src/journal/fsprg.c

   1 /*
   2  * fsprg v0.1  -  (seekable) forward-secure pseudorandom generator
   3  * Copyright (C) 2012 B. Poettering
   4  * Contact: fsprg@point-at-infinity.org
   5  *
   6  * This library is free software; you can redistribute it and/or
   7  * modify it under the terms of the GNU Lesser General Public
   8  * License as published by the Free Software Foundation; either
   9  * version 2.1 of the License, or (at your option) any later version.
  10  *
  11  * This library is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14  * Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public
  17  * License along with this library; if not, write to the Free Software
  18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
  19  * 02110-1301  USA
  20  */
  21
  22 /*
  23  * See "Practical Secure Logging: Seekable Sequential Key Generators"
  24  * by G. A. Marson, B. Poettering for details:
  25  *
  26  * http://eprint.iacr.org/2013/397
  27  */
  28
  29 #include <gcrypt.h>
  30 #include <string.h>
  31
  32 #include "fsprg.h"
  33
  34 #define ISVALID_SECPAR(secpar) (((secpar) % 16 == 0) && ((secpar) >= 16) && ((secpar) <= 16384))
  35 #define VALIDATE_SECPAR(secpar) assert(ISVALID_SECPAR(secpar));
  36
  37 #define RND_HASH GCRY_MD_SHA256
  38 #define RND_GEN_P 0x01
  39 #define RND_GEN_Q 0x02
  40 #define RND_GEN_X 0x03
  41
  42 /******************************************************************************/
  43
  44 static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
  45         unsigned len;
  46         size_t nwritten;
  47
  48         assert(gcry_mpi_cmp_ui(x, 0) >= 0);
  49         len = (gcry_mpi_get_nbits(x) + 7) / 8;
  50         assert(len <= buflen);
  51         memzero(buf, buflen);
  52         gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
  53         assert(nwritten == len);
  54 }
  55
  56 static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
  57         gcry_mpi_t h;
  58         unsigned len;
  59
  60         gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL);
  61         len = (gcry_mpi_get_nbits(h) + 7) / 8;
  62         assert(len <= buflen);
  63         assert(gcry_mpi_cmp_ui(h, 0) >= 0);
  64
  65         return h;
  66 }
  67
  68 static void uint64_export(void *buf, size_t buflen, uint64_t x) {
  69         assert(buflen == 8);
  70         ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
  71         ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
  72         ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
  73         ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
  74         ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
  75         ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
  76         ((uint8_t*) buf)[6] = (x >>  8) & 0xff;
  77         ((uint8_t*) buf)[7] = (x >>  0) & 0xff;
  78 }
  79
  80 _pure_ static uint64_t uint64_import(const void *buf, size_t buflen) {
  81         assert(buflen == 8);
  82         return
  83                 (uint64_t)(((uint8_t*) buf)[0]) << 56 |
  84                 (uint64_t)(((uint8_t*) buf)[1]) << 48 |
  85                 (uint64_t)(((uint8_t*) buf)[2]) << 40 |
  86                 (uint64_t)(((uint8_t*) buf)[3]) << 32 |
  87                 (uint64_t)(((uint8_t*) buf)[4]) << 24 |
  88                 (uint64_t)(((uint8_t*) buf)[5]) << 16 |
  89                 (uint64_t)(((uint8_t*) buf)[6]) <<  8 |
  90                 (uint64_t)(((uint8_t*) buf)[7]) <<  0;
  91 }
  92
  93 /* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
  94 static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
  95         gcry_md_hd_t hd, hd2;
  96         size_t olen, cpylen;
  97         uint32_t ctr;
  98
  99         olen = gcry_md_get_algo_dlen(RND_HASH);
 100         gcry_md_open(&hd, RND_HASH, 0);
 101         gcry_md_write(hd, seed, seedlen);
 102         gcry_md_putc(hd, (idx >> 24) & 0xff);
 103         gcry_md_putc(hd, (idx >> 16) & 0xff);
 104         gcry_md_putc(hd, (idx >>  8) & 0xff);
 105         gcry_md_putc(hd, (idx >>  0) & 0xff);
 106
 107         for (ctr = 0; buflen; ctr++) {
 108                 gcry_md_copy(&hd2, hd);
 109                 gcry_md_putc(hd2, (ctr >> 24) & 0xff);
 110                 gcry_md_putc(hd2, (ctr >> 16) & 0xff);
 111                 gcry_md_putc(hd2, (ctr >>  8) & 0xff);
 112                 gcry_md_putc(hd2, (ctr >>  0) & 0xff);
 113                 gcry_md_final(hd2);
 114                 cpylen = (buflen < olen) ? buflen : olen;
 115                 memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
 116                 gcry_md_close(hd2);
 117                 buf += cpylen;
 118                 buflen -= cpylen;
