зеркало из https://github.com/github/putty.git
114 строки
3.8 KiB
C
114 строки
3.8 KiB
C
/*
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* DSS key generation.
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*/
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#include "misc.h"
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#include "ssh.h"
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#include "mpint.h"
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int dsa_generate(struct dss_key *key, int bits, progfn_t pfn,
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void *pfnparam)
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{
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/*
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* Set up the phase limits for the progress report. We do this
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* by passing minus the phase number.
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*
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* For prime generation: our initial filter finds things
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* coprime to everything below 2^16. Computing the product of
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* (p-1)/p for all prime p below 2^16 gives about 20.33; so
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* among B-bit integers, one in every 20.33 will get through
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* the initial filter to be a candidate prime.
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*
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* Meanwhile, we are searching for primes in the region of 2^B;
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* since pi(x) ~ x/log(x), when x is in the region of 2^B, the
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* prime density will be d/dx pi(x) ~ 1/log(B), i.e. about
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* 1/0.6931B. So the chance of any given candidate being prime
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* is 20.33/0.6931B, which is roughly 29.34 divided by B.
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*
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* So now we have this probability P, we're looking at an
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* exponential distribution with parameter P: we will manage in
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* one attempt with probability P, in two with probability
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* P(1-P), in three with probability P(1-P)^2, etc. The
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* probability that we have still not managed to find a prime
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* after N attempts is (1-P)^N.
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*
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* We therefore inform the progress indicator of the number B
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* (29.34/B), so that it knows how much to increment by each
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* time. We do this in 16-bit fixed point, so 29.34 becomes
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* 0x1D.57C4.
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*/
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pfn(pfnparam, PROGFN_PHASE_EXTENT, 1, 0x2800);
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pfn(pfnparam, PROGFN_EXP_PHASE, 1, -0x1D57C4 / 160);
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pfn(pfnparam, PROGFN_PHASE_EXTENT, 2, 0x40 * bits);
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pfn(pfnparam, PROGFN_EXP_PHASE, 2, -0x1D57C4 / bits);
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/*
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* In phase three we are finding an order-q element of the
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* multiplicative group of p, by finding an element whose order
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* is _divisible_ by q and raising it to the power of (p-1)/q.
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* _Most_ elements will have order divisible by q, since for a
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* start phi(p) of them will be primitive roots. So
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* realistically we don't need to set this much below 1 (64K).
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* Still, we'll set it to 1/2 (32K) to be on the safe side.
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*/
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pfn(pfnparam, PROGFN_PHASE_EXTENT, 3, 0x2000);
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pfn(pfnparam, PROGFN_EXP_PHASE, 3, -32768);
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pfn(pfnparam, PROGFN_READY, 0, 0);
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unsigned pfirst, qfirst;
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invent_firstbits(&pfirst, &qfirst, 0);
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/*
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* Generate q: a prime of length 160.
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*/
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mp_int *q = primegen(160, 2, 2, NULL, 1, pfn, pfnparam, qfirst);
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/*
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* Now generate p: a prime of length `bits', such that p-1 is
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* divisible by q.
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*/
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mp_int *p = primegen(bits-160, 2, 2, q, 2, pfn, pfnparam, pfirst);
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/*
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* Next we need g. Raise 2 to the power (p-1)/q modulo p, and
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* if that comes out to one then try 3, then 4 and so on. As
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* soon as we hit a non-unit (and non-zero!) one, that'll do
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* for g.
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*/
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mp_int *power = mp_div(p, q); /* this is floor(p/q) == (p-1)/q */
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mp_int *h = mp_from_integer(1);
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int progress = 0;
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mp_int *g;
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while (1) {
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pfn(pfnparam, PROGFN_PROGRESS, 3, ++progress);
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g = mp_modpow(h, power, p);
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if (mp_hs_integer(g, 2))
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break; /* got one */
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mp_free(g);
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mp_add_integer_into(h, h, 1);
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}
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mp_free(h);
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mp_free(power);
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/*
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* Now we're nearly done. All we need now is our private key x,
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* which should be a number between 1 and q-1 exclusive, and
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* our public key y = g^x mod p.
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*/
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mp_int *two = mp_from_integer(2);
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mp_int *qm1 = mp_copy(q);
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mp_sub_integer_into(qm1, qm1, 1);
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mp_int *x = mp_random_in_range(two, qm1);
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mp_free(two);
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mp_free(qm1);
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key->sshk.vt = &ssh_dss;
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key->p = p;
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key->q = q;
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key->g = g;
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key->x = x;
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key->y = mp_modpow(key->g, key->x, key->p);
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return 1;
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}
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