From Chaos to Pseudorandomness : A Case Study on the 2-D Coupled Map Lattice

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • Yong Wang
  • Zhuo Liu
  • Leo Yu Zhang
  • Fabio Pareschi
  • Gianluca Setti

Related Research Unit(s)


Original languageEnglish
Pages (from-to)1324-1334
Journal / PublicationIEEE Transactions on Cybernetics
Issue number2
Online published3 Dec 2021
Publication statusPublished - Feb 2023


Applying the chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems are usually heuristic, without theoretic guarantee for the resultant communication scheme. Among all the primitives for secure communications, it is well accepted that (pseudo) random numbers are most essential. Taking the well-studied 2-D coupled map lattice (2D CML) as an example, this article performs a theoretical study toward pseudorandom number generation with the 2D CML. In so doing, an analytical expression of the Lyapunov exponent (LE) spectrum of the 2D CML is first derived. Using the LEs, one can configure system parameters to ensure the 2D CML only exhibits complex dynamic behavior, and then collect pseudorandom numbers from the system orbits. Moreover, based on the observation that least significant bit distributes more evenly in the (pseudo) random distribution, an extraction algorithm E is developed with the property that when applied to the orbits of the 2D CML, it can squeeze uniform bits. In implementation, if fixed-point arithmetic is used in binary format with a precision of z bits after the radix point, E can ensure that the deviation of the squeezed bits is bounded by 2-z. Further simulation results demonstrate that the new method not only guides the 2D CML model to exhibit complex dynamic behavior but also generates uniformly distributed independent bits with good efficiency. In particular, the squeezed pseudorandom bits can pass both NIST 800-22 and TestU01 test suites in various settings. This study thereby provides a theoretical basis for effectively applying the 2D CML to secure communications. © 2021 IEEE.

Research Area(s)

  • 2-D coupled map lattice, chaos, Lyapunov exponent (LE), random number generator, secure communication

Citation Format(s)

From Chaos to Pseudorandomness: A Case Study on the 2-D Coupled Map Lattice. / Wang, Yong; Liu, Zhuo; Zhang, Leo Yu et al.
In: IEEE Transactions on Cybernetics, Vol. 53, No. 2, 02.2023, p. 1324-1334.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review