Keyed hash function using Bernoulli shift map

Abstract

Chaos-based cryptography involves real number computations and hence produces slow algorithms. In order to address this issue, the existing approaches use piece-wise linear maps that speed up computations. High-dimensional linear maps have been chosen to avoid dynamical degradation. In this paper, we claim that a single one-dimensional nonlinear chaotic map can produce ergodic orbits in a fast manner. We propose a keyed hash function that takes advantage of the interplay between chaos-based dynamics and Bernoulli shift dynamics. The proposed Bernoulli keyed hash function proves to be an efficient scheme achieving speeds on par with the existing schemes in the literature. Extensive validation is carried out at byte, block and the whole message level for collision resistance and sensitivity to key analysis. We provide empirical analysis to show that the proposed scheme is preimage and second preimage resistant.