https://doi.org/10.1140/epjp/s13360-026-07421-1
Regular Article
SRA: A sine-based reconstruction approach to improve 2D chaotic map performance
1
Department of Basic Education, Dalian Polytechnic University, 116034, Dalian, China
2
School of Information Science and Engineering, Dalian Polytechnic University, 116034, Dalian, China
3
School of Information Science and Engineering, Jinan University, 250022, Jinan, China
4
Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University, 06830, Ankara, Türkiye
5
Key Laboratory of Computing Power Network and Information Security, Ministry of Education, National Supercomputer Center in Jinan, Qilu University of Technology (Shandong Academy of Sciences), 250353, Jinan, China
6
Shandong Provincial Key Laboratory of Computer Networks, Shandong Fundamental Research Center for Computer Science, 250013, Jinan, China
a
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b
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Received:
18
December
2025
Accepted:
5
February
2026
Published online:
19
February
2026
Abstract
Chaotic keystreams play a critical role in image encryption, and their performance directly affects the security of encryption systems. However, some classical two-dimensional (2D) chaotic maps suffer from insufficient chaotic performance, such as limited attractor coverage and low system complexity. To address these issues, this paper proposes a Sine-based Reconstruction Approach (SRA) aimed at improving the performance of existing 2D chaotic maps. The proposed method first preserves the iterative framework of the original chaotic model, keeping its core dynamical relationships and parameter mechanisms unchanged; then, a new nonlinear transformation is applied to the output at each iteration, reconstructing the state variables. By mapping the original outputs through a periodic or strongly nonlinear function, the method significantly enhances the system’s nonlinear coupling, expands phase-space coverage, and improves the randomness, uniformity, and complexity of the generated sequences. The composite construction strategy of “original map + nonlinear transformation” effectively enhances the chaotic system without altering its fundamental structure, resulting in more complex and diverse dynamic behaviors, which are more suitable for high-security image encryption and random sequence generation. Experimental results on the classical Duffing, Henon, and Tinkerbell maps show that the enhanced SRA-DM (Duffing map), SRA-HM (Henon map), and SRA-TM (Tinkerbell map) outperform the original maps in terms of chaotic performance, indicating that this method provides a general and effective approach for high-security encryption and complex system design.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
