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/export.h>
17 #include <linux/sched.h>
18 #include <linux/string.h>
19
20 #include "mpi-internal.h"
21 #include "longlong.h"
22
23 /****************
24 * RES = BASE ^ EXP mod MOD
25 */
mpi_powm(MPI res,MPI base,MPI exp,MPI mod)26 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
27 {
28 mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
29 struct karatsuba_ctx karactx = {};
30 mpi_ptr_t xp_marker = NULL;
31 mpi_ptr_t tspace = NULL;
32 mpi_ptr_t rp, ep, mp, bp;
33 mpi_size_t esize, msize, bsize, rsize;
34 int msign, bsign, rsign;
35 mpi_size_t size;
36 int mod_shift_cnt;
37 int negative_result;
38 int assign_rp = 0;
39 mpi_size_t tsize = 0; /* to avoid compiler warning */
40 /* fixme: we should check that the warning is void */
41 int rc = -ENOMEM;
42
43 esize = exp->nlimbs;
44 msize = mod->nlimbs;
45 size = 2 * msize;
46 msign = mod->sign;
47
48 rp = res->d;
49 ep = exp->d;
50
51 if (!msize)
52 return -EINVAL;
53
54 if (!esize) {
55 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
56 * depending on if MOD equals 1. */
57 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
58 if (res->nlimbs) {
59 if (mpi_resize(res, 1) < 0)
60 goto enomem;
61 rp = res->d;
62 rp[0] = 1;
63 }
64 res->sign = 0;
65 goto leave;
66 }
67
68 /* Normalize MOD (i.e. make its most significant bit set) as required by
69 * mpn_divrem. This will make the intermediate values in the calculation
70 * slightly larger, but the correct result is obtained after a final
71 * reduction using the original MOD value. */
72 mp = mp_marker = mpi_alloc_limb_space(msize);
73 if (!mp)
74 goto enomem;
75 mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
76 if (mod_shift_cnt)
77 mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
78 else
79 MPN_COPY(mp, mod->d, msize);
80
81 bsize = base->nlimbs;
82 bsign = base->sign;
83 if (bsize > msize) { /* The base is larger than the module. Reduce it. */
84 /* Allocate (BSIZE + 1) with space for remainder and quotient.
85 * (The quotient is (bsize - msize + 1) limbs.) */
86 bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
87 if (!bp)
88 goto enomem;
89 MPN_COPY(bp, base->d, bsize);
90 /* We don't care about the quotient, store it above the remainder,
91 * at BP + MSIZE. */
92 mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
93 bsize = msize;
94 /* Canonicalize the base, since we are going to multiply with it
95 * quite a few times. */
96 MPN_NORMALIZE(bp, bsize);
97 } else
98 bp = base->d;
99
100 if (!bsize) {
101 res->nlimbs = 0;
102 res->sign = 0;
103 goto leave;
104 }
105
106 if (res->alloced < size) {
107 /* We have to allocate more space for RES. If any of the input
108 * parameters are identical to RES, defer deallocation of the old
109 * space. */
110 if (rp == ep || rp == mp || rp == bp) {
111 rp = mpi_alloc_limb_space(size);
112 if (!rp)
113 goto enomem;
114 assign_rp = 1;
115 } else {
116 if (mpi_resize(res, size) < 0)
117 goto enomem;
118 rp = res->d;
119 }
120 } else { /* Make BASE, EXP and MOD not overlap with RES. */
121 if (rp == bp) {
122 /* RES and BASE are identical. Allocate temp. space for BASE. */
123 BUG_ON(bp_marker);
124 bp = bp_marker = mpi_alloc_limb_space(bsize);
125 if (!bp)
126 goto enomem;
127 MPN_COPY(bp, rp, bsize);
128 }
129 if (rp == ep) {
130 /* RES and EXP are identical. Allocate temp. space for EXP. */
131 ep = ep_marker = mpi_alloc_limb_space(esize);
132 if (!ep)
133 goto enomem;
134 MPN_COPY(ep, rp, esize);
135 }
136 if (rp == mp) {
137 /* RES and MOD are identical. Allocate temporary space for MOD. */
138 BUG_ON(mp_marker);
139 mp = mp_marker = mpi_alloc_limb_space(msize);
140 if (!mp)
141 goto enomem;
142 MPN_COPY(mp, rp, msize);
143 }
144 }
145
146 MPN_COPY(rp, bp, bsize);
147 rsize = bsize;
148 rsign = bsign;
149
150 {
151 mpi_size_t i;
152 mpi_ptr_t xp;
153 int c;
154 mpi_limb_t e;
155 mpi_limb_t carry_limb;
156
157 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
158 if (!xp)
159 goto enomem;
160
161 negative_result = (ep[0] & 1) && base->sign;
162
163 i = esize - 1;
164 e = ep[i];
165 c = count_leading_zeros(e);
166 e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
167 c = BITS_PER_MPI_LIMB - 1 - c;
168
169 /* Main loop.
