloc_limb_space(size);
110 if (!rp)
111 goto enomem;
112 assign_rp = 1;
113 } else {
114 if (mpi_resize(res, size) < 0)
115 goto enomem;
116 rp = res->d;
117 }
118 } else { /* Make BASE, EXP and MOD not overlap with RES. */
119 if (rp == bp) {
120 /* RES and BASE are identical. Allocate temp. space for BASE. */
121 BUG_ON(bp_marker);
122 bp = bp_marker = mpi_alloc_limb_space(bsize);
123 if (!bp)
124 goto enomem;
125 MPN_COPY(bp, rp, bsize);
126 }
127 if (rp == ep) {
128 /* RES and EXP are identical. Allocate temp. space for EXP. */
129 ep = ep_marker = mpi_alloc_limb_space(esize);
130 if (!ep)
131 goto enomem;
132 MPN_COPY(ep, rp, esize);
133 }
134 if (rp == mp) {
135 /* RES and MOD are identical. Allocate temporary space for MOD. */
136 BUG_ON(mp_marker);
137 mp = mp_marker = mpi_alloc_limb_space(msize);
138 if (!mp)
139 goto enomem;
140 MPN_COPY(mp, rp, msize);
141 }
142 }
143
144 MPN_COPY(rp, bp, bsize);
145 rsize = bsize;
146 rsign = bsign;
147
148 {
149 mpi_size_t i;
150 mpi_ptr_t xp;
151 int c;
152 mpi_limb_t e;
153 mpi_limb_t carry_limb;
154
155 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
156 if (!xp)
157 goto enomem;
158
159 negative_result = (ep[0] & 1) && base->sign;
160
161 i = esize - 1;
162 e = ep[i];
163 c = count_leading_zeros(e);
164 e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
165 c = BITS_PER_MPI_LIMB - 1 - c;
166
167 /* Main loop.
168 *
169 * Make the result be pointed to alternately by XP and RP. This
170 * helps us avoid block copying, which would otherwise be necessary
171 * with the overlap restrictions of mpihelp_divmod. With 50% probability
172 * the result after this loop will be in the area originally pointed
173 * by RP (==RES->d), and with 50% probability in the area originally
174 * pointed to by XP.
175 */
176
177 for (;;) {
178 while (c) {
179 mpi_size_t xsize;
180
181 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
182 if (rsize < KARATSUBA_THRESHOLD)
183 mpih_sqr_n_basecase(xp, rp, rsize);
184 else {
185 if (!tspace) {
186 tsize = 2 * rsize;
187 tspace =
188 mpi_alloc_limb_space(tsize);
189 if (!tspace)
190 goto enomem;
191 } else if (tsize < (2 * rsize)) {
192 mpi_free_limb_space(tspace);
193 tsize = 2 * rsize;
194 tspace =
195 mpi_alloc_limb_space(tsize);
196 if (!tspace)
197 goto enomem;
198 }
199 mpih_sqr_n(xp, rp, rsize, tspace);
200 }
201
202 xsize = 2 * rsize;
203 if (xsize > msize) {
204 mpihelp_divrem(xp + msize, 0, xp, xsize,
205 mp, msize);
206 xsize = msize;
207 }
208
209 swap(rp, xp);
210 rsize = xsize;
211
212 if ((mpi_limb_signed_t) e < 0) {
213 /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
214 if (bsize < KARATSUBA_THRESHOLD) {
215 mpi_limb_t tmp;
216 if (mpihelp_mul
217 (xp, rp, rsize, bp, bsize,
218 &tmp) < 0)
219 goto enomem;
220 } else {
221 if (mpihelp_mul_karatsuba_case
222 (xp, rp, rsize, bp, bsize,
223 &karactx) < 0)
224 goto enomem;
225 }
226
227 xsize = rsize + bsize;
228 if (xsize > msize) {
229 mpihelp_divrem(xp + msize, 0,
230 xp, xsize, mp,
231 msize);
232 xsize = msize;
233 }
234
235 swap(rp, xp);
236 rsize = xsize;
237 }
238 e <<= 1;
239 c--;
240 cond_resched();
241 }
242
243 i--;
244 if (i < 0)
245 break;
246 e = ep[i];
247 c = BITS_PER_MPI_LIMB;
248 }
249
250 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
251 * steps. Adjust the result by reducing it with the original MOD.
252 *
253 * Also make sure the result is put in RES->d (where it already
254 * might be, see above).
255 */
256 if (mod_shift_cnt) {
257 carry_limb =
258 mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
259 rp = res->d;
260 if (carry_limb) {
261 rp[rsize] = carry_limb;
262 rsize++;
263 }
264 } else {
265 MPN_COPY(res->d, rp, rsize);
266 rp = res->d;
267 }
268
269 if (rsize >= msize) {
270 mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
271 rsize = msize;
272 }
273
274 /* Remove any leading zero words from the result. */
275 if (mod_shift_cnt)
276 mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
277 MPN_NORMALIZE(rp, rsize);
278 }
279
280 if (negative_result && rsize) {
281 if (mod_shift_cnt)
282 mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
283 mpihelp_sub(rp, mp, msize, rp, rsize);
284 rsize = msize;
285 rsign = msign;
286 MPN_NORMALIZE(rp, rsize);
287 }
288 res->nlimbs = rsize;
289 res->sign = rsign;
290
291 leave:
292 rc = 0;
293 enomem:
294 mpihelp_release_karatsuba_ctx(&karactx);
295 if (assign_rp)
296 mpi_assign_limb_space(res, rp, size);
297 if (mp_marker)
298 mpi_free_limb_space(mp_marker);
299 if (bp_marker)
300 mpi_free_limb_space(bp_marker);
301 if (ep_marker)
302 mpi_free_limb_space(ep_marker);
303 if (xp_marker)
304 mpi_free_limb_space(xp_marker);
305 if (tspace)
306 mpi_free_limb_space(tspace);
307 return rc;
308 }
309 EXPORT_SYMBOL_GPL(mpi_powm);
310
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.