jpake.c revision 306195 
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 <string.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    if (ctx == NULL)
120        return NULL;
121
122    JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret);
123
124    return ctx;
125}
126
127void JPAKE_CTX_free(JPAKE_CTX *ctx)
128{
129    JPAKE_CTX_release(ctx);
130    OPENSSL_free(ctx);
131}
132
133static void hashlength(SHA_CTX *sha, size_t l)
134{
135    unsigned char b[2];
136
137    OPENSSL_assert(l <= 0xffff);
138    b[0] = l >> 8;
139    b[1] = l & 0xff;
140    SHA1_Update(sha, b, 2);
141}
142
143static void hashstring(SHA_CTX *sha, const char *string)
144{
145    size_t l = strlen(string);
146
147    hashlength(sha, l);
148    SHA1_Update(sha, string, l);
149}
150
151static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
152{
153    size_t l = BN_num_bytes(bn);
154    unsigned char *bin = OPENSSL_malloc(l);
155
156    if (bin == NULL)
157        return;
158    hashlength(sha, l);
159    BN_bn2bin(bn, bin);
160    SHA1_Update(sha, bin, l);
161    OPENSSL_free(bin);
162}
163
164/* h=hash(g, g^r, g^x, name) */
165static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p,
166                     const char *proof_name)
167{
168    unsigned char md[SHA_DIGEST_LENGTH];
169    SHA_CTX sha;
170
171    /*
172     * XXX: hash should not allow moving of the boundaries - Java code
173     * is flawed in this respect. Length encoding seems simplest.
174     */
175    SHA1_Init(&sha);
176    hashbn(&sha, zkpg);
177    OPENSSL_assert(!BN_is_zero(p->zkpx.gr));
178    hashbn(&sha, p->zkpx.gr);
179    hashbn(&sha, p->gx);
180    hashstring(&sha, proof_name);
181    SHA1_Final(md, &sha);
182    BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
183}
184
185/*
186 * Prove knowledge of x
187 * Note that p->gx has already been calculated
188 */
189static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x,
190                         const BIGNUM *zkpg, JPAKE_CTX *ctx)
191{
192    BIGNUM *r = BN_new();
193    BIGNUM *h = BN_new();
194    BIGNUM *t = BN_new();
195
196   /*-
197    * r in [0,q)
198    * XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
199    */
200    BN_rand_range(r, ctx->p.q);
201    /* g^r */
202    BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx);
203
204    /* h=hash... */
205    zkp_hash(h, zkpg, p, ctx->p.name);
206
207    /* b = r - x*h */
208    BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx);
209    BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx);
210
211    /* cleanup */
212    BN_free(t);
213    BN_free(h);
214    BN_free(r);
215}
216
217static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg,
218                      JPAKE_CTX *ctx)
219{
220    BIGNUM *h = BN_new();
221    BIGNUM *t1 = BN_new();
222    BIGNUM *t2 = BN_new();
223    BIGNUM *t3 = BN_new();
224    int ret = 0;
225
226    if (h == NULL || t1 == NULL || t2 == NULL || t3 == NULL)
227        goto end;
228
229    zkp_hash(h, zkpg, p, ctx->p.peer_name);
230
231    /* t1 = g^b */
232    BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx);
233    /* t2 = (g^x)^h = g^{hx} */
234    BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx);
235    /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */
236    BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx);
237
238    /* verify t3 == g^r */
239    if (BN_cmp(t3, p->zkpx.gr) == 0)
240        ret = 1;
241    else
242        JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED);
243
244end:
245    /* cleanup */
246    BN_free(t3);
247    BN_free(t2);
248    BN_free(t1);
249    BN_free(h);
250
251    return ret;
252}
253
254static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x,
255                               const BIGNUM *g, JPAKE_CTX *ctx)
256{
257    BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx);
258    generate_zkp(p, x, g, ctx);
259}
260
261/* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */
262static void genrand(JPAKE_CTX *ctx)
263{
264    BIGNUM *qm1;
265
266    /* xa in [0, q) */
267    BN_rand_range(ctx->xa, ctx->p.q);
268
269    /* q-1 */
270    qm1 = BN_new();
271    BN_copy(qm1, ctx->p.q);
272    BN_sub_word(qm1, 1);
273
274    /* ... and xb in [0, q-1) */
275    BN_rand_range(ctx->xb, qm1);
276    /* [1, q) */
277    BN_add_word(ctx->xb, 1);
278
279    /* cleanup */
280    BN_free(qm1);
281}
282
283int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx)
284{
285    genrand(ctx);
286    generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx);
287    generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx);
288
289    return 1;
290}
291
292/* g^x is a legal value */
293static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx)
294{
295    BIGNUM *t;
296    int res;
297
298    if (BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0)
299        return 0;
300
301    t = BN_new();
302    BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx);
303    res = BN_is_one(t);
304    BN_free(t);
305
306    return res;
307}
308
309int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received)
310{
311    if (!is_legal(received->p1.gx, ctx)) {
312        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
313                 JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL);
314        return 0;
315    }
316
317    if (!is_legal(received->p2.gx, ctx)) {
318        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS,
