Studies, Public Key Cryptography Based On Automata Theory

Nowadays the computer network technologies have rapidly developed. The securities of the information in the network are more and more important. We know the traditional Cryptosystem use the same key to encrypt and decrypt the information. When we use it to encrypt our information for transfer, we must transfer the key to the receiver too. If the enemy intercepts the key, we will lose the security of our information. So we can see the traditional Cryptosystem is not suitable for the secret communication in the network. But the Public-Key Cryptosystem has two keys: public-key and secret-key. We can use the public-key to encrypt and the secret-key to decrypt. This tells us that it can resolve the problem faced by the traditional Cryptosystem.The Finite Automaton Public Key Cryptosystem bases on invertibility theory of finite automata was proposed by Tao Renji and Chen Shihua in 1985 .In this paper ,we firstly discuss all kinds of public-key cryptosystems based on finite automaton theory and improved two of them. Secondly we introduce the composite cryptosystems and a new system is proposed which use the composite cryptosystems and finite automaton. This algorithm can easily be used to digital signature and it is secure and still retains merits of early FAPKC's such as the fast speed .relatively short public key ,etc. The compound finite automaton of the cryptosystem which we design consists of more than two finite automata. So it's hard to break into this cryptosystem.