git.distorted.org.uk Git - u/mdw/putty/blob - sshdssg.c

   1 /*
   2  * DSS key generation.
   3  */
   4
   5 #include "misc.h"
   6 #include "ssh.h"
   7
   8 int dsa_generate(struct dss_key *key, int bits, progfn_t pfn,
   9                  void *pfnparam)
  10 {
  11     Bignum qm1, power, g, h, tmp;
  12     unsigned pfirst, qfirst;
  13     int progress;
  14
  15     /*
  16      * Set up the phase limits for the progress report. We do this
  17      * by passing minus the phase number.
  18      *
  19      * For prime generation: our initial filter finds things
  20      * coprime to everything below 2^16. Computing the product of
  21      * (p-1)/p for all prime p below 2^16 gives about 20.33; so
  22      * among B-bit integers, one in every 20.33 will get through
  23      * the initial filter to be a candidate prime.
  24      *
  25      * Meanwhile, we are searching for primes in the region of 2^B;
  26      * since pi(x) ~ x/log(x), when x is in the region of 2^B, the
  27      * prime density will be d/dx pi(x) ~ 1/log(B), i.e. about
  28      * 1/0.6931B. So the chance of any given candidate being prime
  29      * is 20.33/0.6931B, which is roughly 29.34 divided by B.
  30      *
  31      * So now we have this probability P, we're looking at an
  32      * exponential distribution with parameter P: we will manage in
  33      * one attempt with probability P, in two with probability
  34      * P(1-P), in three with probability P(1-P)^2, etc. The
  35      * probability that we have still not managed to find a prime
  36      * after N attempts is (1-P)^N.
  37      *
  38      * We therefore inform the progress indicator of the number B
  39      * (29.34/B), so that it knows how much to increment by each
  40      * time. We do this in 16-bit fixed point, so 29.34 becomes
  41      * 0x1D.57C4.
  42      */
  43     pfn(pfnparam, PROGFN_PHASE_EXTENT, 1, 0x2800);
  44     pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / 160);
  45     pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x40 * bits);
  46     pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / bits);
  47
  48     /*
  49      * In phase three we are finding an order-q element of the
  50      * multiplicative group of p, by finding an element whose order
  51      * is _divisible_ by q and raising it to the power of (p-1)/q.
  52      * _Most_ elements will have order divisible by q, since for a
  53      * start phi(p) of them will be primitive roots. So
  54      * realistically we don't need to set this much below 1 (64K).
  55      * Still, we'll set it to 1/2 (32K) to be on the safe side.
  56      */
  57     pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x2000);
  58     pfn(pfnparam, PROGFN_EXP_PHASE, 3, -32768);
  59
  60     /*
  61      * In phase four we are finding an element x between 1 and q-1
  62      * (exclusive), by inventing 160 random bits and hoping they
  63      * come out to a plausible number; so assuming q is uniformly
  64      * distributed between 2^159 and 2^160, the chance of any given
  65      * attempt succeeding is somewhere between 0.5 and 1. Lacking
  66      * the energy to arrange to be able to specify this probability
  67      * _after_ generating q, we'll just set it to 0.75.
  68      */
  69     pfn(pfnparam, PROGFN_PHASE_EXTENT, 4, 0x2000);
  70     pfn(pfnparam, PROGFN_EXP_PHASE, 4, -49152);
  71
  72     pfn(pfnparam, PROGFN_READY, 0, 0);
  73
  74     invent_firstbits(&pfirst, &qfirst);
  75     /*
  76      * Generate q: a prime of length 160.
  77      */
  78     key->q = primegen(160, 2, 2, NULL, 1, pfn, pfnparam, qfirst);
  79     /*
  80      * Now generate p: a prime of length `bits', such that p-1 is
  81      * divisible by q.
  82      */
  83     key->p = primegen(bits-160, 2, 2, key->q, 2, pfn, pfnparam, pfirst);
  84
  85     /*
  86      * Next we need g. Raise 2 to the power (p-1)/q modulo p, and
  87      * if that comes out to one then try 3, then 4 and so on. As
  88      * soon as we hit a non-unit (and non-zero!) one, that'll do
  89      * for g.
  90      */
  91     power = bigdiv(key->p, key->q);    /* this is floor(p/q) == (p-1)/q */
  92     h = bignum_from_long(1);
  93     progress = 0;
  94     while (1) {
  95         pfn(pfnparam, PROGFN_PROGRESS, 3, ++progress);
  96         g = modpow(h, power, key->p);
  97         if (bignum_cmp(g, One) > 0)
  98             break;                     /* got one */
  99         tmp = h;
 100         h = bignum_add_long(h, 1);
 101         freebn(tmp);
 102     }
 103     key->g = g;
 104     freebn(h);
 105
 106     /*
 107      * Now we're nearly done. All we need now is our private key x,
 108      * which should be a number between 1 and q-1 exclusive, and
 109      * our public key y = g^x mod p.
 110      */
 111     qm1 = copybn(key->q);
 112     decbn(qm1);
 113     progress = 0;
 114     while (1) {
 115         int i, v, byte, bitsleft;
 116         Bignum x;
 117
 118         pfn(pfnparam, PROGFN_PROGRESS, 4, ++progress);
 119         x = bn_power_2(159);
 120         byte = 0;
 121         bitsleft = 0;
 122
 123         for (i = 0; i < 160; i++) {
 124             if (bitsleft <= 0)
 125                 bitsleft = 8, byte = random_byte();
 126             v = byte & 1;
 127             byte >>= 1;
 128             bitsleft--;
 129             bignum_set_bit(x, i, v);
 130         }
 131
 132         if (bignum_cmp(x, One) <= 0 || bignum_cmp(x, qm1) >= 0) {
 133             freebn(x);
 134             continue;
 135         } else {
 136             key->x = x;
 137             break;
 138         }
 139     }
 140     freebn(qm1);
 141
 142     key->y = modpow(key->g, key->x, key->p);
 143
 144     return 1;
 145 }