319                 JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL);
320        return 0;
321    }
322
323    /* verify their ZKP(xc) */
324    if (!verify_zkp(&received->p1, ctx->p.g, ctx)) {
325        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED);
326        return 0;
327    }
328
329    /* verify their ZKP(xd) */
330    if (!verify_zkp(&received->p2, ctx->p.g, ctx)) {
331        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED);
332        return 0;
333    }
334
335    /* g^xd != 1 */
336    if (BN_is_one(received->p2.gx)) {
337        JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE);
338        return 0;
339    }
340
341    /* Save the bits we need for later */
342    BN_copy(ctx->p.gxc, received->p1.gx);
343    BN_copy(ctx->p.gxd, received->p2.gx);
344
345    return 1;
346}
347
348int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx)
349{
350    BIGNUM *t1 = BN_new();
351    BIGNUM *t2 = BN_new();
352
353   /*-
354    * X = g^{(xa + xc + xd) * xb * s}
355    * t1 = g^xa
356    */
357    BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx);
358    /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */
359    BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx);
360    /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */
361    BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx);
362    /* t2 = xb * s */
363    BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx);
364
365   /*-
366    * ZKP(xb * s)
367    * XXX: this is kinda funky, because we're using
368    *
369    * g' = g^{xa + xc + xd}
370    *
371    * as the generator, which means X is g'^{xb * s}
372    * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
373    */
374    generate_step_part(send, t2, t1, ctx);
375
376    /* cleanup */
377    BN_free(t1);
378    BN_free(t2);
379
380    return 1;
381}
382
383/* gx = g^{xc + xa + xb} * xd * s */
384static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx)
385{
386    BIGNUM *t1 = BN_new();
387    BIGNUM *t2 = BN_new();
388    BIGNUM *t3 = BN_new();
389
390   /*-
391    * K = (gx/g^{xb * xd * s})^{xb}
392    *   = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
393    *   = (g^{(xa + xc) * xd * s})^{xb}
394    *   = g^{(xa + xc) * xb * xd * s}
395    * [which is the same regardless of who calculates it]
396    */
397
398    /* t1 = (g^{xd})^{xb} = g^{xb * xd} */
399    BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx);
400    /* t2 = -s = q-s */
401    BN_sub(t2, ctx->p.q, ctx->secret);
402    /* t3 = t1^t2 = g^{-xb * xd * s} */
403    BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx);
404    /* t1 = gx * t3 = X/g^{xb * xd * s} */
405    BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx);
406    /* K = t1^{xb} */
407    BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx);
408
409    /* cleanup */
410    BN_free(t3);
411    BN_free(t2);
412    BN_free(t1);
413
414    return 1;
415}
416
417int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received)
418{
419    BIGNUM *t1 = BN_new();
420    BIGNUM *t2 = BN_new();
421    int ret = 0;
422
423   /*-
424    * g' = g^{xc + xa + xb} [from our POV]
425    * t1 = xa + xb
426    */
427    BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx);
428    /* t2 = g^{t1} = g^{xa+xb} */
429    BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx);
430    /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */
431    BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx);
432
433    if (verify_zkp(received, t1, ctx))
434        ret = 1;
435    else
436        JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED);
437
438    compute_key(ctx, received->gx);
439
440    /* cleanup */
441    BN_free(t2);
442    BN_free(t1);
443
444    return ret;
445}
446
447static void quickhashbn(unsigned char *md, const BIGNUM *bn)
448{
449    SHA_CTX sha;
450
451    SHA1_Init(&sha);
452    hashbn(&sha, bn);
453    SHA1_Final(md, &sha);
454}
455
456void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a)
457{
458}
459
460int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx)
461{
462    quickhashbn(send->hhk, ctx->key);
463    SHA1(send->hhk, sizeof send->hhk, send->hhk);
464
465    return 1;
466}
467
468int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received)
469{
470    unsigned char hhk[SHA_DIGEST_LENGTH];
471
472    quickhashbn(hhk, ctx->key);
473    SHA1(hhk, sizeof hhk, hhk);
474    if (memcmp(hhk, received->hhk, sizeof hhk)) {
475        JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS,
476                 JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH);
477        return 0;
478    }
479    return 1;
480}
481
482void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a)
483{
484}
485
486void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b)
487{
488}
489
490int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx)
491{
492    quickhashbn(send->hk, ctx->key);
493
494    return 1;
495}
496
497int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received)
498{
499    unsigned char hk[SHA_DIGEST_LENGTH];
500
501    quickhashbn(hk, ctx->key);
502    if (memcmp(hk, received->hk, sizeof hk)) {
503        JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH);
504        return 0;
505    }
506    return 1;
507}
508
509void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b)
510{
511}
512
513const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx)
514{
515    return ctx->key;
516}
517