1 /*-*- Mode: C; c-basic-offset: 8; indent-tabs-mode: nil -*-*/
4 * fsprg v0.1 - (seekable) forward-secure pseudorandom generator
5 * Copyright (C) 2012 B. Poettering
6 * Contact: fsprg@point-at-infinity.org
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.
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.
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
25 * See "Practical Secure Logging: Seekable Sequential Key Generators"
26 * by G. A. Marson, B. Poettering for details:
28 * http://eprint.iacr.org/2013/397
36 #define ISVALID_SECPAR(secpar) (((secpar) % 16 == 0) && ((secpar) >= 16) && ((secpar) <= 16384))
37 #define VALIDATE_SECPAR(secpar) assert(ISVALID_SECPAR(secpar));
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
44 /******************************************************************************/
46 static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
50 assert(gcry_mpi_cmp_ui(x, 0) >= 0);
51 len = (gcry_mpi_get_nbits(x) + 7) / 8;
52 assert(len <= buflen);
54 gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
55 assert(nwritten == len);
58 static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
62 gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL);
63 len = (gcry_mpi_get_nbits(h) + 7) / 8;
64 assert(len <= buflen);
65 assert(gcry_mpi_cmp_ui(h, 0) >= 0);
70 static void uint64_export(void *buf, size_t buflen, uint64_t x) {
72 ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
73 ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
74 ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
75 ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
76 ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
77 ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
78 ((uint8_t*) buf)[6] = (x >> 8) & 0xff;
79 ((uint8_t*) buf)[7] = (x >> 0) & 0xff;
82 _pure_ static uint64_t uint64_import(const void *buf, size_t buflen) {
85 (uint64_t)(((uint8_t*) buf)[0]) << 56 |
86 (uint64_t)(((uint8_t*) buf)[1]) << 48 |
87 (uint64_t)(((uint8_t*) buf)[2]) << 40 |
88 (uint64_t)(((uint8_t*) buf)[3]) << 32 |
89 (uint64_t)(((uint8_t*) buf)[4]) << 24 |
90 (uint64_t)(((uint8_t*) buf)[5]) << 16 |
91 (uint64_t)(((uint8_t*) buf)[6]) << 8 |
92 (uint64_t)(((uint8_t*) buf)[7]) << 0;
95 /* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
96 static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
101 olen = gcry_md_get_algo_dlen(RND_HASH);
102 gcry_md_open(&hd, RND_HASH, 0);
103 gcry_md_write(hd, seed, seedlen);
104 gcry_md_putc(hd, (idx >> 24) & 0xff);
105 gcry_md_putc(hd, (idx >> 16) & 0xff);
106 gcry_md_putc(hd, (idx >> 8) & 0xff);
107 gcry_md_putc(hd, (idx >> 0) & 0xff);
109 for (ctr = 0; buflen; ctr++) {
110 gcry_md_copy(&hd2, hd);
111 gcry_md_putc(hd2, (ctr >> 24) & 0xff);
112 gcry_md_putc(hd2, (ctr >> 16) & 0xff);
113 gcry_md_putc(hd2, (ctr >> 8) & 0xff);
114 gcry_md_putc(hd2, (ctr >> 0) & 0xff);
116 cpylen = (buflen < olen) ? buflen : olen;
117 memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
125 /* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
126 static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
127 size_t buflen = bits / 8;
131 assert(bits % 8 == 0);
134 det_randomize(buf, buflen, seed, seedlen, idx);
135 buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
136 buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */
138 p = mpi_import(buf, buflen);
139 while (gcry_prime_check(p, 0))
140 gcry_mpi_add_ui(p, p, 4);
145 /* deterministically generate from seed/idx a quadratic residue (mod n) */
146 static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
147 size_t buflen = secpar / 8;
151 det_randomize(buf, buflen, seed, seedlen, idx);
152 buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
153 x = mpi_import(buf, buflen);
154 assert(gcry_mpi_cmp(x, n) < 0);
155 gcry_mpi_mulm(x, x, x, n);
159 /* compute 2^m (mod phi(p)), for a prime p */
160 static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
164 phi = gcry_mpi_new(0);
165 gcry_mpi_sub_ui(phi, p, 1);
167 /* count number of used bits in m */
168 for (n = 0; (1ULL << n) <= m; n++)
172 gcry_mpi_set_ui(r, 1);
173 while (n) { /* square and multiply algorithm for fast exponentiation */
175 gcry_mpi_mulm(r, r, r, phi);
176 if (m & ((uint64_t)1 << n)) {
177 gcry_mpi_add(r, r, r);
178 if (gcry_mpi_cmp(r, phi) >= 0)
179 gcry_mpi_sub(r, r, phi);
183 gcry_mpi_release(phi);
187 /* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
188 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) {
189 *xp = gcry_mpi_new(0);
190 *xq = gcry_mpi_new(0);
191 gcry_mpi_mod(*xp, x, p);
