Break Finite Automata Public Key Cryptosystem

In this paper we break a 10-year's standing public key cryptosystem, Finite Automata Public Key Cryptosystem(FAPKC for short). The security of FAPKC was mainly based on the di culty of nding a special common left factor of two given matrix polynomials. We prove a simple but previously unknown property of the input-memory nite automata. By this property, we reduce the basis of the FAPKC's security to the same problem in module matrix polynomial rings. The problem turns out to be easily solved. Hence, we can break FAPKC by constructing decryption automata from the encryption automaton(public key). We describe a modi cation of FAPKC which can resist above attack.