In this paper, we have proposed the design of an analog two-dimensional (2D) discrete-time chaotic oscillator. 2D chaotic systems are studied because of their more complex chaotic behavior compared to one-dimensional (1D) chaotic systems. The already published works on 2D chaotic systems are mainly focused either on the complex analytical combinations of familiar 1D chaotic maps such as Sine map, Logistic map, Tent map, and so on, or off-the-shelf component-based analog circuits. Due to complex hardware requirements, neither of them is feasible for hardware-efficient integrated circuit (IC) implementations. To the best of our knowledge, this proposed work is the first-ever report of an analog 2D discrete-time chaotic oscillator design that is suitable for hardware-constrained IC implementations. The chaotic performance of the proposed design is analyzed with bifurcation plots, the transient response, 2D Lyapunov exponent, and correlation coefficient measurements. It is demonstrated that the proposed design exhibits promising chaotic behavior with low hardware cost. The real-world application of the proposed 2D chaotic oscillator is presented in a random number generator (RNG) design. The applicability of the RNG in cryptography is verified by passing the generated random sequence through four standard statistical tests namely, NIST, FIPS, TestU01, and Diehard.

中文翻译：

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用于模拟 IC 的二维混沌振荡器

在本文中，我们提出了模拟二维 (2D) 离散时间混沌振荡器的设计。研究二维混沌系统是因为它们的混沌行为比一维 (1D) 混沌系统更复杂。已经发表的关于二维混沌系统的著作主要集中在熟悉的一维混沌映射的复杂分析组合上，例如正弦映射、逻辑映射、帐篷映射等，或者是现成的基于组件的模拟电路。由于复杂的硬件要求，它们都不适用于硬件高效的集成电路 (IC) 实现。据我们所知，这项提议的工作是第一份关于模拟二维离散时间混沌振荡器设计的报告，该设计适用于硬件受限的 IC 实现。使用分岔图、瞬态响应、2D Lyapunov 指数和相关系数测量来分析所提出设计的混沌性能。结果表明，所提出的设计表现出有前途的混沌行为，硬件成本低。所提出的 2D 混沌振荡器的实际应用以随机数发生器 (RNG) 设计形式呈现。通过将生成的随机序列通过 NIST、FIPS、TestU01 和 Diehard 四个标准统计测试来验证 RNG 在密码学中的适用性。所提出的 2D 混沌振荡器的实际应用以随机数发生器 (RNG) 设计形式呈现。通过将生成的随机序列通过 NIST、FIPS、TestU01 和 Diehard 四个标准统计测试来验证 RNG 在密码学中的适用性。所提出的 2D 混沌振荡器的实际应用以随机数发生器 (RNG) 设计形式呈现。通过将生成的随机序列通过 NIST、FIPS、TestU01 和 Diehard 四个标准统计测试来验证 RNG 在密码学中的适用性。