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

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