2 * Digital Signature Standard implementation for PuTTY.
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12 static void sha_mpint(SHA_State * s, Bignum b)
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14 unsigned char lenbuf[4];
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16 len = (bignum_bitcount(b) + 8) / 8;
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17 PUT_32BIT(lenbuf, len);
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18 SHA_Bytes(s, lenbuf, 4);
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20 lenbuf[0] = bignum_byte(b, len);
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21 SHA_Bytes(s, lenbuf, 1);
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23 smemclr(lenbuf, sizeof(lenbuf));
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26 static void sha512_mpint(SHA512_State * s, Bignum b)
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28 unsigned char lenbuf[4];
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30 len = (bignum_bitcount(b) + 8) / 8;
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31 PUT_32BIT(lenbuf, len);
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32 SHA512_Bytes(s, lenbuf, 4);
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34 lenbuf[0] = bignum_byte(b, len);
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35 SHA512_Bytes(s, lenbuf, 1);
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37 smemclr(lenbuf, sizeof(lenbuf));
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40 static void getstring(char **data, int *datalen, char **p, int *length)
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45 *length = toint(GET_32BIT(*data));
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50 if (*datalen < *length)
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54 *datalen -= *length;
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56 static Bignum getmp(char **data, int *datalen)
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62 getstring(data, datalen, &p, &length);
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66 return NULL; /* negative mp */
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67 b = bignum_from_bytes((unsigned char *)p, length);
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71 static Bignum get160(char **data, int *datalen)
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78 b = bignum_from_bytes((unsigned char *)*data, 20);
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85 static void dss_freekey(void *key); /* forward reference */
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87 static void *dss_newkey(char *data, int len)
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91 struct dss_key *dss;
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93 dss = snew(struct dss_key);
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94 getstring(&data, &len, &p, &slen);
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100 for (i = 0; i < len; i++)
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101 printf(" %02x", (unsigned char) (data[i]));
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106 if (!p || slen != 7 || memcmp(p, "ssh-dss", 7)) {
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110 dss->p = getmp(&data, &len);
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111 dss->q = getmp(&data, &len);
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112 dss->g = getmp(&data, &len);
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113 dss->y = getmp(&data, &len);
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116 if (!dss->p || !dss->q || !dss->g || !dss->y ||
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117 !bignum_cmp(dss->q, Zero) || !bignum_cmp(dss->p, Zero)) {
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126 static void dss_freekey(void *key)
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128 struct dss_key *dss = (struct dss_key *) key;
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142 static char *dss_fmtkey(void *key)
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144 struct dss_key *dss = (struct dss_key *) key;
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146 int len, i, pos, nibbles;
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147 static const char hex[] = "0123456789abcdef";
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150 len = 8 + 4 + 1; /* 4 x "0x", punctuation, \0 */
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151 len += 4 * (bignum_bitcount(dss->p) + 15) / 16;
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152 len += 4 * (bignum_bitcount(dss->q) + 15) / 16;
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153 len += 4 * (bignum_bitcount(dss->g) + 15) / 16;
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154 len += 4 * (bignum_bitcount(dss->y) + 15) / 16;
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155 p = snewn(len, char);
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160 pos += sprintf(p + pos, "0x");
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161 nibbles = (3 + bignum_bitcount(dss->p)) / 4;
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164 for (i = nibbles; i--;)
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166 hex[(bignum_byte(dss->p, i / 2) >> (4 * (i % 2))) & 0xF];
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167 pos += sprintf(p + pos, ",0x");
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168 nibbles = (3 + bignum_bitcount(dss->q)) / 4;
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171 for (i = nibbles; i--;)
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173 hex[(bignum_byte(dss->q, i / 2) >> (4 * (i % 2))) & 0xF];
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174 pos += sprintf(p + pos, ",0x");
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175 nibbles = (3 + bignum_bitcount(dss->g)) / 4;
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178 for (i = nibbles; i--;)
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180 hex[(bignum_byte(dss->g, i / 2) >> (4 * (i % 2))) & 0xF];
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181 pos += sprintf(p + pos, ",0x");
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182 nibbles = (3 + bignum_bitcount(dss->y)) / 4;
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185 for (i = nibbles; i--;)
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187 hex[(bignum_byte(dss->y, i / 2) >> (4 * (i % 2))) & 0xF];
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192 static char *dss_fingerprint(void *key)
