sshdss.c

/*
 * Digital Signature Standard implementation for PuTTY.
 */

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>

#include "ssh.h"
#include "misc.h"

static void sha_mpint(SHA_State *s, Bignum b)
{
  unsigned char lenbuf[4];
  int len;
  len = (bignum_bitcount(b) + 8) / 8;
  PUT_32BIT(lenbuf, len);
  SHA_Bytes(s, lenbuf, 4);
  while (len-- > 0) {
    lenbuf[0] = bignum_byte(b, len);
    SHA_Bytes(s, lenbuf, 1);
  }
  smemclr(lenbuf, sizeof(lenbuf));
}

static void sha512_mpint(SHA512_State *s, Bignum b)
{
  unsigned char lenbuf[4];
  int len;
  len = (bignum_bitcount(b) + 8) / 8;
  PUT_32BIT(lenbuf, len);
  SHA512_Bytes(s, lenbuf, 4);
  while (len-- > 0) {
    lenbuf[0] = bignum_byte(b, len);
    SHA512_Bytes(s, lenbuf, 1);
  }
  smemclr(lenbuf, sizeof(lenbuf));
}

static void getstring(const char **data,
                      int *datalen,
                      const char **p,
                      int *length)
{
  *p = NULL;
  if (*datalen < 4)
    return;
  *length = toint(GET_32BIT(*data));
  if (*length < 0)
    return;
  *datalen -= 4;
  *data += 4;
  if (*datalen < *length)
    return;
  *p = *data;
  *data += *length;
  *datalen -= *length;
}
static Bignum getmp(const char **data, int *datalen)
{
  const char *p;
  int length;
  Bignum b;

  getstring(data, datalen, &p, &length);
  if (!p)
    return NULL;
  if (p[0] & 0x80)
    return NULL; /* negative mp */
  b = bignum_from_bytes((const unsigned char *)p, length);
  return b;
}

static Bignum get160(const char **data, int *datalen)
{
  Bignum b;

  if (*datalen < 20)
    return NULL;

  b = bignum_from_bytes((const unsigned char *)*data, 20);
  *data += 20;
  *datalen -= 20;

  return b;
}

static void dss_freekey(void *key); /* forward reference */

static void *dss_newkey(const struct ssh_signkey *self,
                        const char *data,
                        int len)
{
  const char *p;
  int slen;
  struct dss_key *dss;

  dss = snew(struct dss_key);
  getstring(&data, &len, &p, &slen);

#ifdef DEBUG_DSS
  {
    int i;
    printf("key:");
    for (i = 0; i < len; i++)
      printf("  %02x", (unsigned char)(data[i]));
    printf("\n");
  }
#endif

  if (!p || slen != 7 || memcmp(p, "ssh-dss", 7)) {
    sfree(dss);
    return NULL;
  }
  dss->p = getmp(&data, &len);
  dss->q = getmp(&data, &len);
  dss->g = getmp(&data, &len);
  dss->y = getmp(&data, &len);
  dss->x = NULL;

  if (!dss->p || !dss->q || !dss->g || !dss->y || !bignum_cmp(dss->q, Zero) ||
      !bignum_cmp(dss->p, Zero)) {
    /* Invalid key. */
    dss_freekey(dss);
    return NULL;
  }

  return dss;
}

static void dss_freekey(void *key)
{
  struct dss_key *dss = (struct dss_key *)key;
  if (dss->p)
    freebn(dss->p);
  if (dss->q)
    freebn(dss->q);
  if (dss->g)
    freebn(dss->g);
  if (dss->y)
    freebn(dss->y);
  if (dss->x)
    freebn(dss->x);
  sfree(dss);
}

static char *dss_fmtkey(void *key)
{
  struct dss_key *dss = (struct dss_key *)key;
  char *p;
  int len, i, pos, nibbles;
  static const char hex[] = "0123456789abcdef";
  if (!dss->p)
    return NULL;
  len = 8 + 4 + 1; /* 4 x "0x", punctuation, \0 */
  len += 4 * (bignum_bitcount(dss->p) + 15) / 16;
  len += 4 * (bignum_bitcount(dss->q) + 15) / 16;
  len += 4 * (bignum_bitcount(dss->g) + 15) / 16;
  len += 4 * (bignum_bitcount(dss->y) + 15) / 16;
  p = snewn(len, char);
  if (!p)
    return NULL;

