Constructing a Nondegenerate 2D Integer-Domain Hyperchaotic Map Over GF(2n) with Application in Parallel Hashing

Abstract

To solve the problem of finite precision effect of existing chaotic maps on digital platform, first, a nondegenerate 2D integer-domain hyperchaotic map (2D-IDHCM) over GF([Formula: see text]) is constructed. Then, the proof that 2D-IDHCM satisfies Devaney’s definition of chaos and the proof of boundedness of Lyapunov exponents are given. The analytic results of dynamic behaviors demonstrate that 2D-IDHCM has ergodicity and large Lyapunov exponents within a certain parameter range, and without dynamic degradation. Finally, to verify the practicality of 2D-IDHCM, a keyed hash function based on 2D-IDHCM is designed, which can absorb variable-length message and generates 256, 512, 1024-bit or longer hash values in parallel. The experimental results demonstrate that 2D-IDHCM has better dynamic behaviors, and can be used in practical applications.