Increasing Ranks of Linear Finite Automata and Complexity of FA Public Key Cryptosystem

The encryption algorithm of finite automata (FA) public key cryptosystem is implemented by a weakly invertible finite automata (WIFA) which is composed of a nonlinear WIFA with delay 0 and a linear WIFA with delay τ. In this paper, we proved that such an automaton bears the same properties as the linear WIFA and the increasing ranks of the latter are key factors to affecting the former. A probabilistic algorithm is given to realize a ciphertext attack, and its complexity is analysed through the increasing ranks of the linear WIFA. The size of the parameters for safe linear WIFA is estimated.