зеркало из https://github.com/github/putty.git
120 строки
3.6 KiB
C
120 строки
3.6 KiB
C
/*
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* RSA key generation.
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*/
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#include "ssh.h"
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#define RSA_EXPONENT 37 /* we like this prime */
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#if 0 /* bignum diagnostic function */
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static void diagbn(char *prefix, Bignum md)
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{
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int i, nibbles, morenibbles;
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static const char hex[] = "0123456789ABCDEF";
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printf("%s0x", prefix ? prefix : "");
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nibbles = (3 + bignum_bitcount(md)) / 4;
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if (nibbles < 1)
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nibbles = 1;
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morenibbles = 4 * md[0] - nibbles;
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for (i = 0; i < morenibbles; i++)
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putchar('-');
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for (i = nibbles; i--;)
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putchar(hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]);
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if (prefix)
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putchar('\n');
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}
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#endif
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int rsa_generate(struct RSAKey *key, int bits, progfn_t pfn,
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void *pfnparam)
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{
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Bignum pm1, qm1, phi_n;
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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, -1, -0x1D57C4 / (bits / 2));
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pfn(pfnparam, -2, -0x1D57C4 / (bits - bits / 2));
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pfn(pfnparam, -3, 5);
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/*
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* We don't generate e; we just use a standard one always.
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*/
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key->exponent = bignum_from_short(RSA_EXPONENT);
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/*
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* Generate p and q: primes with combined length `bits', not
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* congruent to 1 modulo e. (Strictly speaking, we wanted (p-1)
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* and e to be coprime, and (q-1) and e to be coprime, but in
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* general that's slightly more fiddly to arrange. By choosing
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* a prime e, we can simplify the criterion.)
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*/
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key->p = primegen(bits / 2, RSA_EXPONENT, 1, 1, pfn, pfnparam);
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key->q = primegen(bits - bits / 2, RSA_EXPONENT, 1, 2, pfn, pfnparam);
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/*
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* Ensure p > q, by swapping them if not.
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*/
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if (bignum_cmp(key->p, key->q) < 0) {
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Bignum t = key->p;
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key->p = key->q;
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key->q = t;
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}
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/*
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* Now we have p, q and e. All we need to do now is work out
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* the other helpful quantities: n=pq, d=e^-1 mod (p-1)(q-1),
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* and (q^-1 mod p).
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*/
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pfn(pfnparam, 3, 1);
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key->modulus = bigmul(key->p, key->q);
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pfn(pfnparam, 3, 2);
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pm1 = copybn(key->p);
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decbn(pm1);
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qm1 = copybn(key->q);
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decbn(qm1);
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phi_n = bigmul(pm1, qm1);
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pfn(pfnparam, 3, 3);
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freebn(pm1);
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freebn(qm1);
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key->private_exponent = modinv(key->exponent, phi_n);
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pfn(pfnparam, 3, 4);
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key->iqmp = modinv(key->q, key->p);
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pfn(pfnparam, 3, 5);
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/*
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* Clean up temporary numbers.
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*/
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freebn(phi_n);
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return 1;
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}
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