--- /dev/null
+/*
+ * RSA key generation.
+ */
+
+#include "ssh.h"
+
+#define RSA_EXPONENT 37 /* we like this prime */
+
+static void diagbn(char *prefix, Bignum md) {
+ int i, nibbles, morenibbles;
+ static const char hex[] = "0123456789ABCDEF";
+
+ printf("%s0x", prefix ? prefix : "");
+
+ nibbles = (3 + ssh1_bignum_bitcount(md))/4; if (nibbles<1) nibbles=1;
+ morenibbles = 4*md[0] - nibbles;
+ for (i=0; i<morenibbles; i++) putchar('-');
+ for (i=nibbles; i-- ;)
+ putchar(hex[(bignum_byte(md, i/2) >> (4*(i%2))) & 0xF]);
+
+ if (prefix) putchar('\n');
+}
+
+int rsa_generate(struct RSAKey *key, struct RSAAux *aux, int bits,
+ progfn_t pfn, void *pfnparam) {
+ Bignum pm1, qm1, phi_n;
+
+ /*
+ * 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, -1, -0x1D57C4/(bits/2));
+ pfn(pfnparam, -2, -0x1D57C4/(bits-bits/2));
+ pfn(pfnparam, -3, 5);
+
+ /*
+ * We don't generate e; we just use a standard one always.
+ */
+ key->exponent = bignum_from_short(RSA_EXPONENT);
+ diagbn("e = ",key->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.)
+ */
+ aux->p = primegen(bits/2, RSA_EXPONENT, 1, 1, pfn, pfnparam);
+ aux->q = primegen(bits - bits/2, RSA_EXPONENT, 1, 2, pfn, pfnparam);
+
+ /*
+ * Ensure p > q, by swapping them if not.
+ */
+ if (bignum_cmp(aux->p, aux->q) < 0) {
+ Bignum t = aux->p;
+ aux->p = aux->q;
+ aux->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, 3, 1);
+ key->modulus = bigmul(aux->p, aux->q);
+ pfn(pfnparam, 3, 2);
+ pm1 = copybn(aux->p);
+ decbn(pm1);
+ qm1 = copybn(aux->q);
+ decbn(qm1);
+ phi_n = bigmul(pm1, qm1);
+ pfn(pfnparam, 3, 3);
+ freebn(pm1);
+ freebn(qm1);
+ diagbn("p = ", aux->p);
+ diagbn("q = ", aux->q);
+ diagbn("e = ", key->exponent);
+ diagbn("n = ", key->modulus);
+ diagbn("phi(n) = ", phi_n);
+ key->private_exponent = modinv(key->exponent, phi_n);
+ pfn(pfnparam, 3, 4);
+ diagbn("d = ", key->private_exponent);
+ aux->iqmp = modinv(aux->q, aux->p);
+ pfn(pfnparam, 3, 5);
+ diagbn("iqmp = ", aux->iqmp);
+
+ /*
+ * Clean up temporary numbers.
+ */
+ freebn(phi_n);
+
+ return 1;
+}
~mdw / sgt / putty / blobdiff