8 #define GET_32BIT(cp) \
9 (((unsigned long)(unsigned char)(cp)[0] << 24) | \
10 ((unsigned long)(unsigned char)(cp)[1] << 16) | \
11 ((unsigned long)(unsigned char)(cp)[2] << 8) | \
12 ((unsigned long)(unsigned char)(cp)[3]))
14 #define PUT_32BIT(cp, value) { \
15 (cp)[0] = (unsigned char)((value) >> 24); \
16 (cp)[1] = (unsigned char)((value) >> 16); \
17 (cp)[2] = (unsigned char)((value) >> 8); \
18 (cp)[3] = (unsigned char)(value); }
20 static void sha_mpint(SHA_State
* s
, Bignum b
)
23 unsigned char lenbuf
[4];
25 len
= (bignum_bitcount(b
) + 8) / 8;
26 PUT_32BIT(lenbuf
, len
);
27 SHA_Bytes(s
, lenbuf
, 4);
29 lenbuf
[0] = bignum_byte(b
, len
);
30 SHA_Bytes(s
, lenbuf
, 1);
32 memset(lenbuf
, 0, sizeof(lenbuf
));
35 static void sha512_mpint(SHA512_State
* s
, Bignum b
)
38 unsigned char lenbuf
[4];
40 len
= (bignum_bitcount(b
) + 8) / 8;
41 PUT_32BIT(lenbuf
, len
);
42 SHA512_Bytes(s
, lenbuf
, 4);
44 lenbuf
[0] = bignum_byte(b
, len
);
45 SHA512_Bytes(s
, lenbuf
, 1);
47 memset(lenbuf
, 0, sizeof(lenbuf
));
50 static void getstring(char **data
, int *datalen
, char **p
, int *length
)
55 *length
= GET_32BIT(*data
);
58 if (*datalen
< *length
)
64 static Bignum
getmp(char **data
, int *datalen
)
70 getstring(data
, datalen
, &p
, &length
);
74 return NULL
; /* negative mp */
75 b
= bignum_from_bytes(p
, length
);
79 static Bignum
get160(char **data
, int *datalen
)
83 b
= bignum_from_bytes(*data
, 20);
90 static void *dss_newkey(char *data
, int len
)
96 dss
= smalloc(sizeof(struct dss_key
));
99 getstring(&data
, &len
, &p
, &slen
);
105 for (i
= 0; i
< len
; i
++)
106 printf(" %02x", (unsigned char) (data
[i
]));
111 if (!p
|| memcmp(p
, "ssh-dss", 7)) {
115 dss
->p
= getmp(&data
, &len
);
116 dss
->q
= getmp(&data
, &len
);
117 dss
->g
= getmp(&data
, &len
);
118 dss
->y
= getmp(&data
, &len
);
123 static void dss_freekey(void *key
)
125 struct dss_key
*dss
= (struct dss_key
*) key
;
133 static char *dss_fmtkey(void *key
)
135 struct dss_key
*dss
= (struct dss_key
*) key
;
137 int len
, i
, pos
, nibbles
;
138 static const char hex
[] = "0123456789abcdef";
141 len
= 8 + 4 + 1; /* 4 x "0x", punctuation, \0 */
142 len
+= 4 * (bignum_bitcount(dss
->p
) + 15) / 16;
143 len
+= 4 * (bignum_bitcount(dss
->q
) + 15) / 16;
144 len
+= 4 * (bignum_bitcount(dss
->g
) + 15) / 16;
145 len
+= 4 * (bignum_bitcount(dss
->y
) + 15) / 16;
151 pos
+= sprintf(p
+ pos
, "0x");
152 nibbles
= (3 + bignum_bitcount(dss
->p
)) / 4;
155 for (i
= nibbles
; i
--;)
157 hex
[(bignum_byte(dss
->p
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
158 pos
+= sprintf(p
+ pos
, ",0x");
159 nibbles
= (3 + bignum_bitcount(dss
->q
)) / 4;
162 for (i
= nibbles
; i
--;)
164 hex
[(bignum_byte(dss
->q
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
165 pos
+= sprintf(p
+ pos
, ",0x");
166 nibbles
= (3 + bignum_bitcount(dss
->g
)) / 4;
169 for (i
= nibbles
; i
--;)
171 hex
[(bignum_byte(dss
->g
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
172 pos
+= sprintf(p
+ pos
, ",0x");
173 nibbles
= (3 + bignum_bitcount(dss
->y
)) / 4;
176 for (i
= nibbles
; i
--;)
178 hex
[(bignum_byte(dss
->y
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
183 static char *dss_fingerprint(void *key
)
185 struct dss_key
*dss
= (struct dss_key
*) key
;
186 struct MD5Context md5c
;
187 unsigned char digest
[16], lenbuf
[4];
188 char buffer
[16 * 3 + 40];
193 MD5Update(&md5c
, "\0\0\0\7ssh-dss", 11);
195 #define ADD_BIGNUM(bignum) \
196 numlen = (bignum_bitcount(bignum)+8)/8; \
197 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
198 for (i = numlen; i-- ;) { \
199 unsigned char c = bignum_byte(bignum, i); \
200 MD5Update(&md5c, &c, 1); \
208 MD5Final(digest
, &md5c
);
210 sprintf(buffer
, "ssh-dss %d ", bignum_bitcount(dss
->p
));
211 for (i
= 0; i
< 16; i
++)
212 sprintf(buffer
+ strlen(buffer
), "%s%02x", i ?
