summaryrefslogtreecommitdiffstats
path: root/src/journal/fsprg.c
blob: 7ea72495ef2ed325e4eb20ed90d039508a248544 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
/* SPDX-License-Identifier: LGPL-2.1-or-later
 *
 * fsprg v0.1  -  (seekable) forward-secure pseudorandom generator
 * Copyright © 2012 B. Poettering
 * Contact: fsprg@point-at-infinity.org
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
 * 02110-1301  USA
 */

/*
 * See "Practical Secure Logging: Seekable Sequential Key Generators"
 * by G. A. Marson, B. Poettering for details:
 *
 * http://eprint.iacr.org/2013/397
 */

#include <string.h>

#include "fsprg.h"
#include "gcrypt-util.h"
#include "memory-util.h"

#define ISVALID_SECPAR(secpar) (((secpar) % 16 == 0) && ((secpar) >= 16) && ((secpar) <= 16384))
#define VALIDATE_SECPAR(secpar) assert(ISVALID_SECPAR(secpar));

#define RND_HASH GCRY_MD_SHA256
#define RND_GEN_P 0x01
#define RND_GEN_Q 0x02
#define RND_GEN_X 0x03

#pragma GCC diagnostic ignored "-Wpointer-arith"
/* TODO: remove void* arithmetic and this work-around */

/******************************************************************************/

static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
        unsigned len;
        size_t nwritten;

        assert(gcry_mpi_cmp_ui(x, 0) >= 0);
        len = (gcry_mpi_get_nbits(x) + 7) / 8;
        assert(len <= buflen);
        memzero(buf, buflen);
        gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
        assert(nwritten == len);
}

static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
        gcry_mpi_t h;
        _unused_ unsigned len;

        assert_se(gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL) == 0);
        len = (gcry_mpi_get_nbits(h) + 7) / 8;
        assert(len <= buflen);
        assert(gcry_mpi_cmp_ui(h, 0) >= 0);

        return h;
}

static void uint64_export(void *buf, size_t buflen, uint64_t x) {
        assert(buflen == 8);
        ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
        ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
        ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
        ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
        ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
        ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
        ((uint8_t*) buf)[6] = (x >>  8) & 0xff;
        ((uint8_t*) buf)[7] = (x >>  0) & 0xff;
}

_pure_ static uint64_t uint64_import(const void *buf, size_t buflen) {
        assert(buflen == 8);
        return
                (uint64_t)(((uint8_t*) buf)[0]) << 56 |
                (uint64_t)(((uint8_t*) buf)[1]) << 48 |
                (uint64_t)(((uint8_t*) buf)[2]) << 40 |
                (uint64_t)(((uint8_t*) buf)[3]) << 32 |
                (uint64_t)(((uint8_t*) buf)[4]) << 24 |
                (uint64_t)(((uint8_t*) buf)[5]) << 16 |
                (uint64_t)(((uint8_t*) buf)[6]) <<  8 |
                (uint64_t)(((uint8_t*) buf)[7]) <<  0;
}

/* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
        gcry_md_hd_t hd, hd2;
        size_t olen, cpylen;
        uint32_t ctr;

        olen = gcry_md_get_algo_dlen(RND_HASH);
        gcry_md_open(&hd, RND_HASH, 0);
        gcry_md_write(hd, seed, seedlen);
        gcry_md_putc(hd, (idx >> 24) & 0xff);
        gcry_md_putc(hd, (idx >> 16) & 0xff);
        gcry_md_putc(hd, (idx >>  8) & 0xff);
        gcry_md_putc(hd, (idx >>  0) & 0xff);

        for (ctr = 0; buflen; ctr++) {
                gcry_md_copy(&hd2, hd);
                gcry_md_putc(hd2, (ctr >> 24) & 0xff);
                gcry_md_putc(hd2, (ctr >> 16) & 0xff);
                gcry_md_putc(hd2, (ctr >>  8) & 0xff);
                gcry_md_putc(hd2, (ctr >>  0) & 0xff);
                gcry_md_final(hd2);
                cpylen = (buflen < olen) ? buflen : olen;
                memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
                gcry_md_close(hd2);
                buf += cpylen;
                buflen -= cpylen;
        }
        gcry_md_close(hd);
}

/* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
        size_t buflen = bits / 8;
        uint8_t buf[buflen];
        gcry_mpi_t p;

        assert(bits % 8 == 0);
        assert(buflen > 0);

        det_randomize(buf, buflen, seed, seedlen, idx);
        buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
        buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */

        p = mpi_import(buf, buflen);
        while (gcry_prime_check(p, 0))
                gcry_mpi_add_ui(p, p, 4);

        return p;
}

/* deterministically generate from seed/idx a quadratic residue (mod n) */
static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
        size_t buflen = secpar / 8;
        uint8_t buf[buflen];
        gcry_mpi_t x;

        det_randomize(buf, buflen, seed, seedlen, idx);
        buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
        x = mpi_import(buf, buflen);
        assert(gcry_mpi_cmp(x, n) < 0);
        gcry_mpi_mulm(x, x, x, n);
        return x;
}

