mpi-pow.c

  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 */
 26int 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
293leave:
294	rc = 0;
295enomem:
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}
311EXPORT_SYMBOL_GPL(mpi_powm);