 119         }
 120         gcry_md_close(hd);
 121 }
 122
 123 /* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
 124 static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
 125         size_t buflen = bits / 8;
 126         uint8_t buf[buflen];
 127         gcry_mpi_t p;
 128
 129         assert(bits % 8 == 0);
 130         assert(buflen > 0);
 131
 132         det_randomize(buf, buflen, seed, seedlen, idx);
 133         buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
 134         buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */
 135
 136         p = mpi_import(buf, buflen);
 137         while (gcry_prime_check(p, 0))
 138                 gcry_mpi_add_ui(p, p, 4);
 139
 140         return p;
 141 }
 142
 143 /* deterministically generate from seed/idx a quadratic residue (mod n) */
 144 static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
 145         size_t buflen = secpar / 8;
 146         uint8_t buf[buflen];
 147         gcry_mpi_t x;
 148
 149         det_randomize(buf, buflen, seed, seedlen, idx);
 150         buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
 151         x = mpi_import(buf, buflen);
 152         assert(gcry_mpi_cmp(x, n) < 0);
 153         gcry_mpi_mulm(x, x, x, n);
 154         return x;
 155 }
 156
 157 /* compute 2^m (mod phi(p)), for a prime p */
 158 static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
 159         gcry_mpi_t phi, r;
 160         int n;
 161
 162         phi = gcry_mpi_new(0);
 163         gcry_mpi_sub_ui(phi, p, 1);
 164
 165         /* count number of used bits in m */
 166         for (n = 0; (1ULL << n) <= m; n++)
 167                 ;
 168
 169         r = gcry_mpi_new(0);
 170         gcry_mpi_set_ui(r, 1);
 171         while (n) { /* square and multiply algorithm for fast exponentiation */
 172                 n--;
 173                 gcry_mpi_mulm(r, r, r, phi);
 174                 if (m & ((uint64_t)1 << n)) {
 175                         gcry_mpi_add(r, r, r);
 176                         if (gcry_mpi_cmp(r, phi) >= 0)
 177                                 gcry_mpi_sub(r, r, phi);
 178                 }
 179         }
 180
 181         gcry_mpi_release(phi);
 182         return r;
 183 }
 184
 185 /* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
 186 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) {
 187         *xp = gcry_mpi_new(0);
 188         *xq = gcry_mpi_new(0);
 189         gcry_mpi_mod(*xp, x, p);
 190         gcry_mpi_mod(*xq, x, q);
 191 }
 192
 193 /* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
 194 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) {
 195         gcry_mpi_t a, u;
 196
 197         a = gcry_mpi_new(0);
 198         u = gcry_mpi_new(0);
 199         *x = gcry_mpi_new(0);
 200         gcry_mpi_subm(a, xq, xp, q);
 201         gcry_mpi_invm(u, p, q);
 202         gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p  (mod q) */
 203         gcry_mpi_mul(*x, p, a);
 204         gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
 205         gcry_mpi_release(a);
 206         gcry_mpi_release(u);
 207 }
 208
 209 static void initialize_libgcrypt(void) {
 210         const char *p;
 211         if (gcry_control(GCRYCTL_INITIALIZATION_FINISHED_P))
 212                 return;
 213
 214         p = gcry_check_version("1.4.5");
 215         assert(p);
 216
 217         /* Turn off "secmem". Clients which whish to make use of this
 218          * feature should initialize the library manually */
 219         gcry_control(GCRYCTL_DISABLE_SECMEM);
 220         gcry_control(GCRYCTL_INITIALIZATION_FINISHED, 0);
 221 }
 222
 223 /******************************************************************************/
 224
 225 size_t FSPRG_mskinbytes(unsigned _secpar) {
 226         VALIDATE_SECPAR(_secpar);
 227         return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
 228 }
 229
 230 size_t FSPRG_mpkinbytes(unsigned _secpar) {
 231         VALIDATE_SECPAR(_secpar);
 232         return 2 + _secpar / 8; /* to store header,n */
 233 }
 234
 235 size_t FSPRG_stateinbytes(unsigned _secpar) {
 236         VALIDATE_SECPAR(_secpar);
 237         return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
 238 }
 239
 240 static void store_secpar(void *buf, uint16_t secpar) {
 241         secpar = secpar / 16 - 1;
 242         ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
 243         ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
 244 }
 245
 246 static uint16_t read_secpar(const void *buf) {
 247         uint16_t secpar;
 248         secpar =
 249                 (uint16_t)(((uint8_t*) buf)[0]) << 8 |
 250                 (uint16_t)(((uint8_t*) buf)[1]) << 0;
