Chaotic Encryption Algorithm Based on Gingerbreadman Map with Adaptive Symmetry

Year 2025, Volume: 7 Issue: 1, 31 - 41

Petr Fedoseev , Dmitry Pesterev , Vladislav Rozhkov , Vyacheslav Rybin , Denis Butusov

https://doi.org/10.51537/chaos.1500547

Abstract

The security of sensitive data is a crucial issue in the information age. While the existing encryption protocols cannot always guarantee the required level of security due to the rapidly increasing computational capability of attackers, developing new cryptographically strong encryption techniques is of great importance in modern computer science. One of the advanced approaches in the field of cryptography is chaos-based encryption. In this study, we propose an efficient algorithm for arbitrary multimedia data encryption using the novel finite-difference scheme with adaptive symmetry based on the Gingerbreadman chaotic map. In the experimental part of the study, we use several analysis techniques to prove the presence of chaos in the dynamics of the reported discrete map and investigate the dependence between system dynamics and symmetry coefficient. Parametric chaotic sets and the largest Lyapunov exponent plots are given to evaluate the dynamics of the investigated finite-difference model. NIST statistical tests were applied to assess the properties of the developed pseudo-random numbers generator, and correlation analysis was performed to evaluate the secrecy of the encrypted image. It is experimentally shown, that varying the symmetry coefficient can significantly increase the keyspace for the encryption algorithm based on the symmetric Gingerbreadman map. The results of this study can be used to develop encryption software, including secure text messengers or stream data ciphers.

Keywords

Discrete chaos, Gingerbreadman map, Pseudo-random number generation, Chaos-based encryption, Symmetric map

Supporting Institution

Russian Science Foundation (RSF)

Project Number

20-79-10334

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