Finite Automata and Application to Cryptography The automated inverse theory in cryptography, points to autonomous finite automata, which is relative to the canonical form for one-key cryptosystems based on finite automata, the public key encryption based on finite automata for one-key cipher can be executed by finite automata.
A finite automaton is considered as a natural model for ciphers. The method of converting Ra Rb has been introduced to deal with the structural problem of such automata; then, the public key encryption based on finite automata and a focal type for one key cipher that can be executed by finite automates with limited error propagation and without spreading data is provided.  

What is the application of Finite Automata in cryptography?
In the area of symmetric cryptography , finite automaton have been applied to model the additive differential probability of exclusive-or  and the differential analysis of S-function ref 1 ref 2

another example of automata application on linear model of modular addition ref