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
14 typedef 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
24 struct 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
JPAKE_ZKP_init(JPAKE_ZKP * zkp)33 static void JPAKE_ZKP_init(JPAKE_ZKP *zkp)
34 {
35 zkp->gr = BN_new();
36 zkp->b = BN_new();
37 }
38
JPAKE_ZKP_release(JPAKE_ZKP * zkp)39 static 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
JPAKE_STEP_PART_init(JPAKE_STEP_PART * p)49 void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p)
50 {
51 p->gx = BN_new();
52 JPAKE_ZKP_init(&p->zkpx);
53 }
54
JPAKE_STEP_PART_release(JPAKE_STEP_PART * p)55 void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p)
56 {
57 JPAKE_ZKP_release(&p->zkpx);
58 BN_free(p->gx);
59 }
60
JPAKE_STEP1_init(JPAKE_STEP1 * s1)61 void JPAKE_STEP1_init(JPAKE_STEP1 *s1)
62 {
63 JPAKE_STEP_PART_init(&s1->p1);
64 JPAKE_STEP_PART_init(&s1->p2);
65 }
66
JPAKE_STEP1_release(JPAKE_STEP1 * s1)67 void JPAKE_STEP1_release(JPAKE_STEP1 *s1)
68 {
69 JPAKE_STEP_PART_release(&s1->p2);
70 JPAKE_STEP_PART_release(&s1->p1);
71 }
72
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)73 static 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
JPAKE_CTX_release(JPAKE_CTX * ctx)94 static 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
JPAKE_CTX_new(const char * name,const char * peer_name,const BIGNUM * p,const BIGNUM * g,const BIGNUM * q,const BIGNUM * secret)114 JPAKE_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
JPAKE_CTX_free(JPAKE_CTX * ctx)127 void JPAKE_CTX_free(JPAKE_CTX *ctx)
128 {
129 JPAKE_CTX_release(ctx);
130 OPENSSL_free(ctx);
131 }
132
hashlength(SHA_CTX * sha,size_t l)133 static 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
hashstring(SHA_CTX * sha,const char * string)143 static 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
hashbn(SHA_CTX * sha,const BIGNUM * bn)151 static 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) */
zkp_hash(BIGNUM * h,const BIGNUM * zkpg,const JPAKE_STEP_PART * p,const char * proof_name)165 static 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 */
generate_zkp(JPAKE_STEP_PART * p,const BIGNUM * x,const BIGNUM * zkpg,JPAKE_CTX * ctx)189 static 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
verify_zkp(const JPAKE_STEP_PART * p,const BIGNUM * zkpg,JPAKE_CTX * ctx)217 static 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
244 end:
245 /* cleanup */
246 BN_free(t3);
247 BN_free(t2);
248 BN_free(t1);
249 BN_free(h);
250
251 return ret;
252 }
253
generate_step_part(JPAKE_STEP_PART * p,const BIGNUM * x,const BIGNUM * g,JPAKE_CTX * ctx)254 static 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). */
genrand(JPAKE_CTX * ctx)262 static 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
JPAKE_STEP1_generate(JPAKE_STEP1 * send,JPAKE_CTX * ctx)283 int 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 */
is_legal(const BIGNUM * gx,const JPAKE_CTX * ctx)293 static 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
JPAKE_STEP1_process(JPAKE_CTX * ctx,const JPAKE_STEP1 * received)309 int 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
JPAKE_STEP2_generate(JPAKE_STEP2 * send,JPAKE_CTX * ctx)348 int 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 */
compute_key(JPAKE_CTX * ctx,const BIGNUM * gx)384 static 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
JPAKE_STEP2_process(JPAKE_CTX * ctx,const JPAKE_STEP2 * received)417 int 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
quickhashbn(unsigned char * md,const BIGNUM * bn)447 static 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
JPAKE_STEP3A_init(JPAKE_STEP3A * s3a)456 void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a)
457 {
458 }
459
JPAKE_STEP3A_generate(JPAKE_STEP3A * send,JPAKE_CTX * ctx)460 int 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
JPAKE_STEP3A_process(JPAKE_CTX * ctx,const JPAKE_STEP3A * received)468 int 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
JPAKE_STEP3A_release(JPAKE_STEP3A * s3a)482 void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a)
483 {
484 }
485
JPAKE_STEP3B_init(JPAKE_STEP3B * s3b)486 void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b)
487 {
488 }
489
JPAKE_STEP3B_generate(JPAKE_STEP3B * send,JPAKE_CTX * ctx)490 int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx)
491 {
492 quickhashbn(send->hk, ctx->key);
493
494 return 1;
495 }
496
JPAKE_STEP3B_process(JPAKE_CTX * ctx,const JPAKE_STEP3B * received)497 int 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
JPAKE_STEP3B_release(JPAKE_STEP3B * s3b)509 void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b)
510 {
511 }
512
JPAKE_get_shared_key(JPAKE_CTX * ctx)513 const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx)
514 {
515 return ctx->key;
516 }
517