In the case of RSA, distinct moduli that share exactly one prime factor produces public keys that appear to be distinct but can be computed by taking the GCD. If an attacker can find two moduli N1 and N2 with the same prime factor p, but with dif-ferent second prime factors q1 and q2, the attacker can compute both moduli very easily by computing their GCD p and dividing to find q1 and q2.