Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Bugce Eminaga Tatlicioglu; Hatice Aktöre

doi:10.17776/csj.1557049

EN

Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Abstract

This study introduces and analyzes a novel quadratic Lorenz-like attractor and demonstrates its application as a pseudo-random number generator (PRNG). A theoretical and numerical investigation of the system dynamics is conducted, including equilibrium point analysis, Jacobian eigenvalues, dissipativity, and Lyapunov exponents. The results indicate that the quadratic modification alters the system dynamics, producing stronger chaotic intensity than the classical Lorenz system. This is supported by larger positive Lyapunov exponents and a non-integer Lyapunov dimension (≈2.40), which reflects a more complex attractor geometry. Numerical simulations, time series, phase projections, and bifurcation analysis further illustrate the rich nonlinear dynamics of the system. To validate its applicability, the chaotic sequences generated by the attractor were subjected to standard statistical evaluations, including the NIST SP800-22, Diehard, and ENT test suites. A dataset of 18 million samples was employed, significantly exceeding the minimum requirement for meaningful validation, and the results confirm that the proposed generator produces high-quality randomness. The importance of this work lies in demonstrating that the quadratic Lorenz-like attractor offers both strong chaotic intensity and relatively simple structure, making it a promising candidate for cryptographic applications, secure communications, and other domains requiring reliable pseudo-random number generation.

Keywords

Ethical Statement

no ethıcal

References

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Details

Primary Language

English

Subjects

Dynamical Systems in Applications , Applied Mathematics (Other)

Journal Section

Research Article

Authors

Bugce Eminaga Tatlicioglu ^*
0000-0001-8854-4464
Cyprus

Hatice Aktöre
0000-0003-2455-3681
Cyprus

Publication Date

December 30, 2025

Submission Date

September 27, 2024

Acceptance Date

November 27, 2025

Published in Issue

Year 2025 Volume: 46 Number: 4

DOI

https://doi.org/10.17776/csj.1557049

IZ

https://izlik.org/JA67AC36WJ

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RIS / Bibtex

APA

Eminaga Tatlicioglu, B., & Aktöre, H. (2025). Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. Cumhuriyet Science Journal, 46(4), 891-901. https://doi.org/10.17776/csj.1557049

Öz

Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Abstract

Keywords

Ethical Statement

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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