Abstract: It is a maxim of sound computer security practice that a cryptographic key should have only a single use. But S.Haber and B. Pinkas show that in many cases, the simultaneous use of related keys for two cryptosystems, e.g. for a public key encryption system and for a public key signature system, does not compromise their security. Finite automata public key cryptosystem can be used for both encryption algorithm and signature algorithm, it is a combining cryptosystem. In this paper, it is proved that the combined use of finite automata public key cryptosystem does not compromise the security of the cryptosystem.