 251         return 16 * (secpar + 1);
 252 }
 253
 254 void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
 255         uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
 256         gcry_mpi_t n, p, q;
 257         uint16_t secpar;
 258
 259         VALIDATE_SECPAR(_secpar);
 260         secpar = _secpar;
 261
 262         initialize_libgcrypt();
 263
 264         if (!seed) {
 265                 gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
 266                 seed = iseed;
 267                 seedlen = FSPRG_RECOMMENDED_SEEDLEN;
 268         }
 269
 270         p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
 271         q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);
 272
 273         if (msk) {
 274                 store_secpar(msk + 0, secpar);
 275                 mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
 276                 mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
 277         }
 278
 279         if (mpk) {
 280                 n = gcry_mpi_new(0);
 281                 gcry_mpi_mul(n, p, q);
 282                 assert(gcry_mpi_get_nbits(n) == secpar);
 283
 284                 store_secpar(mpk + 0, secpar);
 285                 mpi_export(mpk + 2, secpar / 8, n);
 286
 287                 gcry_mpi_release(n);
 288         }
 289
 290         gcry_mpi_release(p);
 291         gcry_mpi_release(q);
 292 }
 293
 294 void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
 295         gcry_mpi_t n, x;
 296         uint16_t secpar;
 297
 298         initialize_libgcrypt();
 299
 300         secpar = read_secpar(mpk + 0);
 301         n = mpi_import(mpk + 2, secpar / 8);
 302         x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
 303
 304         memcpy(state, mpk, 2 + secpar / 8);
 305         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
 306         memzero(state + 2 + 2 * secpar / 8, 8);
 307
 308         gcry_mpi_release(n);
 309         gcry_mpi_release(x);
 310 }
 311
 312 void FSPRG_Evolve(void *state) {
 313         gcry_mpi_t n, x;
 314         uint16_t secpar;
 315         uint64_t epoch;
 316
 317         initialize_libgcrypt();
 318
 319         secpar = read_secpar(state + 0);
 320         n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
 321         x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
 322         epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
 323
 324         gcry_mpi_mulm(x, x, x, n);
 325         epoch++;
 326
 327         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
 328         uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
 329
 330         gcry_mpi_release(n);
 331         gcry_mpi_release(x);
 332 }
 333
 334 uint64_t FSPRG_GetEpoch(const void *state) {
 335         uint16_t secpar;
 336         secpar = read_secpar(state + 0);
 337         return uint64_import(state + 2 + 2 * secpar / 8, 8);
 338 }
 339
 340 void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
 341         gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
 342         uint16_t secpar;
 343
 344         initialize_libgcrypt();
 345
 346         secpar = read_secpar(msk + 0);
 347         p  = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
 348         q  = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
 349
 350         n = gcry_mpi_new(0);
 351         gcry_mpi_mul(n, p, q);
 352
 353         x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
 354         CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
 355
 356         kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
 357         kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
 358
 359         gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
 360         gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
 361
 362         CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
 363
 364         store_secpar(state + 0, secpar);
 365         mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
 366         mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
 367         uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
 368
 369         gcry_mpi_release(p);
 370         gcry_mpi_release(q);
 371         gcry_mpi_release(n);
 372         gcry_mpi_release(x);
 373         gcry_mpi_release(xp);
 374         gcry_mpi_release(xq);
 375         gcry_mpi_release(kp);
 376         gcry_mpi_release(kq);
 377         gcry_mpi_release(xm);
 378 }
 379
 380 void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
 381         uint16_t secpar;
 382
 383         initialize_libgcrypt();
 384
 385         secpar = read_secpar(state + 0);
 386         det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);
 387 }