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194 struct dss_key *dss = (struct dss_key *) key;
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195 struct MD5Context md5c;
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196 unsigned char digest[16], lenbuf[4];
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197 char buffer[16 * 3 + 40];
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202 MD5Update(&md5c, (unsigned char *)"\0\0\0\7ssh-dss", 11);
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204 #define ADD_BIGNUM(bignum) \
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205 numlen = (bignum_bitcount(bignum)+8)/8; \
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206 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
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207 for (i = numlen; i-- ;) { \
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208 unsigned char c = bignum_byte(bignum, i); \
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209 MD5Update(&md5c, &c, 1); \
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211 ADD_BIGNUM(dss->p);
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212 ADD_BIGNUM(dss->q);
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213 ADD_BIGNUM(dss->g);
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214 ADD_BIGNUM(dss->y);
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217 MD5Final(digest, &md5c);
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219 sprintf(buffer, "ssh-dss %d ", bignum_bitcount(dss->p));
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220 for (i = 0; i < 16; i++)
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221 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
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223 ret = snewn(strlen(buffer) + 1, char);
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225 strcpy(ret, buffer);
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229 static int dss_verifysig(void *key, char *sig, int siglen,
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230 char *data, int datalen)
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232 struct dss_key *dss = (struct dss_key *) key;
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236 Bignum r, s, w, gu1p, yu2p, gu1yu2p, u1, u2, sha, v;
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246 for (i = 0; i < siglen; i++)
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247 printf(" %02x", (unsigned char) (sig[i]));
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252 * Commercial SSH (2.0.13) and OpenSSH disagree over the format
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253 * of a DSA signature. OpenSSH is in line with RFC 4253:
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254 * it uses a string "ssh-dss", followed by a 40-byte string
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255 * containing two 160-bit integers end-to-end. Commercial SSH
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256 * can't be bothered with the header bit, and considers a DSA
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257 * signature blob to be _just_ the 40-byte string containing
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258 * the two 160-bit integers. We tell them apart by measuring
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259 * the length: length 40 means the commercial-SSH bug, anything
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260 * else is assumed to be RFC-compliant.
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262 if (siglen != 40) { /* bug not present; read admin fields */
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263 getstring(&sig, &siglen, &p, &slen);
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264 if (!p || slen != 7 || memcmp(p, "ssh-dss", 7)) {
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267 sig += 4, siglen -= 4; /* skip yet another length field */
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269 r = get160(&sig, &siglen);
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270 s = get160(&sig, &siglen);
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279 if (!bignum_cmp(s, Zero)) {
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286 * Step 1. w <- s^-1 mod q.
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288 w = modinv(s, dss->q);
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296 * Step 2. u1 <- SHA(message) * w mod q.
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298 SHA_Simple(data, datalen, (unsigned char *)hash);
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301 sha = get160(&p, &slen);
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302 u1 = modmul(sha, w, dss->q);
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305 * Step 3. u2 <- r * w mod q.
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307 u2 = modmul(r, w, dss->q);
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310 * Step 4. v <- (g^u1 * y^u2 mod p) mod q.
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312 gu1p = modpow(dss->g, u1, dss->p);
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313 yu2p = modpow(dss->y, u2, dss->p);
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314 gu1yu2p = modmul(gu1p, yu2p, dss->p);
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315 v = modmul(gu1yu2p, One, dss->q);
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318 * Step 5. v should now be equal to r.
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321 ret = !bignum_cmp(v, r);
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337 static unsigned char *dss_public_blob(void *key, int *len)
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339 struct dss_key *dss = (struct dss_key *) key;
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340 int plen, qlen, glen, ylen, bloblen;
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342 unsigned char *blob, *p;
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344 plen = (bignum_bitcount(dss->p) + 8) / 8;
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345 qlen = (bignum_bitcount(dss->q) + 8) / 8;
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346 glen = (bignum_bitcount(dss->g) + 8) / 8;
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347 ylen = (bignum_bitcount(dss->y) + 8) / 8;
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350 * string "ssh-dss", mpint p, mpint q, mpint g, mpint y. Total
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351 * 27 + sum of lengths. (five length fields, 20+7=27).
