A Nondegenerate n-Dimensional Hyperchaotic Map Model with Application in a Keyed Parallel Hash Function

Mengdi Zhao, Hongjun Liu
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Abstract

The construction of multidimensional discrete hyperchaotic maps with ergodicity and larger Lyapunov exponents is desired in cryptography. Here, we have designed a general [Formula: see text]D ([Formula: see text]) discrete hyperchaotic map ([Formula: see text]D-DHCM) model that can generate any nondegenerate [Formula: see text]D chaotic map with Lyapunov exponents of desired size through setting the control matrix. To verify the effectiveness of the [Formula: see text]D-DHCM, we have provided two illustrative examples and analyzed their dynamic behavior, and the results demonstrated that their state points have ergodicity within a sufficiently large interval. Furthermore, to address the finite precision effect of the simulation platform, we analyzed the relationship between the size of Lyapunov exponent and the randomness of the corresponding state time sequence of the [Formula: see text]D-DHCM. Finally, we designed a keyed parallel hash function based on a 6D-DHCM to evaluate the practicability of the [Formula: see text]D-DHCM. Experimental results have demonstrated that [Formula: see text]D discrete chaotic maps constructed using [Formula: see text]D-DHCM have desirable Lyapunov exponents, and can be applied to practical applications.
一个非退化的n维超混沌映射模型及其在键控并行哈希函数中的应用
在密码学中,需要构造具有遍历性和较大李雅普诺夫指数的多维离散超混沌映射。在这里,我们设计了一个通用的[公式:见文]D([公式:见文])离散超混沌映射([公式:见文]D- dhcm)模型,该模型可以通过设置控制矩阵生成任意具有所需大小的李雅普诺夫指数的非退化[公式:见文]D混沌映射。为了验证[公式:见文]D-DHCM的有效性,我们给出了两个示例,并分析了它们的动力行为,结果表明它们的状态点在足够大的区间内具有遍历性。此外,为了解决仿真平台的有限精度效应,我们分析了李雅普诺夫指数的大小与[公式:见文]D-DHCM对应状态时间序列随机性之间的关系。最后,我们设计了一个基于6D-DHCM的键控并行哈希函数,以评估[公式:见文]D-DHCM的实用性。实验结果表明,使用[公式:见文]D- dhcm构造的D离散混沌映射具有理想的Lyapunov指数,可以应用于实际应用。
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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