aboutsummaryrefslogtreecommitdiffstats
path: root/crypto/jpake/jpake.c
blob: 8c38727e20fd31cafa97b94390f87d943f3e9a5a (plain) (blame)
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
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
#include "jpake.h"

#include <openssl/crypto.h>
#include <openssl/sha.h>
#include <openssl/err.h>
#include <memory.h>
#include <string.h>

/*
 * In the definition, (xa, xb, xc, xd) are Alice's (x1, x2, x3, x4) or
 * Bob's (x3, x4, x1, x2). If you see what I mean.
 */

typedef struct {
    char *name;                 /* Must be unique */
    char *peer_name;
    BIGNUM *p;
    BIGNUM *g;
    BIGNUM *q;
    BIGNUM *gxc;                /* Alice's g^{x3} or Bob's g^{x1} */
    BIGNUM *gxd;                /* Alice's g^{x4} or Bob's g^{x2} */
} JPAKE_CTX_PUBLIC;

struct JPAKE_CTX {
    JPAKE_CTX_PUBLIC p;
    BIGNUM *secret;             /* The shared secret */
    BN_CTX *ctx;
    BIGNUM *xa;                 /* Alice's x1 or Bob's x3 */
    BIGNUM *xb;                 /* Alice's x2 or Bob's x4 */
    BIGNUM *key;                /* The calculated (shared) key */
};

static void JPAKE_ZKP_init(JPAKE_ZKP *zkp)
{
    zkp->gr = BN_new();
    zkp->b = BN_new();
}

static void JPAKE_ZKP_release(JPAKE_ZKP *zkp)
{
    BN_free(zkp->b);
    BN_free(zkp->gr);
}

/* Two birds with one stone - make the global name as expected */
#define JPAKE_STEP_PART_init    JPAKE_STEP2_init
#define JPAKE_STEP_PART_release JPAKE_STEP2_release

void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p)
{
    p->gx = BN_new();
    JPAKE_ZKP_init(&p->zkpx);
}

void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p)
{
    JPAKE_ZKP_release(&p->zkpx);
    BN_free(p->gx);
}

void JPAKE_STEP1_init(JPAKE_STEP1 *s1)
{
    JPAKE_STEP_PART_init(&s1->p1);
    JPAKE_STEP_PART_init(&s1->p2);
}

void JPAKE_STEP1_release(JPAKE_STEP1 *s1)
{
    JPAKE_STEP_PART_release(&s1->p2);
    JPAKE_STEP_PART_release(&s1->p1);
}

static void JPAKE_CTX_init(JPAKE_CTX *ctx, const char *name,
                           const char *peer_name, const BIGNUM *p,
                           const BIGNUM *g, const BIGNUM *q,
                           const BIGNUM *secret)
{
    ctx->p.name = OPENSSL_strdup(name);
    ctx->p.peer_name = OPENSSL_strdup(peer_name);
    ctx->p.p = BN_dup(p);
    ctx->p.g = BN_dup(g);
    ctx->p.q = BN_dup(q);
    ctx->secret = BN_dup(secret);

    ctx->p.gxc = BN_new();
    ctx->p.gxd = BN_new();

    ctx->xa = BN_new();
    ctx->xb = BN_new();
    ctx->key = BN_new();
    ctx->ctx = BN_CTX_new();
}

static void JPAKE_CTX_release(JPAKE_CTX *ctx)
{
    BN_CTX_free(ctx->ctx);
    BN_clear_free(ctx->key);
    BN_clear_free(ctx->xb);
    BN_clear_free(ctx->xa);

    BN_free(ctx->p.gxd);
    BN_free(ctx->p.gxc);

    BN_clear_free(ctx->secret);
    BN_free(ctx->p.q);
    BN_free(ctx->p.g);
    BN_free(ctx->p.p);
    OPENSSL_free(ctx->p.peer_name);
    OPENSSL_free(ctx->p.name);

    memset(ctx, '\0', sizeof *ctx);
}

JPAKE_CTX *JPAKE_CTX_new(const char *name, const char *peer_name,
                         const BIGNUM *p, const BIGNUM *g, const BIGNUM *q,
                         const BIGNUM *secret)
{
    JPAKE_CTX *ctx = OPENSSL_malloc(sizeof *ctx);

    JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret);

    return ctx;
}

void JPAKE_CTX_free(JPAKE_CTX *ctx)
{
    JPAKE_CTX_release(ctx);
    OPENSSL_free(ctx);
}

static void hashlength(SHA_CTX *sha, size_t l)
{
    unsigned char b[2];

    OPENSSL_assert(l <= 0xffff);
    b[0] = l >> 8;
    b[1] = l & 0xff;
    SHA1_Update(sha, b, 2);
}

static void hashstring(SHA_CTX *sha, const char *string)
{
    size_t l = strlen(string);

    hashlength(sha, l);
    SHA1_Update(sha, string, l);
}

static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
{
    size_t l = BN_num_bytes(bn);
    unsigned char *bin = OPENSSL_malloc(l);

    hashlength(sha, l);
    BN_bn2bin(bn, bin);
    SHA1_Update(sha, bin, l);
    OPENSSL_free(bin);
}

/* h=hash(g, g^r, g^x, name) */
static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p,
                     const char *proof_name)
{
    unsigned char md[SHA_DIGEST_LENGTH];
    SHA_CTX sha;

    /*
     * XXX: hash should not allow moving of the boundaries - Java code
     * is flawed in this respect. Length encoding seems simplest.
     */
    SHA1_Init(&sha);
    hashbn(&sha, zkpg);
    OPENSSL_assert(!BN_is_zero(p->zkpx.gr));
    hashbn(&sha, p->zkpx.gr);
    hashbn(&sha, p->gx);
    hashstring(&sha, proof_name);
    SHA1_Final(md, &sha);
    BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
}

/*
 * Prove knowledge of x
 * Note that p->gx has already been calculated
 */
static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x,
                         const BIGNUM *zkpg, JPAKE_CTX *ctx)
{
    BIGNUM *r = BN_new();
    BIGNUM *h = BN_new();
    BIGNUM *t = BN_new();

   /*-
    * r in [0,q)
    * XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
    */
    BN_rand_range(r, ctx->p.q);
    /* g^r */
    BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx);

    /* h=hash... */
    zkp_hash(h, zkpg, p, ctx->p.name);

    /* b = r - x*h */
    BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx);
    BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx);

    /* cleanup */
    BN_free(t);
    BN_free(h);
    BN_free(r);
}

static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg,
                      JPAKE_CTX *ctx)
{
    BIGNUM *h = BN_new();
    BIGNUM *t1 = BN_new();
    BIGNUM *t2 = BN_new();
    BIGNUM *t3 = BN_new();
    int ret = 0;

    zkp_hash(h, zkpg, p, ctx->p.peer_name);

    /* t1 = g^b */
    BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx);
    /* t2 = (g^x)^h = g^{hx} */
    BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx);
    /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */
    BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx);

    /* verify t3 == g^r */
    if (BN_cmp(t3, p->zkpx.gr) == 0)
        ret = 1;
    else
        JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED);

    /* cleanup */
    BN_free(t3);
    BN_free(t2);
    BN_free(t1);
    BN_free(h);

    return ret;
}

static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x,
                               const BIGNUM *g, JPAKE_CTX *ctx)
{
    BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx);
    generate_zkp(p, x, g, ctx);
}

/* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */
static void genrand(JPAKE_CTX *ctx)
{
    BIGNUM *qm1;

    /* xa in [0, q) */
    BN_rand_range(ctx->xa, ctx->p.q);

    /* q-1 */
    qm1 = BN_new();
    BN_copy(qm1, ctx->p.q);
    BN_sub_word(qm1, 1);

    /* ... and xb in [0, q-1) */
    BN_rand_range(ctx->xb, qm1);
    /* [1, q) */
    BN_add_word(ctx->xb, 1);

    /* cleanup */
    BN_free(qm1);
}

int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx)
{
    genrand(ctx);
    generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx);
    generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx);

    return 1;
}

/* g^x is a legal value */
static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx)
{
    BIGNUM *t;
    int res;

    if (BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0)
        return 0;

    t = BN_new();
    BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx);
    res = BN_is_one(t);
    BN_free(t);

    return res;
}

int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received)
{
    if (!is_legal(received->p1.gx, ctx)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
                 JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL);
        return 0;
    }

    if (!is_legal(received->p2.gx, ctx)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
                 JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL);
        return 0;
    }