/* compute 2^m (mod phi(p)), for a prime p */
static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
        gcry_mpi_t phi, r;
        int n;

        phi = gcry_mpi_new(0);
        gcry_mpi_sub_ui(phi, p, 1);

        /* count number of used bits in m */
        for (n = 0; (1ULL << n) <= m; n++)
                ;

        r = gcry_mpi_new(0);
        gcry_mpi_set_ui(r, 1);
        while (n) { /* square and multiply algorithm for fast exponentiation */
                n--;
                gcry_mpi_mulm(r, r, r, phi);
                if (m & ((uint64_t)1 << n)) {
                        gcry_mpi_add(r, r, r);
                        if (gcry_mpi_cmp(r, phi) >= 0)
                                gcry_mpi_sub(r, r, phi);
                }
        }

        gcry_mpi_release(phi);
        return r;
}

/* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
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) {
        *xp = gcry_mpi_new(0);
        *xq = gcry_mpi_new(0);
        gcry_mpi_mod(*xp, x, p);
        gcry_mpi_mod(*xq, x, q);
}

/* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
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) {
        gcry_mpi_t a, u;

        a = gcry_mpi_new(0);
        u = gcry_mpi_new(0);
        *x = gcry_mpi_new(0);
        gcry_mpi_subm(a, xq, xp, q);
        gcry_mpi_invm(u, p, q);
        gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p  (mod q) */
        gcry_mpi_mul(*x, p, a);
        gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
        gcry_mpi_release(a);
        gcry_mpi_release(u);
}

/******************************************************************************/

size_t FSPRG_mskinbytes(unsigned _secpar) {
        VALIDATE_SECPAR(_secpar);
        return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
}

size_t FSPRG_mpkinbytes(unsigned _secpar) {
        VALIDATE_SECPAR(_secpar);
        return 2 + _secpar / 8; /* to store header,n */
}

size_t FSPRG_stateinbytes(unsigned _secpar) {
        VALIDATE_SECPAR(_secpar);
        return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
}

static void store_secpar(void *buf, uint16_t secpar) {
        secpar = secpar / 16 - 1;
        ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
        ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
}

static uint16_t read_secpar(const void *buf) {
        uint16_t secpar;
        secpar =
                (uint16_t)(((uint8_t*) buf)[0]) << 8 |
                (uint16_t)(((uint8_t*) buf)[1]) << 0;
        return 16 * (secpar + 1);
}

void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
        uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
        gcry_mpi_t n, p, q;
        uint16_t secpar;

        VALIDATE_SECPAR(_secpar);
        secpar = _secpar;

        initialize_libgcrypt(false);

        if (!seed) {
                gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
                seed = iseed;
                seedlen = FSPRG_RECOMMENDED_SEEDLEN;
        }

        p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
        q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);

        if (msk) {
                store_secpar(msk + 0, secpar);
                mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
                mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
        }

        if (mpk) {
                n = gcry_mpi_new(0);
                gcry_mpi_mul(n, p, q);
                assert(gcry_mpi_get_nbits(n) == secpar);

                store_secpar(mpk + 0, secpar);
                mpi_export(mpk + 2, secpar / 8, n);

                gcry_mpi_release(n);
        }

        gcry_mpi_release(p);
        gcry_mpi_release(q);
}

void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
        gcry_mpi_t n, x;
        uint16_t secpar;

        initialize_libgcrypt(false);

        secpar = read_secpar(mpk + 0);
        n = mpi_import(mpk + 2, secpar / 8);
        x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);

        memcpy(state, mpk, 2 + secpar / 8);
        mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
        memzero(state + 2 + 2 * secpar / 8, 8);

        gcry_mpi_release(n);
        gcry_mpi_release(x);
}

void FSPRG_Evolve(void *state) {
        gcry_mpi_t n, x;
        uint16_t secpar;
        uint64_t epoch;

        initialize_libgcrypt(false);

        secpar = read_secpar(state + 0);
        n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
        x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
        epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);

        gcry_mpi_mulm(x, x, x, n);
        epoch++;

        mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
        uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);

        gcry_mpi_release(n);
        gcry_mpi_release(x);
}

uint64_t FSPRG_GetEpoch(const void *state) {
        uint16_t secpar;
        secpar = read_secpar(state + 0);
        return uint64_import(state + 2 + 2 * secpar / 8, 8);
}

void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
        gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
        uint16_t secpar;

        initialize_libgcrypt(false);

        secpar = read_secpar(msk + 0);
        p  = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
        q  = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);

        n = gcry_mpi_new(0);
        gcry_mpi_mul(n, p, q);

        x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
        CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */

        kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
        kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */

        gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
        gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */

        CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */

        store_secpar(state + 0, secpar);
        mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
        mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
        uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);

        gcry_mpi_release(p);
        gcry_mpi_release(q);
        gcry_mpi_release(n);
        gcry_mpi_release(x);
        gcry_mpi_release(xp);
        gcry_mpi_release(xq);
        gcry_mpi_release(kp);
        gcry_mpi_release(kq);
        gcry_mpi_release(xm);
}

void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
        uint16_t secpar;

        initialize_libgcrypt(false);

        secpar = read_secpar(state + 0);
        det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);
}