jpake.c revision 296465 
1#include "jpake.h"
2
3#include <openssl/crypto.h>
4#include <openssl/sha.h>
5#include <openssl/err.h>
6#include <memory.h>
7#include <assert.h>
8
9/*
10 * In the definition, (xa, xb, xc, xd) are Alice's (x1, x2, x3, x4) or
11 * Bob's (x3, x4, x1, x2). If you see what I mean.
12 */
13
14typedef struct {
15    char *name;                 /* Must be unique */
16    char *peer_name;
17    BIGNUM *p;
18    BIGNUM *g;
19    BIGNUM *q;
20    BIGNUM *gxc;                /* Alice's g^{x3} or Bob's g^{x1} */
21    BIGNUM *gxd;                /* Alice's g^{x4} or Bob's g^{x2} */
22} JPAKE_CTX_PUBLIC;
23
24struct JPAKE_CTX {
25    JPAKE_CTX_PUBLIC p;
26    BIGNUM *secret;             /* The shared secret */
27    BN_CTX *ctx;
28    BIGNUM *xa;                 /* Alice's x1 or Bob's x3 */
29    BIGNUM *xb;                 /* Alice's x2 or Bob's x4 */
30    BIGNUM *key;                /* The calculated (shared) key */
31};
32
33static void JPAKE_ZKP_init(JPAKE_ZKP *zkp)
34{
35    zkp->gr = BN_new();
36    zkp->b = BN_new();
37}
38
39static void JPAKE_ZKP_release(JPAKE_ZKP *zkp)
40{
41    BN_free(zkp->b);
42    BN_free(zkp->gr);
43}
44
45/* Two birds with one stone - make the global name as expected */
46#define JPAKE_STEP_PART_init    JPAKE_STEP2_init
47#define JPAKE_STEP_PART_release JPAKE_STEP2_release
48
49void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p)
50{
51    p->gx = BN_new();
52    JPAKE_ZKP_init(&p->zkpx);
53}
54
55void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p)
56{
57    JPAKE_ZKP_release(&p->zkpx);
58    BN_free(p->gx);
59}
60
61void JPAKE_STEP1_init(JPAKE_STEP1 *s1)
62{
63    JPAKE_STEP_PART_init(&s1->p1);
64    JPAKE_STEP_PART_init(&s1->p2);
65}
66
67void JPAKE_STEP1_release(JPAKE_STEP1 *s1)
68{
69    JPAKE_STEP_PART_release(&s1->p2);
70    JPAKE_STEP_PART_release(&s1->p1);
71}
72
73static void JPAKE_CTX_init(JPAKE_CTX *ctx, const char *name,
74                           const char *peer_name, const BIGNUM *p,
75                           const BIGNUM *g, const BIGNUM *q,
76                           const BIGNUM *secret)
77{
78    ctx->p.name = OPENSSL_strdup(name);
79    ctx->p.peer_name = OPENSSL_strdup(peer_name);
80    ctx->p.p = BN_dup(p);
81    ctx->p.g = BN_dup(g);
82    ctx->p.q = BN_dup(q);
83    ctx->secret = BN_dup(secret);
84
85    ctx->p.gxc = BN_new();
86    ctx->p.gxd = BN_new();
87
88    ctx->xa = BN_new();
89    ctx->xb = BN_new();
90    ctx->key = BN_new();
91    ctx->ctx = BN_CTX_new();
92}
93
94static void JPAKE_CTX_release(JPAKE_CTX *ctx)
95{
96    BN_CTX_free(ctx->ctx);
97    BN_clear_free(ctx->key);
98    BN_clear_free(ctx->xb);
99    BN_clear_free(ctx->xa);
100
101    BN_free(ctx->p.gxd);
102    BN_free(ctx->p.gxc);
103
104    BN_clear_free(ctx->secret);
105    BN_free(ctx->p.q);
106    BN_free(ctx->p.g);
107    BN_free(ctx->p.p);
108    OPENSSL_free(ctx->p.peer_name);
109    OPENSSL_free(ctx->p.name);
110
111    memset(ctx, '\0', sizeof *ctx);
112}
113
114JPAKE_CTX *JPAKE_CTX_new(const char *name, const char *peer_name,
115                         const BIGNUM *p, const BIGNUM *g, const BIGNUM *q,
116                         const BIGNUM *secret)
117{
118    JPAKE_CTX *ctx = OPENSSL_malloc(sizeof *ctx);
119
120    JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret);
121
122    return ctx;
123}
124
125void JPAKE_CTX_free(JPAKE_CTX *ctx)
126{
127    JPAKE_CTX_release(ctx);
128    OPENSSL_free(ctx);
129}
130
131static void hashlength(SHA_CTX *sha, size_t l)
132{
133    unsigned char b[2];
134
135    assert(l <= 0xffff);
136    b[0] = l >> 8;
137    b[1] = l & 0xff;
138    SHA1_Update(sha, b, 2);
139}
140
141static void hashstring(SHA_CTX *sha, const char *string)
142{
143    size_t l = strlen(string);
144
145    hashlength(sha, l);
146    SHA1_Update(sha, string, l);
147}
148
149static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
150{
151    size_t l = BN_num_bytes(bn);
152    unsigned char *bin = OPENSSL_malloc(l);
153
154    hashlength(sha, l);
155    BN_bn2bin(bn, bin);
156    SHA1_Update(sha, bin, l);
157    OPENSSL_free(bin);
158}
159
160/* h=hash(g, g^r, g^x, name) */
161static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p,
162                     const char *proof_name)
163{
164    unsigned char md[SHA_DIGEST_LENGTH];
165    SHA_CTX sha;
166
167    /*
168     * XXX: hash should not allow moving of the boundaries - Java code
169     * is flawed in this respect. Length encoding seems simplest.
