On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

Authors:
Xiaofeng Liao;Fei Chen;Kwok-wo Wong
Affiliations:
Chongqing Univeristy, Chongqing;Chongqing Univeristy, Chongqing;The City University of Hong Kong
Venue:
IEEE Transactions on Computers
Year:
2010

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CIMMACS'11/ISP'11 Proceedings of the 10th WSEAS international conference on Computational Intelligence, Man-Machine Systems and Cybernetics, and proceedings of the 10th WSEAS international conference on Information Security and Privacy
Security analysis of the public key algorithm based on Chebyshev polynomials over the integer ring ZN

Information Sciences: an International Journal

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Abstract

In this paper, the period distribution of sequences generated by Chebyshev polynomials over the finite field $Z_N$ is analyzed. It is found that the distribution is unsatisfactory if N (the modulus) is not chosen properly. Based on this finding, we present an attack on the public-key algorithm based on Chebyshev polynomials over $Z_N$. Then, we modify the original algorithm to make it suitable for practical purpose. Its security under some existing models is also discussed in detail.