зеркало из https://github.com/github/putty.git
112 строки
3.6 KiB
C
112 строки
3.6 KiB
C
/*
|
|
* RSA key generation.
|
|
*/
|
|
|
|
#include <assert.h>
|
|
|
|
#include "ssh.h"
|
|
|
|
#define RSA_EXPONENT 37 /* we like this prime */
|
|
|
|
int rsa_generate(struct RSAKey *key, int bits, progfn_t pfn,
|
|
void *pfnparam)
|
|
{
|
|
Bignum pm1, qm1, phi_n;
|
|
unsigned pfirst, qfirst;
|
|
|
|
key->sshk.vt = &ssh_rsa;
|
|
|
|
/*
|
|
* 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, 0x10000);
|
|
pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / (bits / 2));
|
|
pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x10000);
|
|
pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / (bits - bits / 2));
|
|
pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x4000);
|
|
pfn(pfnparam, PROGFN_LIN_PHASE, 3, 5);
|
|
pfn(pfnparam, PROGFN_READY, 0, 0);
|
|
|
|
/*
|
|
* We don't generate e; we just use a standard one always.
|
|
*/
|
|
key->exponent = bignum_from_long(RSA_EXPONENT);
|
|
|
|
/*
|
|
* Generate p and q: primes with combined length `bits', not
|
|
* congruent to 1 modulo e. (Strictly speaking, we wanted (p-1)
|
|
* and e to be coprime, and (q-1) and e to be coprime, but in
|
|
* general that's slightly more fiddly to arrange. By choosing
|
|
* a prime e, we can simplify the criterion.)
|
|
*/
|
|
invent_firstbits(&pfirst, &qfirst);
|
|
key->p = primegen(bits / 2, RSA_EXPONENT, 1, NULL,
|
|
1, pfn, pfnparam, pfirst);
|
|
key->q = primegen(bits - bits / 2, RSA_EXPONENT, 1, NULL,
|
|
2, pfn, pfnparam, qfirst);
|
|
|
|
/*
|
|
* Ensure p > q, by swapping them if not.
|
|
*/
|
|
if (bignum_cmp(key->p, key->q) < 0) {
|
|
Bignum t = key->p;
|
|
key->p = key->q;
|
|
key->q = t;
|
|
}
|
|
|
|
/*
|
|
* Now we have p, q and e. All we need to do now is work out
|
|
* the other helpful quantities: n=pq, d=e^-1 mod (p-1)(q-1),
|
|
* and (q^-1 mod p).
|
|
*/
|
|
pfn(pfnparam, PROGFN_PROGRESS, 3, 1);
|
|
key->modulus = bigmul(key->p, key->q);
|
|
pfn(pfnparam, PROGFN_PROGRESS, 3, 2);
|
|
pm1 = copybn(key->p);
|
|
decbn(pm1);
|
|
qm1 = copybn(key->q);
|
|
decbn(qm1);
|
|
phi_n = bigmul(pm1, qm1);
|
|
pfn(pfnparam, PROGFN_PROGRESS, 3, 3);
|
|
freebn(pm1);
|
|
freebn(qm1);
|
|
key->private_exponent = modinv(key->exponent, phi_n);
|
|
assert(key->private_exponent);
|
|
pfn(pfnparam, PROGFN_PROGRESS, 3, 4);
|
|
key->iqmp = modinv(key->q, key->p);
|
|
assert(key->iqmp);
|
|
pfn(pfnparam, PROGFN_PROGRESS, 3, 5);
|
|
|
|
/*
|
|
* Clean up temporary numbers.
|
|
*/
|
|
freebn(phi_n);
|
|
|
|
return 1;
|
|
}
|