  pos = 0;
  pos += sprintf(p + pos, "0x");
  nibbles = (3 + bignum_bitcount(dss->p)) / 4;
  if (nibbles < 1)
    nibbles = 1;
  for (i = nibbles; i--;)
    p[pos++] = hex[(bignum_byte(dss->p, i / 2) >> (4 * (i % 2))) & 0xF];
  pos += sprintf(p + pos, ",0x");
  nibbles = (3 + bignum_bitcount(dss->q)) / 4;
  if (nibbles < 1)
    nibbles = 1;
  for (i = nibbles; i--;)
    p[pos++] = hex[(bignum_byte(dss->q, i / 2) >> (4 * (i % 2))) & 0xF];
  pos += sprintf(p + pos, ",0x");
  nibbles = (3 + bignum_bitcount(dss->g)) / 4;
  if (nibbles < 1)
    nibbles = 1;
  for (i = nibbles; i--;)
    p[pos++] = hex[(bignum_byte(dss->g, i / 2) >> (4 * (i % 2))) & 0xF];
  pos += sprintf(p + pos, ",0x");
  nibbles = (3 + bignum_bitcount(dss->y)) / 4;
  if (nibbles < 1)
    nibbles = 1;
  for (i = nibbles; i--;)
    p[pos++] = hex[(bignum_byte(dss->y, i / 2) >> (4 * (i % 2))) & 0xF];
  p[pos] = '\0';
  return p;
}

static int dss_verifysig(
    void *key, const char *sig, int siglen, const char *data, int datalen)
{
  struct dss_key *dss = (struct dss_key *)key;
  const char *p;
  int slen;
  char hash[20];
  Bignum r, s, w, gu1p, yu2p, gu1yu2p, u1, u2, sha, v;
  int ret;

  if (!dss->p)
    return 0;

#ifdef DEBUG_DSS
  {
    int i;
    printf("sig:");
    for (i = 0; i < siglen; i++)
      printf("  %02x", (unsigned char)(sig[i]));
    printf("\n");
  }
#endif
  /*
   * Commercial SSH (2.0.13) and OpenSSH disagree over the format
   * of a DSA signature. OpenSSH is in line with RFC 4253:
   * it uses a string "ssh-dss", followed by a 40-byte string
   * containing two 160-bit integers end-to-end. Commercial SSH
   * can't be bothered with the header bit, and considers a DSA
   * signature blob to be _just_ the 40-byte string containing
   * the two 160-bit integers. We tell them apart by measuring
   * the length: length 40 means the commercial-SSH bug, anything
   * else is assumed to be RFC-compliant.
   */
  if (siglen != 40) { /* bug not present; read admin fields */
    getstring(&sig, &siglen, &p, &slen);
    if (!p || slen != 7 || memcmp(p, "ssh-dss", 7)) {
      return 0;
    }
    sig += 4, siglen -= 4; /* skip yet another length field */
  }
  r = get160(&sig, &siglen);
  s = get160(&sig, &siglen);
  if (!r || !s) {
    if (r)
      freebn(r);
    if (s)
      freebn(s);
    return 0;
  }

  if (!bignum_cmp(s, Zero)) {
    freebn(r);
    freebn(s);
    return 0;
  }

  /*
   * Step 1. w <- s^-1 mod q.
   */
  w = modinv(s, dss->q);
  if (!w) {
    freebn(r);
    freebn(s);
    return 0;
  }

  /*
   * Step 2. u1 <- SHA(message) * w mod q.
   */
  SHA_Simple(data, datalen, (unsigned char *)hash);
  p = hash;
  slen = 20;
  sha = get160(&p, &slen);
  u1 = modmul(sha, w, dss->q);

  /*
   * Step 3. u2 <- r * w mod q.
   */
  u2 = modmul(r, w, dss->q);

  /*
   * Step 4. v <- (g^u1 * y^u2 mod p) mod q.
   */
  gu1p = modpow(dss->g, u1, dss->p);
  yu2p = modpow(dss->y, u2, dss->p);
  gu1yu2p = modmul(gu1p, yu2p, dss->p);
  v = modmul(gu1yu2p, One, dss->q);