170 *
171 * Make the result be pointed to alternately by XP and RP. This
172 * helps us avoid block copying, which would otherwise be necessary
173 * with the overlap restrictions of mpihelp_divmod. With 50% probability
174 * the result after this loop will be in the area originally pointed
175 * by RP (==RES->d), and with 50% probability in the area originally
176 * pointed to by XP.
177 */
178
179 for (;;) {
180 while (c) {
181 mpi_size_t xsize;
182
183 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
184 if (rsize < KARATSUBA_THRESHOLD)
185 mpih_sqr_n_basecase(xp, rp, rsize);
186 else {
187 if (!tspace) {
188 tsize = 2 * rsize;
189 tspace =
190 mpi_alloc_limb_space(tsize);
191 if (!tspace)
192 goto enomem;
193 } else if (tsize < (2 * rsize)) {
194 mpi_free_limb_space(tspace);
195 tsize = 2 * rsize;
196 tspace =
197 mpi_alloc_limb_space(tsize);
198 if (!tspace)
199 goto enomem;
200 }
201 mpih_sqr_n(xp, rp, rsize, tspace);
202 }
203
204 xsize = 2 * rsize;
205 if (xsize > msize) {
206 mpihelp_divrem(xp + msize, 0, xp, xsize,
207 mp, msize);
208 xsize = msize;
209 }
210
211 swap(rp, xp);
212 rsize = xsize;
213
214 if ((mpi_limb_signed_t) e < 0) {
215 /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
216 if (bsize < KARATSUBA_THRESHOLD) {
217 mpi_limb_t tmp;
218 if (mpihelp_mul
219 (xp, rp, rsize, bp, bsize,
220 &tmp) < 0)
221 goto enomem;
222 } else {
223 if (mpihelp_mul_karatsuba_case
224 (xp, rp, rsize, bp, bsize,
225 &karactx) < 0)
226 goto enomem;
227 }
228
229 xsize = rsize + bsize;
230 if (xsize > msize) {
231 mpihelp_divrem(xp + msize, 0,
232 xp, xsize, mp,
233 msize);
234 xsize = msize;
235 }
236
237 swap(rp, xp);
238 rsize = xsize;
239 }
240 e <<= 1;
241 c--;
242 cond_resched();
243 }
244
245 i--;
246 if (i < 0)
247 break;
248 e = ep[i];
249 c = BITS_PER_MPI_LIMB;
250 }
251
252 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
253 * steps. Adjust the result by reducing it with the original MOD.
254 *
255 * Also make sure the result is put in RES->d (where it already
256 * might be, see above).
257 */
258 if (mod_shift_cnt) {
259 carry_limb =
260 mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
261 rp = res->d;
262 if (carry_limb) {
263 rp[rsize] = carry_limb;
264 rsize++;
265 }
266 } else {
267 MPN_COPY(res->d, rp, rsize);
268 rp = res->d;
269 }
270
271 if (rsize >= msize) {
272 mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
273 rsize = msize;
274 }
275
276 /* Remove any leading zero words from the result. */
277 if (mod_shift_cnt)
278 mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
279 MPN_NORMALIZE(rp, rsize);
280 }
281
282 if (negative_result && rsize) {
283 if (mod_shift_cnt)
284 mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
285 mpihelp_sub(rp, mp, msize, rp, rsize);
286 rsize = msize;
287 rsign = msign;
288 MPN_NORMALIZE(rp, rsize);
289 }
290 res->nlimbs = rsize;
291 res->sign = rsign;
292
293 leave:
294 rc = 0;
295 enomem:
296 mpihelp_release_karatsuba_ctx(&karactx);
297 if (assign_rp)
298 mpi_assign_limb_space(res, rp, size);
299 if (mp_marker)
300 mpi_free_limb_space(mp_marker);
301 if (bp_marker)
302 mpi_free_limb_space(bp_marker);
303 if (ep_marker)
304 mpi_free_limb_space(ep_marker);
305 if (xp_marker)
306 mpi_free_limb_space(xp_marker);
307 if (tspace)
308 mpi_free_limb_space(tspace);
309 return rc;
310 }
311 EXPORT_SYMBOL_GPL(mpi_powm);
312