Line data Source code
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 : #include "memory-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 : #pragma GCC diagnostic ignored "-Wpointer-arith"
46 : /* TODO: remove void* arithmetic and this work-around */
47 :
48 : /******************************************************************************/
49 :
50 0 : static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
51 : unsigned len;
52 : size_t nwritten;
53 :
54 0 : assert(gcry_mpi_cmp_ui(x, 0) >= 0);
55 0 : len = (gcry_mpi_get_nbits(x) + 7) / 8;
56 0 : assert(len <= buflen);
57 0 : memzero(buf, buflen);
58 0 : gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
59 0 : assert(nwritten == len);
60 0 : }
61 :
62 0 : static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
63 : gcry_mpi_t h;
64 : unsigned len;
65 :
66 0 : assert_se(gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL) == 0);
67 0 : len = (gcry_mpi_get_nbits(h) + 7) / 8;
68 0 : assert(len <= buflen);
69 0 : assert(gcry_mpi_cmp_ui(h, 0) >= 0);
70 :
71 0 : return h;
72 : }
73 :
74 0 : static void uint64_export(void *buf, size_t buflen, uint64_t x) {
75 0 : assert(buflen == 8);
76 0 : ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
77 0 : ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
78 0 : ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
79 0 : ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
80 0 : ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
81 0 : ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
82 0 : ((uint8_t*) buf)[6] = (x >> 8) & 0xff;
83 0 : ((uint8_t*) buf)[7] = (x >> 0) & 0xff;
84 0 : }
85 :
86 0 : _pure_ static uint64_t uint64_import(const void *buf, size_t buflen) {
87 0 : assert(buflen == 8);
88 : return
89 0 : (uint64_t)(((uint8_t*) buf)[0]) << 56 |
90 0 : (uint64_t)(((uint8_t*) buf)[1]) << 48 |
91 0 : (uint64_t)(((uint8_t*) buf)[2]) << 40 |
92 0 : (uint64_t)(((uint8_t*) buf)[3]) << 32 |
93 0 : (uint64_t)(((uint8_t*) buf)[4]) << 24 |
94 0 : (uint64_t)(((uint8_t*) buf)[5]) << 16 |
95 0 : (uint64_t)(((uint8_t*) buf)[6]) << 8 |
96 0 : (uint64_t)(((uint8_t*) buf)[7]) << 0;
97 : }
98 :
99 : /* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
100 0 : static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
101 : gcry_md_hd_t hd, hd2;
102 : size_t olen, cpylen;
103 : uint32_t ctr;
104 :
105 0 : olen = gcry_md_get_algo_dlen(RND_HASH);
106 0 : gcry_md_open(&hd, RND_HASH, 0);
107 0 : gcry_md_write(hd, seed, seedlen);
108 0 : gcry_md_putc(hd, (idx >> 24) & 0xff);
109 0 : gcry_md_putc(hd, (idx >> 16) & 0xff);
110 0 : gcry_md_putc(hd, (idx >> 8) & 0xff);
111 0 : gcry_md_putc(hd, (idx >> 0) & 0xff);
112 :
113 0 : for (ctr = 0; buflen; ctr++) {
114 0 : gcry_md_copy(&hd2, hd);
115 0 : gcry_md_putc(hd2, (ctr >> 24) & 0xff);
116 0 : gcry_md_putc(hd2, (ctr >> 16) & 0xff);
117 0 : gcry_md_putc(hd2, (ctr >> 8) & 0xff);
118 0 : gcry_md_putc(hd2, (ctr >> 0) & 0xff);
119 0 : gcry_md_final(hd2);
120 0 : cpylen = (buflen < olen) ? buflen : olen;
121 0 : memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
122 0 : gcry_md_close(hd2);
123 0 : buf += cpylen;
124 0 : buflen -= cpylen;
125 : }
126 0 : gcry_md_close(hd);
127 0 : }
128 :
129 : /* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
130 0 : static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
131 0 : size_t buflen = bits / 8;
132 0 : uint8_t buf[buflen];
133 : gcry_mpi_t p;
134 :
135 0 : assert(bits % 8 == 0);
136 0 : assert(buflen > 0);
137 :
138 0 : det_randomize(buf, buflen, seed, seedlen, idx);
139 0 : buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
140 0 : buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */
141 :
142 0 : p = mpi_import(buf, buflen);
