The application of modified Chebyshev polynomials in asymmetric cryptography

Marcin Lawnik; Adrian Kapczyński

doi:10.7494/csci.2019.20.3.3307

Authors

Marcin Lawnik Silesian University of Technology, Faculty of Applied Mathematics http://orcid.org/0000-0002-0235-0878
Adrian Kapczyński Silesian University of Technology, Faculty of Applied Mathematics

DOI:

https://doi.org/10.7494/csci.2019.20.3.3307

Keywords:

asymmetric encryption, Chebyshev polynomials, chaos

Abstract

Based on Chebyshev polynomials, you can create an asymmetric cryptosystem that allows secure communication. Such a cryptosystem uses the fact that these polynomials form a semi-group due to the composition operation. This article presents new cryptosystems that use other than semi-group property dependencies. Based on these dependencies as well as modifications of Chebyshev's polynomials, two cryptosystems have been proposed. The presented analysis shows that their security is the same as in the case of algorithms associated with the problem of discrete logarithms. The article also shows methods that allow faster calculation of Chebyshev polynomials.

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