  /*
   * Step 5. v should now be equal to r.
   */

  ret = !bignum_cmp(v, r);

  freebn(w);
  freebn(sha);
  freebn(u1);
  freebn(u2);
  freebn(gu1p);
  freebn(yu2p);
  freebn(gu1yu2p);
  freebn(v);
  freebn(r);
  freebn(s);

  return ret;
}

static unsigned char *dss_public_blob(void *key, int *len)
{
  struct dss_key *dss = (struct dss_key *)key;
  int plen, qlen, glen, ylen, bloblen;
  int i;
  unsigned char *blob, *p;

  plen = (bignum_bitcount(dss->p) + 8) / 8;
  qlen = (bignum_bitcount(dss->q) + 8) / 8;
  glen = (bignum_bitcount(dss->g) + 8) / 8;
  ylen = (bignum_bitcount(dss->y) + 8) / 8;

  /*
   * string "ssh-dss", mpint p, mpint q, mpint g, mpint y. Total
   * 27 + sum of lengths. (five length fields, 20+7=27).
   */
  bloblen = 27 + plen + qlen + glen + ylen;
  blob = snewn(bloblen, unsigned char);
  p = blob;
  PUT_32BIT(p, 7);
  p += 4;
  memcpy(p, "ssh-dss", 7);
  p += 7;
  PUT_32BIT(p, plen);
  p += 4;
  for (i = plen; i--;)
    *p++ = bignum_byte(dss->p, i);
  PUT_32BIT(p, qlen);
  p += 4;
  for (i = qlen; i--;)
    *p++ = bignum_byte(dss->q, i);
  PUT_32BIT(p, glen);
  p += 4;
  for (i = glen; i--;)
    *p++ = bignum_byte(dss->g, i);
  PUT_32BIT(p, ylen);
  p += 4;
  for (i = ylen; i--;)
    *p++ = bignum_byte(dss->y, i);
  assert(p == blob + bloblen);
  *len = bloblen;
  return blob;
}

static unsigned char *dss_private_blob(void *key, int *len)
{
  struct dss_key *dss = (struct dss_key *)key;
  int xlen, bloblen;
  int i;
  unsigned char *blob, *p;

  xlen = (bignum_bitcount(dss->x) + 8) / 8;

  /*
   * mpint x, string[20] the SHA of p||q||g. Total 4 + xlen.
   */
  bloblen = 4 + xlen;
  blob = snewn(bloblen, unsigned char);
  p = blob;
  PUT_32BIT(p, xlen);
  p += 4;
  for (i = xlen; i--;)
    *p++ = bignum_byte(dss->x, i);
  assert(p == blob + bloblen);
  *len = bloblen;
  return blob;
}

static void *dss_createkey(const struct ssh_signkey *self,
                           const unsigned char *pub_blob,
                           int pub_len,
                           const unsigned char *priv_blob,
                           int priv_len)
{
  struct dss_key *dss;
  const char *pb = (const char *)priv_blob;
  const char *hash;
  int hashlen;
  SHA_State s;
  unsigned char digest[20];
  Bignum ytest;

  dss = dss_newkey(self, (char *)pub_blob, pub_len);
  if (!dss)
    return NULL;
  dss->x = getmp(&pb, &priv_len);
  if (!dss->x) {
    dss_freekey(dss);
    return NULL;
  }

  /*
   * Check the obsolete hash in the old DSS key format.
   */
  hashlen = -1;
  getstring(&pb, &priv_len, &hash, &hashlen);
  if (hashlen == 20) {
    SHA_Init(&s);
    sha_mpint(&s, dss->p);
    sha_mpint(&s, dss->q);
    sha_mpint(&s, dss->g);
    SHA_Final(&s, digest);
    if (0 != memcmp(hash, digest, 20)) {
      dss_freekey(dss);
      return NULL;
    }
  }

