sshdssg.c

/*
 * DSS key generation.
 */

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

int dsa_generate(struct dss_key *key, int bits, progfn_t pfn, void *pfnparam)
{
  Bignum qm1, power, g, h, tmp;
  unsigned pfirst, qfirst;
  int progress;

  /*
   * Set up the phase limits for the progress report. We do this
   * by passing minus the phase number.
   *
   * For prime generation: our initial filter finds things
   * coprime to everything below 2^16. Computing the product of
   * (p-1)/p for all prime p below 2^16 gives about 20.33; so
   * among B-bit integers, one in every 20.33 will get through
   * the initial filter to be a candidate prime.
   *
   * Meanwhile, we are searching for primes in the region of 2^B;
   * since pi(x) ~ x/log(x), when x is in the region of 2^B, the
   * prime density will be d/dx pi(x) ~ 1/log(B), i.e. about
   * 1/0.6931B. So the chance of any given candidate being prime
   * is 20.33/0.6931B, which is roughly 29.34 divided by B.
   *
   * So now we have this probability P, we're looking at an
   * exponential distribution with parameter P: we will manage in
   * one attempt with probability P, in two with probability
   * P(1-P), in three with probability P(1-P)^2, etc. The
   * probability that we have still not managed to find a prime
   * after N attempts is (1-P)^N.
   *
   * We therefore inform the progress indicator of the number B
   * (29.34/B), so that it knows how much to increment by each
   * time. We do this in 16-bit fixed point, so 29.34 becomes
   * 0x1D.57C4.
   */
  pfn(pfnparam, PROGFN_PHASE_EXTENT, 1, 0x2800);
  pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / 160);
  pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x40 * bits);
  pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / bits);

  /*
   * In phase three we are finding an order-q element of the
   * multiplicative group of p, by finding an element whose order
   * is _divisible_ by q and raising it to the power of (p-1)/q.
   * _Most_ elements will have order divisible by q, since for a
   * start phi(p) of them will be primitive roots. So
   * realistically we don't need to set this much below 1 (64K).
   * Still, we'll set it to 1/2 (32K) to be on the safe side.
   */
  pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x2000);
  pfn(pfnparam, PROGFN_EXP_PHASE, 3, -32768);

  /*
   * In phase four we are finding an element x between 1 and q-1
   * (exclusive), by inventing 160 random bits and hoping they
   * come out to a plausible number; so assuming q is uniformly
   * distributed between 2^159 and 2^160, the chance of any given
   * attempt succeeding is somewhere between 0.5 and 1. Lacking
   * the energy to arrange to be able to specify this probability
   * _after_ generating q, we'll just set it to 0.75.
   */
  pfn(pfnparam, PROGFN_PHASE_EXTENT, 4, 0x2000);
  pfn(pfnparam, PROGFN_EXP_PHASE, 4, -49152);

  pfn(pfnparam, PROGFN_READY, 0, 0);

  invent_firstbits(&pfirst, &qfirst);
  /*
   * Generate q: a prime of length 160.
   */
  key->q = primegen(160, 2, 2, NULL, 1, pfn, pfnparam, qfirst);
  /*
   * Now generate p: a prime of length `bits', such that p-1 is
   * divisible by q.
   */
  key->p = primegen(bits - 160, 2, 2, key->q, 2, pfn, pfnparam, pfirst);

  /*
   * Next we need g. Raise 2 to the power (p-1)/q modulo p, and
   * if that comes out to one then try 3, then 4 and so on. As
   * soon as we hit a non-unit (and non-zero!) one, that'll do
   * for g.
   */
  power = bigdiv(key->p, key->q); /* this is floor(p/q) == (p-1)/q */
  h = bignum_from_long(1);
  progress = 0;
  while (1) {
    pfn(pfnparam, PROGFN_PROGRESS, 3, ++progress);
    g = modpow(h, power, key->p);
    if (bignum_cmp(g, One) > 0)
      break; /* got one */
    tmp = h;
    h = bignum_add_long(h, 1);
    freebn(tmp);
  }
  key->g = g;
  freebn(h);

  /*
   * Now we're nearly done. All we need now is our private key x,
   * which should be a number between 1 and q-1 exclusive, and
   * our public key y = g^x mod p.
   */
  qm1 = copybn(key->q);
  decbn(qm1);
  progress = 0;
  while (1) {
    int i, v, byte, bitsleft;
    Bignum x;

    pfn(pfnparam, PROGFN_PROGRESS, 4, ++progress);
    x = bn_power_2(159);
    byte = 0;
    bitsleft = 0;

    for (i = 0; i < 160; i++) {
      if (bitsleft <= 0)
        bitsleft = 8, byte = random_byte();
      v = byte & 1;
      byte >>= 1;
      bitsleft--;
      bignum_set_bit(x, i, v);
    }

    if (bignum_cmp(x, One) <= 0 || bignum_cmp(x, qm1) >= 0) {
      freebn(x);
      continue;
    } else {
      key->x = x;
      break;
    }
  }
  freebn(qm1);

  key->y = modpow(key->g, key->x, key->p);

  return 1;
}