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