143 0 : while (gcry_prime_check(p, 0))
144 0 : gcry_mpi_add_ui(p, p, 4);
145 :
146 0 : return p;
147 : }
148 :
149 : /* deterministically generate from seed/idx a quadratic residue (mod n) */
150 0 : static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
151 0 : size_t buflen = secpar / 8;
152 0 : uint8_t buf[buflen];
153 : gcry_mpi_t x;
154 :
155 0 : det_randomize(buf, buflen, seed, seedlen, idx);
156 0 : buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
157 0 : x = mpi_import(buf, buflen);
158 0 : assert(gcry_mpi_cmp(x, n) < 0);
159 0 : gcry_mpi_mulm(x, x, x, n);
160 0 : return x;
161 : }
162 :
163 : /* compute 2^m (mod phi(p)), for a prime p */
164 0 : static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
165 : gcry_mpi_t phi, r;
166 : int n;
167 :
168 0 : phi = gcry_mpi_new(0);
169 0 : gcry_mpi_sub_ui(phi, p, 1);
170 :
171 : /* count number of used bits in m */
172 0 : for (n = 0; (1ULL << n) <= m; n++)
173 : ;
174 :
175 0 : r = gcry_mpi_new(0);
176 0 : gcry_mpi_set_ui(r, 1);
177 0 : while (n) { /* square and multiply algorithm for fast exponentiation */
178 0 : n--;
179 0 : gcry_mpi_mulm(r, r, r, phi);
180 0 : if (m & ((uint64_t)1 << n)) {
181 0 : gcry_mpi_add(r, r, r);
182 0 : if (gcry_mpi_cmp(r, phi) >= 0)
183 0 : gcry_mpi_sub(r, r, phi);
184 : }
185 : }
186 :
187 0 : gcry_mpi_release(phi);
188 0 : return r;
189 : }
190 :
191 : /* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
192 0 : 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) {
193 0 : *xp = gcry_mpi_new(0);
194 0 : *xq = gcry_mpi_new(0);
195 0 : gcry_mpi_mod(*xp, x, p);
196 0 : gcry_mpi_mod(*xq, x, q);
197 0 : }
198 :
199 : /* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
200 0 : 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 : gcry_mpi_t a, u;
202 :
203 0 : a = gcry_mpi_new(0);
204 0 : u = gcry_mpi_new(0);
205 0 : *x = gcry_mpi_new(0);
206 0 : gcry_mpi_subm(a, xq, xp, q);
207 0 : gcry_mpi_invm(u, p, q);
208 0 : gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p (mod q) */
209 0 : gcry_mpi_mul(*x, p, a);
210 0 : gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
211 0 : gcry_mpi_release(a);
212 0 : gcry_mpi_release(u);
213 0 : }
214 :
215 : /******************************************************************************/
216 :
217 0 : size_t FSPRG_mskinbytes(unsigned _secpar) {
218 0 : VALIDATE_SECPAR(_secpar);
219 0 : return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
220 : }
221 :
222 0 : size_t FSPRG_mpkinbytes(unsigned _secpar) {
223 0 : VALIDATE_SECPAR(_secpar);
224 0 : return 2 + _secpar / 8; /* to store header,n */
225 : }
226 :
227 0 : size_t FSPRG_stateinbytes(unsigned _secpar) {
228 0 : VALIDATE_SECPAR(_secpar);
229 0 : return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
230 : }
231 :
232 0 : static void store_secpar(void *buf, uint16_t secpar) {
233 0 : secpar = secpar / 16 - 1;
234 0 : ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
235 0 : ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
236 0 : }
237 :
238 0 : static uint16_t read_secpar(const void *buf) {
239 : uint16_t secpar;
240 0 : secpar =
241 0 : (uint16_t)(((uint8_t*) buf)[0]) << 8 |
242 0 : (uint16_t)(((uint8_t*) buf)[1]) << 0;
243 0 : return 16 * (secpar + 1);
244 : }
245 :
246 0 : void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
247 : uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
248 : gcry_mpi_t n, p, q;
249 : uint16_t secpar;
250 :
251 0 : VALIDATE_SECPAR(_secpar);
252 0 : secpar = _secpar;
253 :
254 0 : initialize_libgcrypt(false);
255 :
256 0 : if (!seed) {
257 0 : gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
258 0 : seed = iseed;
259 0 : seedlen = FSPRG_RECOMMENDED_SEEDLEN;
260 : }
261 :
