On New Examples of Families of Multivariate Stable Maps and their Cryptographical Applications

Abstract

Let K be a general finite commutative ring. We refer to a familyg^n, n = 1; 2;... of bijective polynomial multivariate maps of K^n as a family with invertible decomposition gn = g^1^n g^2^n...g^k^n , such that the knowledge of the composition of g^2^nallows computation of g^2^n for O(n^s) (s > 0) elementary steps. Apolynomial map g is stable if all non-identical elements of kind g^t, t > 0 are of the same degree.We construct a new family of stable elements with invertible decomposition.This is the first construction of the family of maps based on walks on the bipartitealgebraic graphs defined over K, which are not edge transitive. We describe theapplication of the above mentioned construction for the development of streamciphers, public key algorithms and key exchange protocols. The absence of edgetransitive group essentially complicates cryptanalysis.