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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On the Effectiveness of a Common Attack to Chebyshev Chaotic Encryption Scheme

by
Xiaoqi Liu
1,† and
Guillermo Morales-Luna
2,*,†
1
Mathematics & Computer Science Program, Guangdong Technion Israel Institute of Technology, Shantou 515063, China
2
Computer Science Department, Cinvestav, Mexico City 07300, Mexico
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Cryptography 2025, 9(1), 10; https://doi.org/10.3390/cryptography9010010
Submission received: 7 December 2024 / Revised: 18 January 2025 / Accepted: 27 January 2025 / Published: 29 January 2025
Versions Notes

Abstract

Chebyshev polynomials define a rather canonical chaotic cryptosystem and some strong attacks have been designed to that cryptosystem. We report the numerical experiments performed with multiple precision arithmetic using conventional software as gmp and mpfr to test the Chebyshev cryptosystem and Bergamo’s attack. As a conclusion, we point out the relevance in the cryptosystem robustness of the number of significant digits (length) of plaintexts and the number of correct digits (precision) of the arithmetical calculations. Furthermore, after the observed experimental results, we use techniques of Numerical Analysis to explain the occurrences of the observed results and to reinforce the importance of the above-mentioned parameters ℓ and m.
Keywords: chaotic encryption; Chebyshev polynomials; Bergamo’s attack; multiple precision arithmetic chaotic encryption; Chebyshev polynomials; Bergamo’s attack; multiple precision arithmetic

Share and Cite

MDPI and ACS Style

Liu, X.; Morales-Luna, G. On the Effectiveness of a Common Attack to Chebyshev Chaotic Encryption Scheme. Cryptography 2025, 9, 10. https://doi.org/10.3390/cryptography9010010

AMA Style

Liu X, Morales-Luna G. On the Effectiveness of a Common Attack to Chebyshev Chaotic Encryption Scheme. Cryptography. 2025; 9(1):10. https://doi.org/10.3390/cryptography9010010

Chicago/Turabian Style

Liu, Xiaoqi, and Guillermo Morales-Luna. 2025. "On the Effectiveness of a Common Attack to Chebyshev Chaotic Encryption Scheme" Cryptography 9, no. 1: 10. https://doi.org/10.3390/cryptography9010010

APA Style

Liu, X., & Morales-Luna, G. (2025). On the Effectiveness of a Common Attack to Chebyshev Chaotic Encryption Scheme. Cryptography, 9(1), 10. https://doi.org/10.3390/cryptography9010010

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