262 0 : p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
263 0 : q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);
264 :
265 0 : if (msk) {
266 0 : store_secpar(msk + 0, secpar);
267 0 : mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
268 0 : mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
269 : }
270 :
271 0 : if (mpk) {
272 0 : n = gcry_mpi_new(0);
273 0 : gcry_mpi_mul(n, p, q);
274 0 : assert(gcry_mpi_get_nbits(n) == secpar);
275 :
276 0 : store_secpar(mpk + 0, secpar);
277 0 : mpi_export(mpk + 2, secpar / 8, n);
278 :
279 0 : gcry_mpi_release(n);
280 : }
281 :
282 0 : gcry_mpi_release(p);
283 0 : gcry_mpi_release(q);
284 0 : }
285 :
286 0 : void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
287 : gcry_mpi_t n, x;
288 : uint16_t secpar;
289 :
290 0 : initialize_libgcrypt(false);
291 :
292 0 : secpar = read_secpar(mpk + 0);
293 0 : n = mpi_import(mpk + 2, secpar / 8);
294 0 : x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
295 :
296 0 : memcpy(state, mpk, 2 + secpar / 8);
297 0 : mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
298 0 : memzero(state + 2 + 2 * secpar / 8, 8);
299 :
300 0 : gcry_mpi_release(n);
301 0 : gcry_mpi_release(x);
302 0 : }
303 :
304 0 : void FSPRG_Evolve(void *state) {
305 : gcry_mpi_t n, x;
306 : uint16_t secpar;
307 : uint64_t epoch;
308 :
309 0 : initialize_libgcrypt(false);
310 :
311 0 : secpar = read_secpar(state + 0);
312 0 : n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
313 0 : x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
314 0 : epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
315 :
316 0 : gcry_mpi_mulm(x, x, x, n);
317 0 : epoch++;
318 :
319 0 : mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
320 0 : uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
321 :
322 0 : gcry_mpi_release(n);
323 0 : gcry_mpi_release(x);
324 0 : }
325 :
326 0 : uint64_t FSPRG_GetEpoch(const void *state) {
327 : uint16_t secpar;
328 0 : secpar = read_secpar(state + 0);
329 0 : return uint64_import(state + 2 + 2 * secpar / 8, 8);
330 : }
331 :
332 0 : void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
333 : gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
334 : uint16_t secpar;
335 :
336 0 : initialize_libgcrypt(false);
337 :
338 0 : secpar = read_secpar(msk + 0);
339 0 : p = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
340 0 : q = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
341 :
342 0 : n = gcry_mpi_new(0);
343 0 : gcry_mpi_mul(n, p, q);
344 :
345 0 : x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
346 0 : CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
347 :
348 0 : kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
349 0 : kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
350 :
351 0 : gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
352 0 : gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
353 :
354 0 : CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
355 :
356 0 : store_secpar(state + 0, secpar);
357 0 : mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
358 0 : mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
359 0 : uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
360 :
361 0 : gcry_mpi_release(p);
362 0 : gcry_mpi_release(q);
363 0 : gcry_mpi_release(n);
364 0 : gcry_mpi_release(x);
365 0 : gcry_mpi_release(xp);
366 0 : gcry_mpi_release(xq);
367 0 : gcry_mpi_release(kp);
368 0 : gcry_mpi_release(kq);
369 0 : gcry_mpi_release(xm);
370 0 : }
371 :
372 0 : void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
373 : uint16_t secpar;
374 :
375 0 : initialize_libgcrypt(false);
376 :
377 0 : secpar = read_secpar(state + 0);
378 0 : det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);
379 0 : }
|