  /*
   * Now ensure g^x mod p really is y.
   */
  ytest = modpow(dss->g, dss->x, dss->p);
  if (0 != bignum_cmp(ytest, dss->y)) {
    dss_freekey(dss);
    freebn(ytest);
    return NULL;
  }
  freebn(ytest);

  return dss;
}

static void *dss_openssh_createkey(const struct ssh_signkey *self,
                                   const unsigned char **blob,
                                   int *len)
{
  const char **b = (const char **)blob;
  struct dss_key *dss;

  dss = snew(struct dss_key);

  dss->p = getmp(b, len);
  dss->q = getmp(b, len);
  dss->g = getmp(b, len);
  dss->y = getmp(b, len);
  dss->x = getmp(b, len);

  if (!dss->p || !dss->q || !dss->g || !dss->y || !dss->x ||
      !bignum_cmp(dss->q, Zero) || !bignum_cmp(dss->p, Zero)) {
    /* Invalid key. */
    dss_freekey(dss);
    return NULL;
  }

  return dss;
}

static int dss_openssh_fmtkey(void *key, unsigned char *blob, int len)
{
  struct dss_key *dss = (struct dss_key *)key;
  int bloblen, i;

  bloblen = ssh2_bignum_length(dss->p) + ssh2_bignum_length(dss->q) +
            ssh2_bignum_length(dss->g) + ssh2_bignum_length(dss->y) +
            ssh2_bignum_length(dss->x);

  if (bloblen > len)
    return bloblen;

  bloblen = 0;
#define ENC(x)                                                                 \
  PUT_32BIT(blob + bloblen, ssh2_bignum_length((x)) - 4);                      \
  bloblen += 4;                                                                \
  for (i = ssh2_bignum_length((x)) - 4; i--;)                                  \
    blob[bloblen++] = bignum_byte((x), i);
  ENC(dss->p);
  ENC(dss->q);
  ENC(dss->g);
  ENC(dss->y);
  ENC(dss->x);

  return bloblen;
}

static int dss_pubkey_bits(const struct ssh_signkey *self,
                           const void *blob,
                           int len)
{
  struct dss_key *dss;
  int ret;

  dss = dss_newkey(self, (const char *)blob, len);
  if (!dss)
    return -1;
  ret = bignum_bitcount(dss->p);
  dss_freekey(dss);

  return ret;
}

Bignum *dss_gen_k(const char *id_string,
                  Bignum modulus,
                  Bignum private_key,
                  unsigned char *digest,
                  int digest_len)
{
  /*
   * The basic DSS signing algorithm is:
   *
   *  - invent a random k between 1 and q-1 (exclusive).
   *  - Compute r = (g^k mod p) mod q.
   *  - Compute s = k^-1 * (hash + x*r) mod q.
   *
   * This has the dangerous properties that:
   *
   *  - if an attacker in possession of the public key _and_ the
   *    signature (for example, the host you just authenticated
   *    to) can guess your k, he can reverse the computation of s
   *    and work out x = r^-1 * (s*k - hash) mod q. That is, he
   *    can deduce the private half of your key, and masquerade
   *    as you for as long as the key is still valid.
   *
   *  - since r is a function purely of k and the public key, if
   *    the attacker only has a _range of possibilities_ for k
   *    it's easy for him to work through them all and check each
   *    one against r; he'll never be unsure of whether he's got
   *    the right one.
   *
   *  - if you ever sign two different hashes with the same k, it
   *    will be immediately obvious because the two signatures
   *    will have the same r, and moreover an attacker in
   *    possession of both signatures (and the public key of
   *    course) can compute k = (hash1-hash2) * (s1-s2)^-1 mod q,
   *    and from there deduce x as before.
   *
   *  - the Bleichenbacher attack on DSA makes use of methods of
   *    generating k which are significantly non-uniformly
   *    distributed; in particular, generating a 160-bit random
   *    number and reducing it mod q is right out.
   *
   * For this reason we must be pretty careful about how we
   * generate our k. Since this code runs on Windows, with no
   * particularly good system entropy sources, we can't trust our
   * RNG itself to produce properly unpredictable data. Hence, we
   * use a totally different scheme instead.
   *
   * What we do is to take a SHA-512 (_big_) hash of the private
   * key x, and then feed this into another SHA-512 hash that
   * also includes the message hash being signed. That is:
   *
   *   proto_k = SHA512 ( SHA512(x) || SHA160(message) )
   *
   * This number is 512 bits long, so reducing it mod q won't be
   * noticeably non-uniform. So
   *
   *   k = proto_k mod q
   *
   * This has the interesting property that it's _deterministic_:
   * signing the same hash twice with the same key yields the
   * same signature.
   *
   * Despite this determinism, it's still not predictable to an
   * attacker, because in order to repeat the SHA-512
   * construction that created it, the attacker would have to
   * know the private key value x - and by assumption he doesn't,
   * because if he knew that he wouldn't be attacking k!
   *
   * (This trick doesn't, _per se_, protect against reuse of k.
   * Reuse of k is left to chance; all it does is prevent
   * _excessively high_ chances of reuse of k due to entropy
   * problems.)
   *
   * Thanks to Colin Plumb for the general idea of using x to
   * ensure k is hard to guess, and to the Cambridge University
   * Computer Security Group for helping to argue out all the
   * fine details.
   */
  SHA512_State ss;
  unsigned char digest512[64];
  Bignum proto_k, k;

