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 */ 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