Hash function based on hierarchy of 2D piecewise nonlinear chaotic maps

Abstract

In this paper, at first a hierarchy of two-dimensional piecewise nonlinear chaotic map with an invariant measure is constructed. These maps have interesting features such as invariant measure, ergodicity and the possibility of KS-entropy calculation. Then by using significant properties of chaos such as one-way computation, and random-like behavior, which is favorable to hash functions, a novel hash function based on these chaotic maps, is suggested. The nonlinearity and complexity of 2D piecewise map yields strong bit confusion and diffusion with the low expense of floating point computations. Theoretical analysis and simulation results indicate that the proposed scheme has desired statistical properties, high flexibility and strong collision resistance. The scheme is efficient, practicable and reliable, with high potential to be adopted for network security and secure communications.