8 static void sha_mpint(SHA_State * s, Bignum b)
10 unsigned char lenbuf[4];
12 len = (bignum_bitcount(b) + 8) / 8;
13 PUT_32BIT(lenbuf, len);
14 SHA_Bytes(s, lenbuf, 4);
16 lenbuf[0] = bignum_byte(b, len);
17 SHA_Bytes(s, lenbuf, 1);
19 memset(lenbuf, 0, sizeof(lenbuf));
22 static void sha512_mpint(SHA512_State * s, Bignum b)
24 unsigned char lenbuf[4];
26 len = (bignum_bitcount(b) + 8) / 8;
27 PUT_32BIT(lenbuf, len);
28 SHA512_Bytes(s, lenbuf, 4);
30 lenbuf[0] = bignum_byte(b, len);
31 SHA512_Bytes(s, lenbuf, 1);
33 memset(lenbuf, 0, sizeof(lenbuf));
36 static void getstring(char **data, int *datalen, char **p, int *length)
41 *length = GET_32BIT(*data);
44 if (*datalen < *length)
50 static Bignum getmp(char **data, int *datalen)
56 getstring(data, datalen, &p, &length);
60 return NULL; /* negative mp */
61 b = bignum_from_bytes((unsigned char *)p, length);
65 static Bignum get160(char **data, int *datalen)
69 b = bignum_from_bytes((unsigned char *)*data, 20);
76 static void *dss_newkey(char *data, int len)
82 dss = snew(struct dss_key);
85 getstring(&data, &len, &p, &slen);
91 for (i = 0; i < len; i++)
92 printf(" %02x", (unsigned char) (data[i]));
97 if (!p || memcmp(p, "ssh-dss", 7)) {
101 dss->p = getmp(&data, &len);
102 dss->q = getmp(&data, &len);
103 dss->g = getmp(&data, &len);
104 dss->y = getmp(&data, &len);
109 static void dss_freekey(void *key)
111 struct dss_key *dss = (struct dss_key *) key;
119 static char *dss_fmtkey(void *key)
121 struct dss_key *dss = (struct dss_key *) key;
123 int len, i, pos, nibbles;
124 static const char hex[] = "0123456789abcdef";
127 len = 8 + 4 + 1; /* 4 x "0x", punctuation, \0 */
128 len += 4 * (bignum_bitcount(dss->p) + 15) / 16;
129 len += 4 * (bignum_bitcount(dss->q) + 15) / 16;
130 len += 4 * (bignum_bitcount(dss->g) + 15) / 16;
131 len += 4 * (bignum_bitcount(dss->y) + 15) / 16;
132 p = snewn(len, char);
137 pos += sprintf(p + pos, "0x");
138 nibbles = (3 + bignum_bitcount(dss->p)) / 4;
141 for (i = nibbles; i--;)
143 hex[(bignum_byte(dss->p, i / 2) >> (4 * (i % 2))) & 0xF];
144 pos += sprintf(p + pos, ",0x");
145 nibbles = (3 + bignum_bitcount(dss->q)) / 4;
148 for (i = nibbles; i--;)
150 hex[(bignum_byte(dss->q, i / 2) >> (4 * (i % 2))) & 0xF];
151 pos += sprintf(p + pos, ",0x");
152 nibbles = (3 + bignum_bitcount(dss->g)) / 4;
155 for (i = nibbles; i--;)
157 hex[(bignum_byte(dss->g, i / 2) >> (4 * (i % 2))) & 0xF];
158 pos += sprintf(p + pos, ",0x");
159 nibbles = (3 + bignum_bitcount(dss->y)) / 4;
162 for (i = nibbles; i--;)
164 hex[(bignum_byte(dss->y, i / 2) >> (4 * (i % 2))) & 0xF];
169 static char *dss_fingerprint(void *key)
171 struct dss_key *dss = (struct dss_key *) key;
172 struct MD5Context md5c;
173 unsigned char digest[16], lenbuf[4];
174 char buffer[16 * 3 + 40];
179 MD5Update(&md5c, (unsigned char *)"\0\0\0\7ssh-dss", 11);
181 #define ADD_BIGNUM(bignum) \
182 numlen = (bignum_bitcount(bignum)+8)/8; \
183 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
184 for (i = numlen; i-- ;) { \
185 unsigned char c = bignum_byte(bignum, i); \
186 MD5Update(&md5c, &c, 1); \
194 MD5Final(digest, &md5c);
196 sprintf(buffer, "ssh-dss %d ", bignum_bitcount(dss->p));
197 for (i = 0; i < 16; i++)
198 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
200 ret = snewn(strlen(buffer) + 1, char);
206 static int dss_verifysig(void *key, char *sig, int siglen,
207 char *data, int datalen)
209 struct dss_key *dss = (struct dss_key *) key;
213 Bignum r, s, w, gu1p, yu2p, gu1yu2p, u1, u2, sha, v;
223 for (i = 0; i < siglen; i++)
224 printf(" %02x", (unsigned char) (sig[i]));
229 * Commercial SSH (2.0.13) and OpenSSH disagree over the format
230 * of a DSA signature. OpenSSH is in line with the IETF drafts:
231 * it uses a string "ssh-dss", followed by a 40-byte string
232 * containing two 160-bit integers end-to-end. Commercial SSH
233 * can't be bothered with the header bit, and considers a DSA
234 * signature blob to be _just_ the 40-byte string containing
235 * the two 160-bit integers. We tell them apart by measuring
236 * the length: length 40 means the commercial-SSH bug, anything
237 * else is assumed to be IETF-compliant.
