构建 GF(2n) 上的非生成二维整数域超混沌映射并应用于并行哈希算法

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2023-12-11 DOI:10.1142/s021812742350181x

Yafei Cao, Hongjun Liu, Dongya Xu

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引用次数: 0

摘要

为了解决现有混沌图在数字平台上的有限精度效应问题，首先构造了一个在GF([公式：见正文])上的非enerate二维整数域超混沌图（2D-IDHCM）。然后，给出了 2D-IDHCM 满足 Devaney 混沌定义的证明和 Lyapunov 指数有界性的证明。动态行为的分析结果表明，2D-IDHCM 在一定参数范围内具有遍历性和较大的 Lyapunov 指数，并且没有动态退化。最后，为了验证 2D-IDHCM 的实用性，设计了一种基于 2D-IDHCM 的密钥哈希函数，它可以吸收变长信息，并行生成 256、512、1024 位或更长的哈希值。实验结果表明，2D-IDHCM 具有更好的动态性能，可以在实际应用中使用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.