On the complexity of analysis of automata over a finite ring

Abstract

A general scheme is investigated that is destined for obtaining estimates based on the cardinality of subsets of a fixed set of automata over some finite commutative-associative ring with unit element. A scheme is proposed to solve parametric systems of polynomial equations based on classes of associated elements of the ring. Some general characteristics of automata over the ring are established.

Analysis of families of hash functions defined by automata over a finite ring

“…One of such applied directions is the investigation of the possibility of using reversible automata over finite rings as mathematical models of stream ciphers [1][2][3][4], which is topical in connection with the passage to combinatorial-algebraic models in solving problems of modern cryptography [5,6]. Another direction is connected with investigating the possibility of application of automata over finite rings in solving problems of compact representation of information.…”

Some subsets of automata over a finite ring

“…In [3,4], autonomous automata and, in [5], Mealy and Moore automata over a ring Z p k are characterized (where p is a prime number, k Î N), and, in [6], models and methods underlying the analysis of automata over a finite commutative-associative ring with identity [7] are considered.…”