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

   1 /*
   2  * RSA key generation.
   3  */
   4
   5 #include "ssh.h"
   6
   7 #define RSA_EXPONENT 37                /* we like this prime */
   8
   9 int rsa_generate(struct RSAKey *key, int bits, progfn_t pfn,
  10                  void *pfnparam)
  11 {
  12     Bignum pm1, qm1, phi_n;
  13     unsigned pfirst, qfirst;
  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, 0x10000);
  44     pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / (bits / 2));
  45     pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x10000);
  46     pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / (bits - bits / 2));
  47     pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x4000);
  48     pfn(pfnparam, PROGFN_LIN_PHASE, 3, 5);
  49     pfn(pfnparam, PROGFN_READY, 0, 0);
  50
  51     /*
  52      * We don't generate e; we just use a standard one always.
  53      */
  54     key->exponent = bignum_from_long(RSA_EXPONENT);
  55
  56     /*
  57      * Generate p and q: primes with combined length `bits', not
  58      * congruent to 1 modulo e. (Strictly speaking, we wanted (p-1)
  59      * and e to be coprime, and (q-1) and e to be coprime, but in
  60      * general that's slightly more fiddly to arrange. By choosing
  61      * a prime e, we can simplify the criterion.)
  62      */
  63     invent_firstbits(&pfirst, &qfirst);
  64     key->p = primegen(bits / 2, RSA_EXPONENT, 1, NULL,
  65                       1, pfn, pfnparam, pfirst);
  66     key->q = primegen(bits - bits / 2, RSA_EXPONENT, 1, NULL,
  67                       2, pfn, pfnparam, qfirst);
  68
  69     /*
  70      * Ensure p > q, by swapping them if not.
  71      */
  72     if (bignum_cmp(key->p, key->q) < 0) {
  73         Bignum t = key->p;
  74         key->p = key->q;
  75         key->q = t;
  76     }
  77
  78     /*
  79      * Now we have p, q and e. All we need to do now is work out
  80      * the other helpful quantities: n=pq, d=e^-1 mod (p-1)(q-1),
  81      * and (q^-1 mod p).
  82      */
  83     pfn(pfnparam, PROGFN_PROGRESS, 3, 1);
  84     key->modulus = bigmul(key->p, key->q);
  85     pfn(pfnparam, PROGFN_PROGRESS, 3, 2);
  86     pm1 = copybn(key->p);
  87     decbn(pm1);
  88     qm1 = copybn(key->q);
  89     decbn(qm1);
  90     phi_n = bigmul(pm1, qm1);
  91     pfn(pfnparam, PROGFN_PROGRESS, 3, 3);
  92     freebn(pm1);
  93     freebn(qm1);
  94     key->private_exponent = modinv(key->exponent, phi_n);
  95     pfn(pfnparam, PROGFN_PROGRESS, 3, 4);
  96     key->iqmp = modinv(key->q, key->p);
  97     pfn(pfnparam, PROGFN_PROGRESS, 3, 5);
  98
  99     /*
 100      * Clean up temporary numbers.
 101      */
 102     freebn(phi_n);
 103
 104     return 1;
 105 }