{"title":"Constructing a Nondegenerate 2D Integer-Domain Hyperchaotic Map Over GF(2n) with Application in Parallel Hashing","authors":"Yafei Cao, Hongjun Liu, Dongya Xu","doi":"10.1142/s021812742350181x","DOIUrl":null,"url":null,"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.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"26 6","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Bifurcation and Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s021812742350181x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.
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