On the Constructions of New Symmetric Ciphers Based on Nonbijective Multivariate Maps of Prescribed Degree

Abstract

The main purpose of this paper is to introduce stream ciphers with the nonbijective encryption function of multivariate nature constructed in terms of algebraic graph theory. More precisely, we describe the two main symmetric algorithms for creation of multivariate encryption transformations based on three families of bipartite graphs with partition sets isomorphic to Kn, where K is selected as the finite commutative ring. The plainspace of the algorithm is Ω={x∣∑xi∈K⁎,  x∈Kn}⊂Kn,Ω≅K⁎×Kn-1. The second algorithm is a generalization of the first one with using the jump operator, where generalized encryption map has an essentially higher degree in comparison with the previous version. Moreover, the degree of this generalized map is not bounded by some constant. This property guarantees resistance of the cipher to linearization attacks.