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353 bloblen = 27 + plen + qlen + glen + ylen;
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354 blob = snewn(bloblen, unsigned char);
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358 memcpy(p, "ssh-dss", 7);
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360 PUT_32BIT(p, plen);
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362 for (i = plen; i--;)
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363 *p++ = bignum_byte(dss->p, i);
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364 PUT_32BIT(p, qlen);
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366 for (i = qlen; i--;)
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367 *p++ = bignum_byte(dss->q, i);
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368 PUT_32BIT(p, glen);
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370 for (i = glen; i--;)
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371 *p++ = bignum_byte(dss->g, i);
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372 PUT_32BIT(p, ylen);
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374 for (i = ylen; i--;)
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375 *p++ = bignum_byte(dss->y, i);
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376 assert(p == blob + bloblen);
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381 static unsigned char *dss_private_blob(void *key, int *len)
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383 struct dss_key *dss = (struct dss_key *) key;
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386 unsigned char *blob, *p;
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388 xlen = (bignum_bitcount(dss->x) + 8) / 8;
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391 * mpint x, string[20] the SHA of p||q||g. Total 4 + xlen.
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393 bloblen = 4 + xlen;
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394 blob = snewn(bloblen, unsigned char);
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396 PUT_32BIT(p, xlen);
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398 for (i = xlen; i--;)
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399 *p++ = bignum_byte(dss->x, i);
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400 assert(p == blob + bloblen);
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405 static void *dss_createkey(unsigned char *pub_blob, int pub_len,
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406 unsigned char *priv_blob, int priv_len)
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408 struct dss_key *dss;
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409 char *pb = (char *) priv_blob;
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413 unsigned char digest[20];
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416 dss = dss_newkey((char *) pub_blob, pub_len);
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419 dss->x = getmp(&pb, &priv_len);
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426 * Check the obsolete hash in the old DSS key format.
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429 getstring(&pb, &priv_len, &hash, &hashlen);
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430 if (hashlen == 20) {
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432 sha_mpint(&s, dss->p);
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433 sha_mpint(&s, dss->q);
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434 sha_mpint(&s, dss->g);
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435 SHA_Final(&s, digest);
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436 if (0 != memcmp(hash, digest, 20)) {
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443 * Now ensure g^x mod p really is y.
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445 ytest = modpow(dss->g, dss->x, dss->p);
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446 if (0 != bignum_cmp(ytest, dss->y)) {
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456 static void *dss_openssh_createkey(unsigned char **blob, int *len)
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458 char **b = (char **) blob;
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459 struct dss_key *dss;
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461 dss = snew(struct dss_key);
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463 dss->p = getmp(b, len);
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464 dss->q = getmp(b, len);
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465 dss->g = getmp(b, len);
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466 dss->y = getmp(b, len);
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467 dss->x = getmp(b, len);
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469 if (!dss->p || !dss->q || !dss->g || !dss->y || !dss->x ||
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470 !bignum_cmp(dss->q, Zero) || !bignum_cmp(dss->p, Zero)) {
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479 static int dss_openssh_fmtkey(void *key, unsigned char *blob, int len)
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481 struct dss_key *dss = (struct dss_key *) key;
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485 ssh2_bignum_length(dss->p) +
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486 ssh2_bignum_length(dss->q) +
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487 ssh2_bignum_length(dss->g) +
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488 ssh2_bignum_length(dss->y) +
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489 ssh2_bignum_length(dss->x);
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496 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
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497 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
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507 static int dss_pubkey_bits(void *blob, int len)
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509 struct dss_key *dss;
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512 dss = dss_newkey((char *) blob, len);
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515 ret = bignum_bitcount(dss->p);
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521 static unsigned char *dss_sign(void *key, char *data, int datalen, int *siglen)
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524 * The basic DSS signing algorithm is:
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526 * - invent a random k between 1 and q-1 (exclusive).
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527 * - Compute r = (g^k mod p) mod q.
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528 * - Compute s = k^-1 * (hash + x*r) mod q.
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530 * This has the dangerous properties that:
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532 * - if an attacker in possession of the public key _and_ the
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533 * signature (for example, the host you just authenticated
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534 * to) can guess your k, he can reverse the computation of s
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535 * and work out x = r^-1 * (s*k - hash) mod q. That is, he
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536 * can deduce the private half of your key, and masquerade
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537 * as you for as long as the key is still valid.
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539 * - since r is a function purely of k and the public key, if
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540 * the attacker only has a _range of possibilities_ for k
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541 * it's easy for him to work through them all and check each
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542 * one against r; he'll never be unsure of whether he's got
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545 * - if you ever sign two different hashes with the same k, it
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546 * will be immediately obvious because the two signatures
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547 * will have the same r, and moreover an attacker in
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548 * possession of both signatures (and the public key of
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549 * course) can compute k = (hash1-hash2) * (s1-s2)^-1 mod q,
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550 * and from there deduce x as before.
