src/journal/fsprg.c

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