":" : "",
214 ret
= smalloc(strlen(buffer
) + 1);
220 static int dss_verifysig(void *key
, char *sig
, int siglen
,
221 char *data
, int datalen
)
223 struct dss_key
*dss
= (struct dss_key
*) key
;
227 Bignum r
, s
, w
, gu1p
, yu2p
, gu1yu2p
, u1
, u2
, sha
, v
;
237 for (i
= 0; i
< siglen
; i
++)
238 printf(" %02x", (unsigned char) (sig
[i
]));
243 * Commercial SSH (2.0.13) and OpenSSH disagree over the format
244 * of a DSA signature. OpenSSH is in line with the IETF drafts:
245 * it uses a string "ssh-dss", followed by a 40-byte string
246 * containing two 160-bit integers end-to-end. Commercial SSH
247 * can't be bothered with the header bit, and considers a DSA
248 * signature blob to be _just_ the 40-byte string containing
249 * the two 160-bit integers. We tell them apart by measuring
250 * the length: length 40 means the commercial-SSH bug, anything
251 * else is assumed to be IETF-compliant.
253 if (siglen
!= 40) { /* bug not present; read admin fields */
254 getstring(&sig
, &siglen
, &p
, &slen
);
255 if (!p
|| slen
!= 7 || memcmp(p
, "ssh-dss", 7)) {
258 sig
+= 4, siglen
-= 4; /* skip yet another length field */
260 r
= get160(&sig
, &siglen
);
261 s
= get160(&sig
, &siglen
);
266 * Step 1. w <- s^-1 mod q.
268 w
= modinv(s
, dss
->q
);
271 * Step 2. u1 <- SHA(message) * w mod q.
273 SHA_Simple(data
, datalen
, hash
);
276 sha
= get160(&p
, &slen
);
277 u1
= modmul(sha
, w
, dss
->q
);
280 * Step 3. u2 <- r * w mod q.
282 u2
= modmul(r
, w
, dss
->q
);
285 * Step 4. v <- (g^u1 * y^u2 mod p) mod q.
287 gu1p
= modpow(dss
->g
, u1
, dss
->p
);
288 yu2p
= modpow(dss
->y
, u2
, dss
->p
);
289 gu1yu2p
= modmul(gu1p
, yu2p
, dss
->p
);
290 v
= modmul(gu1yu2p
, One
, dss
->q
);
293 * Step 5. v should now be equal to r.
296 ret
= !bignum_cmp(v
, r
);
310 static unsigned char *dss_public_blob(void *key
, int *len
)
312 struct dss_key
*dss
= (struct dss_key
*) key
;
313 int plen
, qlen
, glen
, ylen
, bloblen
;
315 unsigned char *blob
, *p
;
317 plen
= (bignum_bitcount(dss
->p
) + 8) / 8;
318 qlen
= (bignum_bitcount(dss
->q
) + 8) / 8;
319 glen
= (bignum_bitcount(dss
->g
) + 8) / 8;
320 ylen
= (bignum_bitcount(dss
->y
) + 8) / 8;
323 * string "ssh-dss", mpint p, mpint q, mpint g, mpint y. Total
324 * 27 + sum of lengths. (five length fields, 20+7=27).
