One Key Cryptosystems and Latin Arrays

Abstract

In the first seven chapters, theory of finite automata is developed. From now on, some applications to cryptography are presented. This chapter proposes a canonical form for one key cryptosystems in the sense: for any one key cryptosystem without data expansion and with bounded error propagation implementable by a finite automaton, we always find a one key cryptosystem in canonical form such that they are equivalent in behavior. This assertion is affirmative by results concerned on feedforward invertibility in Sects. 1.5 and 5.2. Under the framework of the canonical form, the next is to study its three components: an autonomous finite automaton, a family of permutations, and a nonlinear transformation. Theory of autonomous finite automata has been discussed in the preceding chapter. As to permutational family, theory of Latin arrays, a topic on combinatory theory, is presented in this chapter also.