  /*
   * Hash some identifying text plus x.
   */
  SHA512_Init(&ss);
  SHA512_Bytes(&ss, id_string, strlen(id_string) + 1);
  sha512_mpint(&ss, private_key);
  SHA512_Final(&ss, digest512);

  /*
   * Now hash that digest plus the message hash.
   */
  SHA512_Init(&ss);
  SHA512_Bytes(&ss, digest512, sizeof(digest512));
  SHA512_Bytes(&ss, digest, digest_len);

  while (1) {
    SHA512_State ss2 = ss; /* structure copy */
    SHA512_Final(&ss2, digest512);

    smemclr(&ss2, sizeof(ss2));

    /*
     * Now convert the result into a bignum, and reduce it mod q.
     */
    proto_k = bignum_from_bytes(digest512, 64);
    k = bigmod(proto_k, modulus);
    freebn(proto_k);

    if (bignum_cmp(k, One) != 0 && bignum_cmp(k, Zero) != 0) {
      smemclr(&ss, sizeof(ss));
      smemclr(digest512, sizeof(digest512));
      return k;
    }

    /* Very unlikely we get here, but if so, k was unsuitable. */
    freebn(k);
    /* Perturb the hash to think of a different k. */
    SHA512_Bytes(&ss, "x", 1);
    /* Go round and try again. */
  }
}

static unsigned char *dss_sign(void *key,
                               const char *data,
                               int datalen,
                               int *siglen)
{
  struct dss_key *dss = (struct dss_key *)key;
  Bignum k, gkp, hash, kinv, hxr, r, s;
  unsigned char digest[20];
  unsigned char *bytes;
  int nbytes, i;

  SHA_Simple(data, datalen, digest);

  k = dss_gen_k(
      "DSA deterministic k generator", dss->q, dss->x, digest, sizeof(digest));
  kinv = modinv(k, dss->q); /* k^-1 mod q */
  assert(kinv);

  /*
   * Now we have k, so just go ahead and compute the signature.
   */
  gkp = modpow(dss->g, k, dss->p); /* g^k mod p */
  r = bigmod(gkp, dss->q);         /* r = (g^k mod p) mod q */
  freebn(gkp);

  hash = bignum_from_bytes(digest, 20);
  hxr = bigmuladd(dss->x, r, hash); /* hash + x*r */
  s = modmul(kinv, hxr, dss->q);    /* s = k^-1 * (hash + x*r) mod q */
  freebn(hxr);
  freebn(kinv);
  freebn(k);
  freebn(hash);

  /*
   * Signature blob is
   *
   *   string  "ssh-dss"
   *   string  two 20-byte numbers r and s, end to end
   *
   * i.e. 4+7 + 4+40 bytes.
   */
  nbytes = 4 + 7 + 4 + 40;
  bytes = snewn(nbytes, unsigned char);
  PUT_32BIT(bytes, 7);
  memcpy(bytes + 4, "ssh-dss", 7);
  PUT_32BIT(bytes + 4 + 7, 40);
  for (i = 0; i < 20; i++) {
    bytes[4 + 7 + 4 + i] = bignum_byte(r, 19 - i);
    bytes[4 + 7 + 4 + 20 + i] = bignum_byte(s, 19 - i);
  }
  freebn(r);
  freebn(s);

  *siglen = nbytes;
  return bytes;
}

const struct ssh_signkey ssh_dss = {
    dss_newkey,
    dss_freekey,
    dss_fmtkey,
    dss_public_blob,
    dss_private_blob,
    dss_createkey,
    dss_openssh_createkey,
    dss_openssh_fmtkey,
    5 /* p,q,g,y,x */,
    dss_pubkey_bits,
    dss_verifysig,
    dss_sign,
    "ssh-dss",
    "dss",
    NULL,
};