Chaos Robustness and Computation Complexity of Piecewise Linear and Smooth Chaotic Chua's System

D. Vinko, K. Miličević, Ivan Vidovic, Bruno Zoric
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Abstract

Chaotic systems are often considered to be a basis for various cryptographic methods due to their properties, which correspond to cryptographic properties like confusion, diffusion and algorithm (attack) complexity. In these kinds of applications, chaos robustness is desired. It can be defined by the absence of periodic windows and coexisting attractors in some neighborhoods of the parameter space. On the other hand, when used as a basis for neuromorphic modeling, chaos robustness is to be avoided, and the edge-of-chaos regime is needed. This paper analyses the robustness and edge-of-chaos for Chua’s systems, comprising either a piecewise linear or a smooth function nonlinearity, using a novel figure of merit based on correlation coefficient and Lyapunov exponent. Calculation complexity, which is important when a chaotic system is implemented, is evaluated for double and decimal data types, where needed calculation time varies by a factor of about 1500, depending on the nonlinearity function and the data type. On the other hand, different data types result in different number precision, which has some practical advantages and drawbacks presented in the paper.
分段线性光滑混沌Chua系统的混沌鲁棒性和计算复杂度
混沌系统通常被认为是各种密码方法的基础,因为它们的性质对应于密码的性质,如混乱、扩散和算法(攻击)复杂性。在这些类型的应用中,需要混沌鲁棒性。它可以定义为在参数空间的某些邻域中不存在周期窗口和共存吸引子。另一方面,当用作神经形态建模的基础时,要避免混沌鲁棒性,并且需要混沌边缘状态。本文采用一种基于相关系数和李雅普诺夫指数的新的优值图,分析了分段线性和光滑函数非线性Chua系统的鲁棒性和混沌边缘。计算复杂性在实现混沌系统时是很重要的,对双精度和十进制数据类型进行了评估,其中所需的计算时间变化了约1500倍,这取决于非线性函数和数据类型。另一方面,不同的数据类型导致不同的数字精度,这在本文中有一些实际的优点和缺点。
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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