src/journal/fsprg.c

   1 /* SPDX-License-Identifier: LGPL-2.1+
   2  *
   3  * fsprg v0.1  -  (seekable) forward-secure pseudorandom generator
   4  * Copyright © 2012 B. Poettering
   5  * Contact: fsprg@point-at-infinity.org
   6  *
   7  * This library is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU Lesser General Public
   9  * License as published by the Free Software Foundation; either
  10  * version 2.1 of the License, or (at your option) any later version.
  11  *
  12  * This library is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public
  18  * License along with this library; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
  20  * 02110-1301  USA
  21  */
  22
  23 /*
  24  * See "Practical Secure Logging: Seekable Sequential Key Generators"
  25  * by G. A. Marson, B. Poettering for details:
  26  *
  27  * http://eprint.iacr.org/2013/397
  28  */
  29
  30 #include <gcrypt.h>
  31 #include <string.h>
  32
  33 #include "fsprg.h"
  34 #include "gcrypt-util.h"
  35
  36 #define ISVALID_SECPAR(secpar) (((secpar) % 16 == 0) && ((secpar) >= 16) && ((secpar) <= 16384))
  37 #define VALIDATE_SECPAR(secpar) assert(ISVALID_SECPAR(secpar));
  38
  39 #define RND_HASH GCRY_MD_SHA256
  40 #define RND_GEN_P 0x01
  41 #define RND_GEN_Q 0x02
  42 #define RND_GEN_X 0x03
  43
  44 #pragma GCC diagnostic ignored "-Wpointer-arith"
  45 /* TODO: remove void* arithmetic and this work-around */
  46
  47 /******************************************************************************/
  48
  49 static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
  50         unsigned len;
  51         size_t nwritten;
  52
  53         assert(gcry_mpi_cmp_ui(x, 0) >= 0);
  54         len = (gcry_mpi_get_nbits(x) + 7) / 8;
  55         assert(len <= buflen);
  56         memzero(buf, buflen);
  57         gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
  58         assert(nwritten == len);
  59 }
  60
  61 static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
  62         gcry_mpi_t h;
  63         unsigned len;
  64
  65         assert_se(gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL) == 0);
  66         len = (gcry_mpi_get_nbits(h) + 7) / 8;
  67         assert(len <= buflen);
  68         assert(gcry_mpi_cmp_ui(h, 0) >= 0);
  69
  70         return h;
  71 }
  72
  73 static void uint64_export(void *buf, size_t buflen, uint64_t x) {
  74         assert(buflen == 8);
  75         ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
  76         ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
  77         ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
  78         ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
  79         ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
  80         ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
  81         ((uint8_t*) buf)[6] = (x >>  8) & 0xff;
  82         ((uint8_t*) buf)[7] = (x >>  0) & 0xff;
  83 }
  84
  85 _pure_ static uint64_t uint64_import(const void *buf, size_t buflen) {
  86         assert(buflen == 8);
  87         return
  88                 (uint64_t)(((uint8_t*) buf)[0]) << 56 |
  89                 (uint64_t)(((uint8_t*) buf)[1]) << 48 |
  90                 (uint64_t)(((uint8_t*) buf)[2]) << 40 |
  91                 (uint64_t)(((uint8_t*) buf)[3]) << 32 |
  92                 (uint64_t)(((uint8_t*) buf)[4]) << 24 |
  93                 (uint64_t)(((uint8_t*) buf)[5]) << 16 |
  94                 (uint64_t)(((uint8_t*) buf)[6]) <<  8 |
  95                 (uint64_t)(((uint8_t*) buf)[7]) <<  0;
  96 }
  97
  98 /* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
  99 static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
 100         gcry_md_hd_t hd, hd2;
 101         size_t olen, cpylen;
 102         uint32_t ctr;
 103
 104         olen = gcry_md_get_algo_dlen(RND_HASH);
 105         gcry_md_open(&hd, RND_HASH, 0);
 106         gcry_md_write(hd, seed, seedlen);
 107         gcry_md_putc(hd, (idx >> 24) & 0xff);
 108         gcry_md_putc(hd, (idx >> 16) & 0xff);
 109         gcry_md_putc(hd, (idx >>  8) & 0xff);
 110         gcry_md_putc(hd, (idx >>  0) & 0xff);
 111
 112         for (ctr = 0; buflen; ctr++) {
 113                 gcry_md_copy(&hd2, hd);
 114                 gcry_md_putc(hd2, (ctr >> 24) & 0xff);
 115                 gcry_md_putc(hd2, (ctr >> 16) & 0xff);
 116                 gcry_md_putc(hd2, (ctr >>  8) & 0xff);
 117                 gcry_md_putc(hd2, (ctr >>  0) & 0xff);
 118                 gcry_md_final(hd2);
 119                 cpylen = (buflen < olen) ? buflen : olen;
