Sending secret messages is no any longer the business of spies. We are living in times with exponentially increasing electronic information exchange, and almost every day we make use of modern encryption systems (e.g., smart cards). Many of these cryptosystems, like the famous RSA, rely on the observation that it is simple to multiply integers but, conversely, that it is rather diﬃcult to ﬁnd the prime factorization of a given large integer. Factoring methods for large integers can be used to test how secure such cryptosystems are. In this chapter we shall consider the continued fraction method CFRAC.