[Adlai]

From http://nosuchlabs.com/theory

An RSA public key consists of a modulus n and an exponent e. Modulus n is a product of two large primes, p and q. If one knows p or q, one can derive the private key corresponding to the given public key.

A typical GPG public key contains one or more RSA moduli, depending on the number of sub-keys.

Under certain conditions, a public key modulus will share a common factor with an existing modulus belonging to someone else. This may happen if both keys were generated on a system with a thoroughly-broken entropy source, or if a particular GPG implementation has been back-doored.