src/TortoisePlink/sshrsag.c

   1 /*
   2  * RSA key generation.
   3  */
   4
   5 #include <assert.h>
   6
   7 #include "ssh.h"
   8
   9 #define RSA_EXPONENT 37                /* we like this prime */
  10
  11 int rsa_generate(struct RSAKey *key, int bits, progfn_t pfn,
  12                  void *pfnparam)
  13 {
  14     Bignum pm1, qm1, phi_n;
  15     unsigned pfirst, qfirst;
  16
  17     /*
  18      * Set up the phase limits for the progress report. We do this
  19      * by passing minus the phase number.
  20      *
  21      * For prime generation: our initial filter finds things
  22      * coprime to everything below 2^16. Computing the product of
  23      * (p-1)/p for all prime p below 2^16 gives about 20.33; so
  24      * among B-bit integers, one in every 20.33 will get through
  25      * the initial filter to be a candidate prime.
  26      *
  27      * Meanwhile, we are searching for primes in the region of 2^B;
  28      * since pi(x) ~ x/log(x), when x is in the region of 2^B, the
  29      * prime density will be d/dx pi(x) ~ 1/log(B), i.e. about
  30      * 1/0.6931B. So the chance of any given candidate being prime
  31      * is 20.33/0.6931B, which is roughly 29.34 divided by B.
  32      *
  33      * So now we have this probability P, we're looking at an
  34      * exponential distribution with parameter P: we will manage in
  35      * one attempt with probability P, in two with probability
  36      * P(1-P), in three with probability P(1-P)^2, etc. The
  37      * probability that we have still not managed to find a prime
  38      * after N attempts is (1-P)^N.
  39      *
  40      * We therefore inform the progress indicator of the number B
  41      * (29.34/B), so that it knows how much to increment by each
  42      * time. We do this in 16-bit fixed point, so 29.34 becomes
  43      * 0x1D.57C4.
  44      */
  45     pfn(pfnparam, PROGFN_PHASE_EXTENT, 1, 0x10000);
  46     pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / (bits / 2));
  47     pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x10000);
  48     pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / (bits - bits / 2));
  49     pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x4000);
  50     pfn(pfnparam, PROGFN_LIN_PHASE, 3, 5);
  51     pfn(pfnparam, PROGFN_READY, 0, 0);
  52
  53     /*
  54      * We don't generate e; we just use a standard one always.
  55      */
  56     key->exponent = bignum_from_long(RSA_EXPONENT);
  57
  58     /*
  59      * Generate p and q: primes with combined length `bits', not
  60      * congruent to 1 modulo e. (Strictly speaking, we wanted (p-1)
  61      * and e to be coprime, and (q-1) and e to be coprime, but in
  62      * general that's slightly more fiddly to arrange. By choosing
  63      * a prime e, we can simplify the criterion.)
  64      */
  65     invent_firstbits(&pfirst, &qfirst);
  66     key->p = primegen(bits / 2, RSA_EXPONENT, 1, NULL,
  67                       1, pfn, pfnparam, pfirst);
  68     key->q = primegen(bits - bits / 2, RSA_EXPONENT, 1, NULL,
  69                       2, pfn, pfnparam, qfirst);
  70
  71     /*
  72      * Ensure p > q, by swapping them if not.
  73      */
  74     if (bignum_cmp(key->p, key->q) < 0) {
  75         Bignum t = key->p;
  76         key->p = key->q;
  77         key->q = t;
  78     }
  79
  80     /*
  81      * Now we have p, q and e. All we need to do now is work out
  82      * the other helpful quantities: n=pq, d=e^-1 mod (p-1)(q-1),
  83      * and (q^-1 mod p).
  84      */
  85     pfn(pfnparam, PROGFN_PROGRESS, 3, 1);
  86     key->modulus = bigmul(key->p, key->q);
  87     pfn(pfnparam, PROGFN_PROGRESS, 3, 2);
  88     pm1 = copybn(key->p);
  89     decbn(pm1);
  90     qm1 = copybn(key->q);
  91     decbn(qm1);
  92     phi_n = bigmul(pm1, qm1);
  93     pfn(pfnparam, PROGFN_PROGRESS, 3, 3);
  94     freebn(pm1);
  95     freebn(qm1);
  96     key->private_exponent = modinv(key->exponent, phi_n);
  97     assert(key->private_exponent);
  98     pfn(pfnparam, PROGFN_PROGRESS, 3, 4);
  99     key->iqmp = modinv(key->q, key->p);
 100     assert(key->iqmp);
 101     pfn(pfnparam, PROGFN_PROGRESS, 3, 5);
 102
 103     /*
 104      * Clean up temporary numbers.
 105      */
 106     freebn(phi_n);
 107
 108     return 1;
 109 }