Constructing a Nondegenerate 2D Integer-Domain Hyperchaotic Map Over GF(2n) with Application in Parallel Hashing
Yafei Cao, Hongjun Liu, Dongya Xu
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.