170     */
171    SHA1_Init(&sha);
172    hashbn(&sha, zkpg);
173    assert(!BN_is_zero(p->zkpx.gr));
174    hashbn(&sha, p->zkpx.gr);
175    hashbn(&sha, p->gx);
176    hashstring(&sha, proof_name);
177    SHA1_Final(md, &sha);
178    BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
179}
180
181/*
182 * Prove knowledge of x
183 * Note that p->gx has already been calculated
184 */
185static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x,
186                         const BIGNUM *zkpg, JPAKE_CTX *ctx)
187{
188    BIGNUM *r = BN_new();
189    BIGNUM *h = BN_new();
190    BIGNUM *t = BN_new();
191
192   /*-
193    * r in [0,q)
194    * XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
195    */
196    BN_rand_range(r, ctx->p.q);
197    /* g^r */
198    BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx);
199
200    /* h=hash... */
201    zkp_hash(h, zkpg, p, ctx->p.name);
202
203    /* b = r - x*h */
204    BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx);
205    BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx);
206
207    /* cleanup */
208    BN_free(t);
209    BN_free(h);
210    BN_free(r);
211}
212
213static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg,
214                      JPAKE_CTX *ctx)
215{
216    BIGNUM *h = BN_new();
217    BIGNUM *t1 = BN_new();
218    BIGNUM *t2 = BN_new();
219    BIGNUM *t3 = BN_new();
220    int ret = 0;
221
222    zkp_hash(h, zkpg, p, ctx->p.peer_name);
223
224    /* t1 = g^b */
225    BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx);
226    /* t2 = (g^x)^h = g^{hx} */
227    BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx);
228    /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */
229    BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx);
230
231    /* verify t3 == g^r */
232    if (BN_cmp(t3, p->zkpx.gr) == 0)
233        ret = 1;
234    else
235        JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED);
236
237    /* cleanup */
238    BN_free(t3);
239    BN_free(t2);
240    BN_free(t1);
241    BN_free(h);
242
243    return ret;
244}
245
246static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x,
247                               const BIGNUM *g, JPAKE_CTX *ctx)
248{
249    BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx);
250    generate_zkp(p, x, g, ctx);
251}
252
253/* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */
254static void genrand(JPAKE_CTX *ctx)
255{
256    BIGNUM *qm1;
257
258    /* xa in [0, q) */
259    BN_rand_range(ctx->xa, ctx->p.q);
260
261    /* q-1 */
262    qm1 = BN_new();
263    BN_copy(qm1, ctx->p.q);
264    BN_sub_word(qm1, 1);
265
266    /* ... and xb in [0, q-1) */
267    BN_rand_range(ctx->xb, qm1);
268    /* [1, q) */
269    BN_add_word(ctx->xb, 1);
270
271    /* cleanup */
272    BN_free(qm1);
273}
274
275int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx)
276{
277    genrand(ctx);
278    generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx);
279    generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx);
280
281    return 1;
282}
283
284/* g^x is a legal value */
285static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx)
286{
287    BIGNUM *t;
288    int res;
289
290    if (BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0)
291        return 0;
292
293    t = BN_new();
294    BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx);
295    res = BN_is_one(t);
296    BN_free(t);
297
298    return res;
299}
300
301int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received)
302{
303    if (!is_legal(received->p1.gx, ctx)) {
304        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
305                 JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL);
306        return 0;
307    }
308
309    if (!is_legal(received->p2.gx, ctx)) {
310        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
311                 JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL);
312        return 0;
313    }
314
315    /* verify their ZKP(xc) */
316    if (!verify_zkp(&received->p1, ctx->p.g, ctx)) {
317        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED);
318        return 0;
319    }
320
321    /* verify their ZKP(xd) */
322    if (!verify_zkp(&received->p2, ctx->p.g, ctx)) {
323        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED);
324        return 0;
325    }
326
327    /* g^xd != 1 */
328    if (BN_is_one(received->p2.gx)) {
329        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE);
330        return 0;
331    }
332
333    /* Save the bits we need for later */
334    BN_copy(ctx->p.gxc, received->p1.gx);
335    BN_copy(ctx->p.gxd, received->p2.gx);