326 bloblen
= 27 + plen
+ qlen
+ glen
+ ylen
;
327 blob
= smalloc(bloblen
);
331 memcpy(p
, "ssh-dss", 7);
336 *p
++ = bignum_byte(dss
->p
, i
);
340 *p
++ = bignum_byte(dss
->q
, i
);
344 *p
++ = bignum_byte(dss
->g
, i
);
348 *p
++ = bignum_byte(dss
->y
, i
);
349 assert(p
== blob
+ bloblen
);
354 static unsigned char *dss_private_blob(void *key
, int *len
)
356 struct dss_key
*dss
= (struct dss_key
*) key
;
359 unsigned char *blob
, *p
;
361 unsigned char digest
[20];
363 xlen
= (bignum_bitcount(dss
->x
) + 8) / 8;
366 * mpint x, string[20] the SHA of p||q||g. Total 28 + xlen.
367 * (two length fields and twenty bytes, 20+8=28).
370 blob
= smalloc(bloblen
);
375 *p
++ = bignum_byte(dss
->x
, i
);
378 sha_mpint(&s
, dss
->p
);
379 sha_mpint(&s
, dss
->q
);
380 sha_mpint(&s
, dss
->g
);
381 SHA_Final(&s
, digest
);
383 for (i
= 0; i
< 20; i
++)
385 assert(p
== blob
+ bloblen
);
390 static void *dss_createkey(unsigned char *pub_blob
, int pub_len
,
391 unsigned char *priv_blob
, int priv_len
)
394 char *pb
= (char *) priv_blob
;
398 unsigned char digest
[20];
401 dss
= dss_newkey((char *) pub_blob
, pub_len
);
402 dss
->x
= getmp(&pb
, &priv_len
);
403 getstring(&pb
, &priv_len
, &hash
, &hashlen
);
406 * Verify details of the key. First check that the hash is
407 * indeed a hash of p||q||g.
414 sha_mpint(&s
, dss
->p
);
415 sha_mpint(&s
, dss
->q
);
416 sha_mpint(&s
, dss
->g
);
417 SHA_Final(&s
, digest
);
418 if (0 != memcmp(hash
, digest
, 20)) {
424 * Now ensure g^x mod p really is y.
426 ytest
= modpow(dss
->g
, dss
->x
, dss
->p
);
427 if (0 != bignum_cmp(ytest
, dss
->y
)) {
436 static void *dss_openssh_createkey(unsigned char **blob
, int *len
)
438 char **b
= (char **) blob
;
441 dss
= smalloc(sizeof(struct dss_key
));
445 dss
->p
= getmp(b
, len
);
446 dss
->q
= getmp(b
, len
);
447 dss
->g
= getmp(b
, len
);
448 dss
->y
= getmp(b
, len
);
449 dss
->x
= getmp(b
, len
);
451 if (!dss
->p
|| !dss
->q
|| !dss
->g
|| !dss
->y
|| !dss
->x
) {
464 static int dss_openssh_fmtkey(void *key
, unsigned char *blob
, int len
)
466 struct dss_key
*dss
= (struct dss_key
*) key
;
470 ssh2_bignum_length(dss
->p
) +
471 ssh2_bignum_length(dss
->q
) +
472 ssh2_bignum_length(dss
->g
) +
473 ssh2_bignum_length(dss
->y
) +
474 ssh2_bignum_length(dss
->x
);
481 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
482 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
492 unsigned char *dss_sign(void *key
, char *data
, int datalen
, int *siglen
)
495 * The basic DSS signing algorithm is:
497 * - invent a random k between 1 and q-1 (exclusive).
498 * - Compute r = (g^k mod p) mod q.
499 * - Compute s = k^-1 * (hash + x*r) mod q.
501 * This has the dangerous properties that:
503 * - if an attacker in possession of the public key _and_ the
504 * signature (for example, the host you just authenticated
505 * to) can guess your k, he can reverse the computation of s
506 * and work out x = r^-1 * (s*k - hash) mod q. That is, he
507 * can deduce the private half of your key, and masquerade
508 * as you for as long as the key is still valid.