239 if (siglen != 40) { /* bug not present; read admin fields */
240 getstring(&sig, &siglen, &p, &slen);
241 if (!p || slen != 7 || memcmp(p, "ssh-dss", 7)) {
244 sig += 4, siglen -= 4; /* skip yet another length field */
246 r = get160(&sig, &siglen);
247 s = get160(&sig, &siglen);
252 * Step 1. w <- s^-1 mod q.
254 w = modinv(s, dss->q);
257 * Step 2. u1 <- SHA(message) * w mod q.
259 SHA_Simple(data, datalen, (unsigned char *)hash);
262 sha = get160(&p, &slen);
263 u1 = modmul(sha, w, dss->q);
266 * Step 3. u2 <- r * w mod q.
268 u2 = modmul(r, w, dss->q);
271 * Step 4. v <- (g^u1 * y^u2 mod p) mod q.
273 gu1p = modpow(dss->g, u1, dss->p);
274 yu2p = modpow(dss->y, u2, dss->p);
275 gu1yu2p = modmul(gu1p, yu2p, dss->p);
276 v = modmul(gu1yu2p, One, dss->q);
279 * Step 5. v should now be equal to r.
282 ret = !bignum_cmp(v, r);
296 static unsigned char *dss_public_blob(void *key, int *len)
298 struct dss_key *dss = (struct dss_key *) key;
299 int plen, qlen, glen, ylen, bloblen;
301 unsigned char *blob, *p;
303 plen = (bignum_bitcount(dss->p) + 8) / 8;
304 qlen = (bignum_bitcount(dss->q) + 8) / 8;
305 glen = (bignum_bitcount(dss->g) + 8) / 8;
306 ylen = (bignum_bitcount(dss->y) + 8) / 8;
309 * string "ssh-dss", mpint p, mpint q, mpint g, mpint y. Total
310 * 27 + sum of lengths. (five length fields, 20+7=27).
312 bloblen = 27 + plen + qlen + glen + ylen;
313 blob = snewn(bloblen, unsigned char);
317 memcpy(p, "ssh-dss", 7);
322 *p++ = bignum_byte(dss->p, i);
326 *p++ = bignum_byte(dss->q, i);
330 *p++ = bignum_byte(dss->g, i);
334 *p++ = bignum_byte(dss->y, i);
335 assert(p == blob + bloblen);
340 static unsigned char *dss_private_blob(void *key, int *len)
342 struct dss_key *dss = (struct dss_key *) key;
345 unsigned char *blob, *p;
347 xlen = (bignum_bitcount(dss->x) + 8) / 8;
350 * mpint x, string[20] the SHA of p||q||g. Total 4 + xlen.
353 blob = snewn(bloblen, unsigned char);
358 *p++ = bignum_byte(dss->x, i);
359 assert(p == blob + bloblen);
364 static void *dss_createkey(unsigned char *pub_blob, int pub_len,
365 unsigned char *priv_blob, int priv_len)
368 char *pb = (char *) priv_blob;
372 unsigned char digest[20];
375 dss = dss_newkey((char *) pub_blob, pub_len);
376 dss->x = getmp(&pb, &priv_len);
379 * Check the obsolete hash in the old DSS key format.
382 getstring(&pb, &priv_len, &hash, &hashlen);
385 sha_mpint(&s, dss->p);
386 sha_mpint(&s, dss->q);
387 sha_mpint(&s, dss->g);
388 SHA_Final(&s, digest);
389 if (0 != memcmp(hash, digest, 20)) {
396 * Now ensure g^x mod p really is y.
398 ytest = modpow(dss->g, dss->x, dss->p);
399 if (0 != bignum_cmp(ytest, dss->y)) {
408 static void *dss_openssh_createkey(unsigned char **blob, int *len)
410 char **b = (char **) blob;
413 dss = snew(struct dss_key);
417 dss->p = getmp(b, len);
418 dss->q = getmp(b, len);
419 dss->g = getmp(b, len);
420 dss->y = getmp(b, len);
421 dss->x = getmp(b, len);
423 if (!dss->p || !dss->q || !dss->g || !dss->y || !dss->x) {
436 static int dss_openssh_fmtkey(void *key, unsigned char *blob, int len)
438 struct dss_key *dss = (struct dss_key *) key;
442 ssh2_bignum_length(dss->p) +
443 ssh2_bignum_length(dss->q) +
444 ssh2_bignum_length(dss->g) +
445 ssh2_bignum_length(dss->y) +
446 ssh2_bignum_length(dss->x);
453 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
454 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
464 static int dss_pubkey_bits(void *blob, int len)
469 dss = dss_newkey((char *) blob, len);
470 ret = bignum_bitcount(dss->p);
476 static unsigned char *dss_sign(void *key, char *data, int datalen, int *siglen)
479 * The basic DSS signing algorithm is:
481 * - invent a random k between 1 and q-1 (exclusive).
