pair<Rsa::KeyPub, RsaCrt::KeyPriv> RsaCrt::generateRSAKeys(uint exponent, uint keySizeBits)
{
- mpz_class phi;
+ mpz_class phi, d;
Rsa::KeyPub kPub;
KeyPriv kPriv;
do
{
- kPub.e = kPriv.e = exponent;
+ kPub.e = exponent;
kPriv.p = Rand::randPrime(keySizeBits / 2);
kPriv.q = Rand::randPrime(keySizeBits / 2);
- kPriv.n = kPub.n = kPriv.p * kPriv.q;
+ kPub.n = kPriv.p * kPriv.q;
phi = (kPriv.p - 1) * (kPriv.q - 1);
- } while (mpz_invert(kPriv.d.get_mpz_t(), kPub.e.get_mpz_t(), phi.get_mpz_t()) == 0);
+ // d = e^-1 (mode phi).
+ } while (mpz_invert(d.get_mpz_t(), kPub.e.get_mpz_t(), phi.get_mpz_t()) == 0);
- kPriv.dp = kPriv.d % (kPriv.p - 1);
- kPriv.dq = kPriv.d % (kPriv.q - 1);
+ kPriv.dp = d % (kPriv.p - 1);
+ kPriv.dq = d % (kPriv.q - 1);
+ // qInv = q^-1 (mod p).
mpz_invert(kPriv.qInv.get_mpz_t(), kPriv.q.get_mpz_t(), kPriv.p.get_mpz_t());
return make_pair(kPub, kPriv);
}
mpz_class RsaCrt::sign(const mpz_class& m, const KeyPriv& kPriv)
+{
+ return sign(m, kPriv, false);
+}
+
+mpz_class RsaCrt::signWithFaultySp(const mpz_class& m, const KeyPriv& kPriv)
+{
+ return sign(m, kPriv, true);
+}
+
+mpz_class RsaCrt::sign(const mpz_class& m, const KeyPriv& kPriv, bool withError)
{
mpz_class sp, sq;
mpz_powm_sec(sp.get_mpz_t(), m.get_mpz_t(), kPriv.dp.get_mpz_t(), kPriv.p.get_mpz_t());
mpz_powm_sec(sq.get_mpz_t(), m.get_mpz_t(), kPriv.dq.get_mpz_t(), kPriv.q.get_mpz_t());
+ if (withError)
+ mpz_combit(sp.get_mpz_t(), 42); // Flip the fourty second bit.
+
return sq + ((kPriv.qInv * (sp - sq)) % kPriv.p) * kPriv.q;
}