    /* verify their ZKP(xc) */
    if (!verify_zkp(&received->p1, ctx->p.g, ctx)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED);
        return 0;
    }

    /* verify their ZKP(xd) */
    if (!verify_zkp(&received->p2, ctx->p.g, ctx)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED);
        return 0;
    }

    /* g^xd != 1 */
    if (BN_is_one(received->p2.gx)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE);
        return 0;
    }

    /* Save the bits we need for later */
    BN_copy(ctx->p.gxc, received->p1.gx);
    BN_copy(ctx->p.gxd, received->p2.gx);

    return 1;
}

int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx)
{
    BIGNUM *t1 = BN_new();
    BIGNUM *t2 = BN_new();

   /*-
    * X = g^{(xa + xc + xd) * xb * s}
    * t1 = g^xa
    */
    BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx);
    /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */
    BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx);
    /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */
    BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx);
    /* t2 = xb * s */
    BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx);

   /*-
    * ZKP(xb * s)
    * XXX: this is kinda funky, because we're using
    *
    * g' = g^{xa + xc + xd}
    *
    * as the generator, which means X is g'^{xb * s}
    * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
    */
    generate_step_part(send, t2, t1, ctx);

    /* cleanup */
    BN_free(t1);
    BN_free(t2);

    return 1;
}

/* gx = g^{xc + xa + xb} * xd * s */
static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx)
{
    BIGNUM *t1 = BN_new();
    BIGNUM *t2 = BN_new();
    BIGNUM *t3 = BN_new();

   /*-
    * K = (gx/g^{xb * xd * s})^{xb}
    *   = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
    *   = (g^{(xa + xc) * xd * s})^{xb}
    *   = g^{(xa + xc) * xb * xd * s}
    * [which is the same regardless of who calculates it]
    */

    /* t1 = (g^{xd})^{xb} = g^{xb * xd} */
    BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx);
    /* t2 = -s = q-s */
    BN_sub(t2, ctx->p.q, ctx->secret);
    /* t3 = t1^t2 = g^{-xb * xd * s} */
    BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx);
    /* t1 = gx * t3 = X/g^{xb * xd * s} */
    BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx);
    /* K = t1^{xb} */
    BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx);

    /* cleanup */
    BN_free(t3);
    BN_free(t2);
    BN_free(t1);

    return 1;
}

int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received)
{
    BIGNUM *t1 = BN_new();
    BIGNUM *t2 = BN_new();
    int ret = 0;

   /*-
    * g' = g^{xc + xa + xb} [from our POV]
    * t1 = xa + xb
    */
    BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx);
    /* t2 = g^{t1} = g^{xa+xb} */
    BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx);
    /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */
    BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx);

    if (verify_zkp(received, t1, ctx))
        ret = 1;
    else
        JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED);

    compute_key(ctx, received->gx);

    /* cleanup */
    BN_free(t2);
    BN_free(t1);

    return ret;
}

static void quickhashbn(unsigned char *md, const BIGNUM *bn)
{
    SHA_CTX sha;

    SHA1_Init(&sha);
    hashbn(&sha, bn);
    SHA1_Final(md, &sha);
}

void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a)
{
}

int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx)
{
    quickhashbn(send->hhk, ctx->key);
    SHA1(send->hhk, sizeof send->hhk, send->hhk);

    return 1;
}

int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received)
{
    unsigned char hhk[SHA_DIGEST_LENGTH];

    quickhashbn(hhk, ctx->key);
    SHA1(hhk, sizeof hhk, hhk);
    if (memcmp(hhk, received->hhk, sizeof hhk)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS,
                 JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH);
        return 0;
    }
    return 1;
}

void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a)
{
}

void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b)
{
}

int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx)
{
    quickhashbn(send->hk, ctx->key);

    return 1;
}

int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received)
{
    unsigned char hk[SHA_DIGEST_LENGTH];

    quickhashbn(hk, ctx->key);
    if (memcmp(hk, received->hk, sizeof hk)) {
        JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH);
        return 0;
    }
    return 1;
}

void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b)
{
}

const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx)
{
    return ctx->key;
}