A Pseudorandom Number Generator Based on the Chaotic Map and Quantum Random Walks

Zhao, Wenbo; Chang, Zhenhai; Ma, Caochuan; Shen, Zhuozhuo

doi:10.3390/e25010166

Cited by 9 publications

(2 citation statements)

References 37 publications

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“…Another issue with PRNGs based on chaotic maps is having a narrow range of parameters suitable for exhibiting dynamical chaos, which reduces the keyspace in encryption tasks. To expand the keyspace of the designed system, Zhao et al [20] combined a sequence based on quantum random walks with chaotic system outputs, creating a new system with high randomization, unpredictability, and uniform output distribution. The digital implementation of chaotic maps also has a negative influence on the properties of PRNGs.…”

Section: Introductionmentioning

confidence: 99%

Fractal Tent Map with Application to Surrogate Testing

Kopets,

Rybin,

Vasilchenko

et al. 2024

Fractal Fract

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Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.

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Section: Introductionmentioning

confidence: 99%

Fractal Tent Map with Application to Surrogate Testing

Kopets,

Rybin,

Vasilchenko

et al. 2024

Fractal Fract

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“…However, problems such as unpredictability and short cycle may occur when implementing chaotic systems in digital devices (digital chaos) [21,22]. This will result in successful attacks on a cryptographic systems based on the original digital chaotic maps.…”

Section: Introductionmentioning

confidence: 99%

A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

Zhang,

Ma,

Zhao

et al. 2023

Mathematics

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For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems.

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