510 * - since r is a function purely of k and the public key, if
511 * the attacker only has a _range of possibilities_ for k
512 * it's easy for him to work through them all and check each
513 * one against r; he'll never be unsure of whether he's got
516 * - if you ever sign two different hashes with the same k, it
517 * will be immediately obvious because the two signatures
518 * will have the same r, and moreover an attacker in
519 * possession of both signatures (and the public key of
520 * course) can compute k = (hash1-hash2) * (s1-s2)^-1 mod q,
521 * and from there deduce x as before.
523 * - the Bleichenbacher attack on DSA makes use of methods of
524 * generating k which are significantly non-uniformly
525 * distributed; in particular, generating a 160-bit random
526 * number and reducing it mod q is right out.
528 * For this reason we must be pretty careful about how we
529 * generate our k. Since this code runs on Windows, with no
530 * particularly good system entropy sources, we can't trust our
531 * RNG itself to produce properly unpredictable data. Hence, we
532 * use a totally different scheme instead.
534 * What we do is to take a SHA-512 (_big_) hash of the private
535 * key x, and then feed this into another SHA-512 hash that
536 * also includes the message hash being signed. That is:
538 * proto_k = SHA512 ( SHA512(x) || SHA160(message) )
540 * This number is 512 bits long, so reducing it mod q won't be
541 * noticeably non-uniform. So
545 * This has the interesting property that it's _deterministic_:
546 * signing the same hash twice with the same key yields the
549 * Despite this determinism, it's still not predictable to an
550 * attacker, because in order to repeat the SHA-512
551 * construction that created it, the attacker would have to
552 * know the private key value x - and by assumption he doesn't,
553 * because if he knew that he wouldn't be attacking k!
555 * (This trick doesn't, _per se_, protect against reuse of k.
556 * Reuse of k is left to chance; all it does is prevent
557 * _excessively high_ chances of reuse of k due to entropy
560 * Thanks to Colin Plumb for the general idea of using x to
561 * ensure k is hard to guess, and to the Cambridge University
562 * Computer Security Group for helping to argue out all the
565 struct dss_key
*dss
= (struct dss_key
*) key
;
567 unsigned char digest
[20], digest512
[64];
568 Bignum proto_k
, k
, gkp
, hash
, kinv
, hxr
, r
, s
;
569 unsigned char *bytes
;
572 SHA_Simple(data
, datalen
, digest
);
575 * Hash some identifying text plus x.
578 SHA512_Bytes(&ss
, "DSA deterministic k generator", 30);
579 sha512_mpint(&ss
, dss
->x
);
580 SHA512_Final(&ss
, digest512
);
583 * Now hash that digest plus the message hash.
586 SHA512_Bytes(&ss
, digest512
, sizeof(digest512
));
587 SHA512_Bytes(&ss
, digest
, sizeof(digest
));
588 SHA512_Final(&ss
, digest512
);
590 memset(&ss
, 0, sizeof(ss
));
593 * Now convert the result into a bignum, and reduce it mod q.
595 proto_k
= bignum_from_bytes(digest512
, 64);
596 k
= bigmod(proto_k
, dss
->q
);
599 memset(digest512
, 0, sizeof(digest512
));
602 * Now we have k, so just go ahead and compute the signature.
604 gkp
= modpow(dss
->g
, k
, dss
->p
); /* g^k mod p */
605 r
= bigmod(gkp
, dss
->q
); /* r = (g^k mod p) mod q */
608 hash
= bignum_from_bytes(digest
, 20);
609 kinv
= modinv(k
, dss
->q
); /* k^-1 mod q */
610 hxr
= bigmuladd(dss
->x
, r
, hash
); /* hash + x*r */
611 s
= modmul(kinv
, hxr
, dss
->q
); /* s = k^-1 * (hash + x*r) mod q */
620 * string two 20-byte numbers r and s, end to end
622 * i.e. 4+7 + 4+40 bytes.
624 nbytes
= 4 + 7 + 4 + 40;
625 bytes
= smalloc(nbytes
);
627 memcpy(bytes
+ 4, "ssh-dss", 7);
628 PUT_32BIT(bytes
+ 4 + 7, 40);
629 for (i
= 0; i
< 20; i
++) {
630 bytes
[4 + 7 + 4 + i
] = bignum_byte(r
, 19 - i
);
631 bytes
[4 + 7 + 4 + 20 + i
] = bignum_byte(s
, 19 - i
);
640 const struct ssh_signkey ssh_dss
= {
647 dss_openssh_createkey
,