482 * - Compute r = (g^k mod p) mod q.
483 * - Compute s = k^-1 * (hash + x*r) mod q.
485 * This has the dangerous properties that:
487 * - if an attacker in possession of the public key _and_ the
488 * signature (for example, the host you just authenticated
489 * to) can guess your k, he can reverse the computation of s
490 * and work out x = r^-1 * (s*k - hash) mod q. That is, he
491 * can deduce the private half of your key, and masquerade
492 * as you for as long as the key is still valid.
494 * - since r is a function purely of k and the public key, if
495 * the attacker only has a _range of possibilities_ for k
496 * it's easy for him to work through them all and check each
497 * one against r; he'll never be unsure of whether he's got
500 * - if you ever sign two different hashes with the same k, it
501 * will be immediately obvious because the two signatures
502 * will have the same r, and moreover an attacker in
503 * possession of both signatures (and the public key of
504 * course) can compute k = (hash1-hash2) * (s1-s2)^-1 mod q,
505 * and from there deduce x as before.
507 * - the Bleichenbacher attack on DSA makes use of methods of
508 * generating k which are significantly non-uniformly
509 * distributed; in particular, generating a 160-bit random
510 * number and reducing it mod q is right out.
512 * For this reason we must be pretty careful about how we
513 * generate our k. Since this code runs on Windows, with no
514 * particularly good system entropy sources, we can't trust our
515 * RNG itself to produce properly unpredictable data. Hence, we
516 * use a totally different scheme instead.
518 * What we do is to take a SHA-512 (_big_) hash of the private
519 * key x, and then feed this into another SHA-512 hash that
520 * also includes the message hash being signed. That is:
522 * proto_k = SHA512 ( SHA512(x) || SHA160(message) )
524 * This number is 512 bits long, so reducing it mod q won't be
525 * noticeably non-uniform. So
529 * This has the interesting property that it's _deterministic_:
530 * signing the same hash twice with the same key yields the
533 * Despite this determinism, it's still not predictable to an
534 * attacker, because in order to repeat the SHA-512
535 * construction that created it, the attacker would have to
536 * know the private key value x - and by assumption he doesn't,
537 * because if he knew that he wouldn't be attacking k!
539 * (This trick doesn't, _per se_, protect against reuse of k.
540 * Reuse of k is left to chance; all it does is prevent
541 * _excessively high_ chances of reuse of k due to entropy
544 * Thanks to Colin Plumb for the general idea of using x to
545 * ensure k is hard to guess, and to the Cambridge University
546 * Computer Security Group for helping to argue out all the
549 struct dss_key *dss = (struct dss_key *) key;
551 unsigned char digest[20], digest512[64];
552 Bignum proto_k, k, gkp, hash, kinv, hxr, r, s;
553 unsigned char *bytes;
556 SHA_Simple(data, datalen, digest);
559 * Hash some identifying text plus x.
562 SHA512_Bytes(&ss, "DSA deterministic k generator", 30);
563 sha512_mpint(&ss, dss->x);
564 SHA512_Final(&ss, digest512);
567 * Now hash that digest plus the message hash.
570 SHA512_Bytes(&ss, digest512, sizeof(digest512));
571 SHA512_Bytes(&ss, digest, sizeof(digest));
572 SHA512_Final(&ss, digest512);
574 memset(&ss, 0, sizeof(ss));
577 * Now convert the result into a bignum, and reduce it mod q.
579 proto_k = bignum_from_bytes(digest512, 64);
580 k = bigmod(proto_k, dss->q);
583 memset(digest512, 0, sizeof(digest512));
586 * Now we have k, so just go ahead and compute the signature.
588 gkp = modpow(dss->g, k, dss->p); /* g^k mod p */
589 r = bigmod(gkp, dss->q); /* r = (g^k mod p) mod q */
592 hash = bignum_from_bytes(digest, 20);
593 kinv = modinv(k, dss->q); /* k^-1 mod q */
594 hxr = bigmuladd(dss->x, r, hash); /* hash + x*r */
595 s = modmul(kinv, hxr, dss->q); /* s = k^-1 * (hash + x*r) mod q */
604 * string two 20-byte numbers r and s, end to end
606 * i.e. 4+7 + 4+40 bytes.
608 nbytes = 4 + 7 + 4 + 40;
609 bytes = snewn(nbytes, unsigned char);
611 memcpy(bytes + 4, "ssh-dss", 7);
612 PUT_32BIT(bytes + 4 + 7, 40);
613 for (i = 0; i < 20; i++) {
614 bytes[4 + 7 + 4 + i] = bignum_byte(r, 19 - i);
615 bytes[4 + 7 + 4 + 20 + i] = bignum_byte(s, 19 - i);
624 const struct ssh_signkey ssh_dss = {
631 dss_openssh_createkey,