 120                 memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
 121                 gcry_md_close(hd2);
 122                 buf += cpylen;
 123                 buflen -= cpylen;
 124         }
 125         gcry_md_close(hd);
 126 }
 127
 128 /* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
 129 static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
 130         size_t buflen = bits / 8;
 131         uint8_t buf[buflen];
 132         gcry_mpi_t p;
 133
 134         assert(bits % 8 == 0);
 135         assert(buflen > 0);
 136
 137         det_randomize(buf, buflen, seed, seedlen, idx);
 138         buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
 139         buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */
 140
 141         p = mpi_import(buf, buflen);
 142         while (gcry_prime_check(p, 0))
 143                 gcry_mpi_add_ui(p, p, 4);
 144
 145         return p;
 146 }
 147
 148 /* deterministically generate from seed/idx a quadratic residue (mod n) */
 149 static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
 150         size_t buflen = secpar / 8;
 151         uint8_t buf[buflen];
 152         gcry_mpi_t x;
 153
 154         det_randomize(buf, buflen, seed, seedlen, idx);
 155         buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
 156         x = mpi_import(buf, buflen);
 157         assert(gcry_mpi_cmp(x, n) < 0);
 158         gcry_mpi_mulm(x, x, x, n);
 159         return x;
 160 }
 161
 162 /* compute 2^m (mod phi(p)), for a prime p */
 163 static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
 164         gcry_mpi_t phi, r;
 165         int n;
 166
 167         phi = gcry_mpi_new(0);
 168         gcry_mpi_sub_ui(phi, p, 1);
 169
 170         /* count number of used bits in m */
 171         for (n = 0; (1ULL << n) <= m; n++)
 172                 ;
 173
 174         r = gcry_mpi_new(0);
 175         gcry_mpi_set_ui(r, 1);
 176         while (n) { /* square and multiply algorithm for fast exponentiation */
 177                 n--;
 178                 gcry_mpi_mulm(r, r, r, phi);
 179                 if (m & ((uint64_t)1 << n)) {
 180                         gcry_mpi_add(r, r, r);
 181                         if (gcry_mpi_cmp(r, phi) >= 0)
 182                                 gcry_mpi_sub(r, r, phi);
 183                 }
 184         }
 185
 186         gcry_mpi_release(phi);
 187         return r;
 188 }
 189
 190 /* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
 191 static void CRT_decompose(gcry_mpi_t *xp, gcry_mpi_t *xq, const gcry_mpi_t x, const gcry_mpi_t p, const gcry_mpi_t q) {
 192         *xp = gcry_mpi_new(0);
 193         *xq = gcry_mpi_new(0);
 194         gcry_mpi_mod(*xp, x, p);
 195         gcry_mpi_mod(*xq, x, q);
 196 }
 197
 198 /* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
 199 static void CRT_compose(gcry_mpi_t *x, const gcry_mpi_t xp, const gcry_mpi_t xq, const gcry_mpi_t p, const gcry_mpi_t q) {
 200         gcry_mpi_t a, u;
 201
 202         a = gcry_mpi_new(0);
 203         u = gcry_mpi_new(0);
 204         *x = gcry_mpi_new(0);
 205         gcry_mpi_subm(a, xq, xp, q);
 206         gcry_mpi_invm(u, p, q);
 207         gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p  (mod q) */
 208         gcry_mpi_mul(*x, p, a);
 209         gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
 210         gcry_mpi_release(a);
 211         gcry_mpi_release(u);
 212 }
 213
 214 /******************************************************************************/
 215
 216 size_t FSPRG_mskinbytes(unsigned _secpar) {
 217         VALIDATE_SECPAR(_secpar);
 218         return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
 219 }
 220
 221 size_t FSPRG_mpkinbytes(unsigned _secpar) {
 222         VALIDATE_SECPAR(_secpar);
 223         return 2 + _secpar / 8; /* to store header,n */
 224 }
 225
 226 size_t FSPRG_stateinbytes(unsigned _secpar) {
 227         VALIDATE_SECPAR(_secpar);
 228         return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
 229 }
 230
 231 static void store_secpar(void *buf, uint16_t secpar) {
 232         secpar = secpar / 16 - 1;
 233         ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
 234         ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
 235 }
 236
 237 static uint16_t read_secpar(const void *buf) {
 238         uint16_t secpar;
 239         secpar =
 240                 (uint16_t)(((uint8_t*) buf)[0]) << 8 |
 241                 (uint16_t)(((uint8_t*) buf)[1]) << 0;
 242         return 16 * (secpar + 1);
 243 }
 244
 245 void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