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552 * - the Bleichenbacher attack on DSA makes use of methods of
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553 * generating k which are significantly non-uniformly
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554 * distributed; in particular, generating a 160-bit random
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555 * number and reducing it mod q is right out.
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557 * For this reason we must be pretty careful about how we
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558 * generate our k. Since this code runs on Windows, with no
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559 * particularly good system entropy sources, we can't trust our
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560 * RNG itself to produce properly unpredictable data. Hence, we
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561 * use a totally different scheme instead.
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563 * What we do is to take a SHA-512 (_big_) hash of the private
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564 * key x, and then feed this into another SHA-512 hash that
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565 * also includes the message hash being signed. That is:
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567 * proto_k = SHA512 ( SHA512(x) || SHA160(message) )
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569 * This number is 512 bits long, so reducing it mod q won't be
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570 * noticeably non-uniform. So
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572 * k = proto_k mod q
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574 * This has the interesting property that it's _deterministic_:
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575 * signing the same hash twice with the same key yields the
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578 * Despite this determinism, it's still not predictable to an
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579 * attacker, because in order to repeat the SHA-512
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580 * construction that created it, the attacker would have to
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581 * know the private key value x - and by assumption he doesn't,
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582 * because if he knew that he wouldn't be attacking k!
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584 * (This trick doesn't, _per se_, protect against reuse of k.
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585 * Reuse of k is left to chance; all it does is prevent
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586 * _excessively high_ chances of reuse of k due to entropy
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589 * Thanks to Colin Plumb for the general idea of using x to
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590 * ensure k is hard to guess, and to the Cambridge University
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591 * Computer Security Group for helping to argue out all the
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594 struct dss_key *dss = (struct dss_key *) key;
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596 unsigned char digest[20], digest512[64];
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597 Bignum proto_k, k, gkp, hash, kinv, hxr, r, s;
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598 unsigned char *bytes;
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601 SHA_Simple(data, datalen, digest);
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604 * Hash some identifying text plus x.
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607 SHA512_Bytes(&ss, "DSA deterministic k generator", 30);
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608 sha512_mpint(&ss, dss->x);
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609 SHA512_Final(&ss, digest512);
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612 * Now hash that digest plus the message hash.
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615 SHA512_Bytes(&ss, digest512, sizeof(digest512));
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616 SHA512_Bytes(&ss, digest, sizeof(digest));
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619 SHA512_State ss2 = ss; /* structure copy */
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620 SHA512_Final(&ss2, digest512);
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622 smemclr(&ss2, sizeof(ss2));
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625 * Now convert the result into a bignum, and reduce it mod q.
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627 proto_k = bignum_from_bytes(digest512, 64);
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628 k = bigmod(proto_k, dss->q);
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630 kinv = modinv(k, dss->q); /* k^-1 mod q */
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631 if (!kinv) { /* very unlikely */
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633 /* Perturb the hash to think of a different k. */
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634 SHA512_Bytes(&ss, "x", 1);
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635 /* Go round and try again. */
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642 smemclr(&ss, sizeof(ss));
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644 smemclr(digest512, sizeof(digest512));
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647 * Now we have k, so just go ahead and compute the signature.
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649 gkp = modpow(dss->g, k, dss->p); /* g^k mod p */
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650 r = bigmod(gkp, dss->q); /* r = (g^k mod p) mod q */
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653 hash = bignum_from_bytes(digest, 20);
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654 hxr = bigmuladd(dss->x, r, hash); /* hash + x*r */
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655 s = modmul(kinv, hxr, dss->q); /* s = k^-1 * (hash + x*r) mod q */
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662 * Signature blob is
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665 * string two 20-byte numbers r and s, end to end
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667 * i.e. 4+7 + 4+40 bytes.
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669 nbytes = 4 + 7 + 4 + 40;
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670 bytes = snewn(nbytes, unsigned char);
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671 PUT_32BIT(bytes, 7);
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672 memcpy(bytes + 4, "ssh-dss", 7);
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673 PUT_32BIT(bytes + 4 + 7, 40);
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674 for (i = 0; i < 20; i++) {
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675 bytes[4 + 7 + 4 + i] = bignum_byte(r, 19 - i);
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676 bytes[4 + 7 + 4 + 20 + i] = bignum_byte(s, 19 - i);
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685 const struct ssh_signkey ssh_dss = {
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692 dss_openssh_createkey,
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693 dss_openssh_fmtkey,
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