192 gcry_mpi_mod(*xq, x, q);
195 /* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
196 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) {
201 *x = gcry_mpi_new(0);
202 gcry_mpi_subm(a, xq, xp, q);
203 gcry_mpi_invm(u, p, q);
204 gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p (mod q) */
205 gcry_mpi_mul(*x, p, a);
206 gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
211 static void initialize_libgcrypt(void) {
213 if (gcry_control(GCRYCTL_INITIALIZATION_FINISHED_P))
216 p = gcry_check_version("1.4.5");
219 /* Turn off "secmem". Clients which whish to make use of this
220 * feature should initialize the library manually */
221 gcry_control(GCRYCTL_DISABLE_SECMEM);
222 gcry_control(GCRYCTL_INITIALIZATION_FINISHED, 0);
225 /******************************************************************************/
227 size_t FSPRG_mskinbytes(unsigned _secpar) {
228 VALIDATE_SECPAR(_secpar);
229 return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
232 size_t FSPRG_mpkinbytes(unsigned _secpar) {
233 VALIDATE_SECPAR(_secpar);
234 return 2 + _secpar / 8; /* to store header,n */
237 size_t FSPRG_stateinbytes(unsigned _secpar) {
238 VALIDATE_SECPAR(_secpar);
239 return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
242 static void store_secpar(void *buf, uint16_t secpar) {
243 secpar = secpar / 16 - 1;
244 ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
245 ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
248 static uint16_t read_secpar(const void *buf) {
251 (uint16_t)(((uint8_t*) buf)[0]) << 8 |
252 (uint16_t)(((uint8_t*) buf)[1]) << 0;
253 return 16 * (secpar + 1);
256 void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
257 uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
261 VALIDATE_SECPAR(_secpar);
264 initialize_libgcrypt();
267 gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
269 seedlen = FSPRG_RECOMMENDED_SEEDLEN;
272 p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
273 q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);
276 store_secpar(msk + 0, secpar);
277 mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
278 mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
283 gcry_mpi_mul(n, p, q);
284 assert(gcry_mpi_get_nbits(n) == secpar);
286 store_secpar(mpk + 0, secpar);
287 mpi_export(mpk + 2, secpar / 8, n);
296 void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
300 initialize_libgcrypt();
302 secpar = read_secpar(mpk + 0);
303 n = mpi_import(mpk + 2, secpar / 8);
304 x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
306 memcpy(state, mpk, 2 + secpar / 8);
307 mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
308 memzero(state + 2 + 2 * secpar / 8, 8);
314 void FSPRG_Evolve(void *state) {
319 initialize_libgcrypt();
321 secpar = read_secpar(state + 0);
322 n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
323 x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
324 epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
326 gcry_mpi_mulm(x, x, x, n);
329 mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
330 uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
336 uint64_t FSPRG_GetEpoch(const void *state) {
338 secpar = read_secpar(state + 0);
339 return uint64_import(state + 2 + 2 * secpar / 8, 8);
342 void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
343 gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
346 initialize_libgcrypt();
348 secpar = read_secpar(msk + 0);
349 p = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
350 q = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
353 gcry_mpi_mul(n, p, q);
355 x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
356 CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
358 kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
359 kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
361 gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
362 gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
364 CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
366 store_secpar(state + 0, secpar);
367 mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
368 mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
369 uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
375 gcry_mpi_release(xp);
376 gcry_mpi_release(xq);
377 gcry_mpi_release(kp);
378 gcry_mpi_release(kq);
379 gcry_mpi_release(xm);
382 void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
385 initialize_libgcrypt();
387 secpar = read_secpar(state + 0);
388 det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);