336
337    return 1;
338}
339
340int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx)
341{
342    BIGNUM *t1 = BN_new();
343    BIGNUM *t2 = BN_new();
344
345   /*-
346    * X = g^{(xa + xc + xd) * xb * s}
347    * t1 = g^xa
348    */
349    BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx);
350    /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */
351    BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx);
352    /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */
353    BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx);
354    /* t2 = xb * s */
355    BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx);
356
357   /*-
358    * ZKP(xb * s)
359    * XXX: this is kinda funky, because we're using
360    *
361    * g' = g^{xa + xc + xd}
362    *
363    * as the generator, which means X is g'^{xb * s}
364    * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
365    */
366    generate_step_part(send, t2, t1, ctx);
367
368    /* cleanup */
369    BN_free(t1);
370    BN_free(t2);
371
372    return 1;
373}
374
375/* gx = g^{xc + xa + xb} * xd * s */
376static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx)
377{
378    BIGNUM *t1 = BN_new();
379    BIGNUM *t2 = BN_new();
380    BIGNUM *t3 = BN_new();
381
382   /*-
383    * K = (gx/g^{xb * xd * s})^{xb}
384    *   = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
385    *   = (g^{(xa + xc) * xd * s})^{xb}
386    *   = g^{(xa + xc) * xb * xd * s}
387    * [which is the same regardless of who calculates it]
388    */
389
390    /* t1 = (g^{xd})^{xb} = g^{xb * xd} */
391    BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx);
392    /* t2 = -s = q-s */
393    BN_sub(t2, ctx->p.q, ctx->secret);
394    /* t3 = t1^t2 = g^{-xb * xd * s} */
395    BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx);
396    /* t1 = gx * t3 = X/g^{xb * xd * s} */
397    BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx);
398    /* K = t1^{xb} */
399    BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx);
400
401    /* cleanup */
402    BN_free(t3);
403    BN_free(t2);
404    BN_free(t1);
405
406    return 1;
407}
408
409int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received)
410{
411    BIGNUM *t1 = BN_new();
412    BIGNUM *t2 = BN_new();
413    int ret = 0;
414
415   /*-
416    * g' = g^{xc + xa + xb} [from our POV]
417    * t1 = xa + xb
418    */
419    BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx);
420    /* t2 = g^{t1} = g^{xa+xb} */
421    BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx);
422    /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */
423    BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx);
424
425    if (verify_zkp(received, t1, ctx))
426        ret = 1;
427    else
428        JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED);
429
430    compute_key(ctx, received->gx);
431
432    /* cleanup */
433    BN_free(t2);
434    BN_free(t1);
435
436    return ret;
437}
438
439static void quickhashbn(unsigned char *md, const BIGNUM *bn)
440{
441    SHA_CTX sha;
442
443    SHA1_Init(&sha);
444    hashbn(&sha, bn);
445    SHA1_Final(md, &sha);
446}
447
448void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a)
449{
450}
451
452int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx)
453{
454    quickhashbn(send->hhk, ctx->key);
455    SHA1(send->hhk, sizeof send->hhk, send->hhk);
456
457    return 1;
458}
459
460int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received)
461{
462    unsigned char hhk[SHA_DIGEST_LENGTH];
463
464    quickhashbn(hhk, ctx->key);
465    SHA1(hhk, sizeof hhk, hhk);
466    if (memcmp(hhk, received->hhk, sizeof hhk)) {
467        JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS,
468                 JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH);
469        return 0;
470    }
471    return 1;
472}
473
474void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a)
475{
476}
477
478void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b)
479{
480}
481
482int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx)
483{
484    quickhashbn(send->hk, ctx->key);
485
486    return 1;
487}
488
489int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received)
490{
491    unsigned char hk[SHA_DIGEST_LENGTH];
492
493    quickhashbn(hk, ctx->key);
494    if (memcmp(hk, received->hk, sizeof hk)) {
495        JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH);
496        return 0;
497    }
498    return 1;
499}
500
501void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b)
502{
503}
504
505const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx)
506{
507    return ctx->key;
508}
509