 246         uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
 247         gcry_mpi_t n, p, q;
 248         uint16_t secpar;
 249
 250         VALIDATE_SECPAR(_secpar);
 251         secpar = _secpar;
 252
 253         initialize_libgcrypt(false);
 254
 255         if (!seed) {
 256                 gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
 257                 seed = iseed;
 258                 seedlen = FSPRG_RECOMMENDED_SEEDLEN;
 259         }
 260
 261         p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
 262         q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);
 263
 264         if (msk) {
 265                 store_secpar(msk + 0, secpar);
 266                 mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
 267                 mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
 268         }
 269
 270         if (mpk) {
 271                 n = gcry_mpi_new(0);
 272                 gcry_mpi_mul(n, p, q);
 273                 assert(gcry_mpi_get_nbits(n) == secpar);
 274
 275                 store_secpar(mpk + 0, secpar);
 276                 mpi_export(mpk + 2, secpar / 8, n);
 277
 278                 gcry_mpi_release(n);
 279         }
 280
 281         gcry_mpi_release(p);
 282         gcry_mpi_release(q);
 283 }
 284
 285 void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
 286         gcry_mpi_t n, x;
 287         uint16_t secpar;
 288
 289         initialize_libgcrypt(false);
 290
 291         secpar = read_secpar(mpk + 0);
 292         n = mpi_import(mpk + 2, secpar / 8);
 293         x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
 294
 295         memcpy(state, mpk, 2 + secpar / 8);
 296         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
 297         memzero(state + 2 + 2 * secpar / 8, 8);
 298
 299         gcry_mpi_release(n);
 300         gcry_mpi_release(x);
 301 }
 302
 303 void FSPRG_Evolve(void *state) {
 304         gcry_mpi_t n, x;
 305         uint16_t secpar;
 306         uint64_t epoch;
 307
 308         initialize_libgcrypt(false);
 309
 310         secpar = read_secpar(state + 0);
 311         n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
 312         x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
 313         epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
 314
 315         gcry_mpi_mulm(x, x, x, n);
 316         epoch++;
 317
 318         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
 319         uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
 320
 321         gcry_mpi_release(n);
 322         gcry_mpi_release(x);
 323 }
 324
 325 uint64_t FSPRG_GetEpoch(const void *state) {
 326         uint16_t secpar;
 327         secpar = read_secpar(state + 0);
 328         return uint64_import(state + 2 + 2 * secpar / 8, 8);
 329 }
 330
 331 void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
 332         gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
 333         uint16_t secpar;
 334
 335         initialize_libgcrypt(false);
 336
 337         secpar = read_secpar(msk + 0);
 338         p  = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
 339         q  = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
 340
 341         n = gcry_mpi_new(0);
 342         gcry_mpi_mul(n, p, q);
 343
 344         x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
 345         CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
 346
 347         kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
 348         kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
 349
 350         gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
 351         gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
 352
 353         CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
 354
 355         store_secpar(state + 0, secpar);
 356         mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
 357         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
 358         uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
 359
 360         gcry_mpi_release(p);
 361         gcry_mpi_release(q);
 362         gcry_mpi_release(n);
 363         gcry_mpi_release(x);
 364         gcry_mpi_release(xp);
 365         gcry_mpi_release(xq);
 366         gcry_mpi_release(kp);
 367         gcry_mpi_release(kq);
 368         gcry_mpi_release(xm);
 369 }
 370
 371 void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
 372         uint16_t secpar;
 373
 374         initialize_libgcrypt(false);
 375
 376         secpar = read_secpar(state + 0);
 377         det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);
 378 }