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

Let K be a general nite commutative ring. We refer to a family gn, n = 1, 2, . . . of bijective polynomial multivariate maps of K as a family with invertible decomposition gn = g ng 2 n . . . g k n, such that the knowledge of the composition of g n allows computation of g i n for O(n ) (s > 0) elementary steps. A polynomial map g is stable if all non-identical elements of kind g, t > 0 are of the same degree. We construct a new family of stable elements with invertible decomposition. This is the rst construction of the family of maps based on walks on the bipartite algebraic graphs de ned over K, which are not edge transitive. We describe the application of the above mentioned construction for the development of stream ciphers, public key algorithms and key exchange protocols. The absence of edge transitive group essentially complicates cryptanalysis.