Issue No. 10 - October (2010 vol. 59)
ISSN: 0018-9340
pp: 1392-1401
Kwok-Wo Wong , The City University of Hong Kong
Fei Chen , Chongqing Univeristy, Chongqing
Xiaofeng Liao , Chongqing Univeristy, Chongqing
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.
INDEX TERMS
Chaos, Chebyshev polynomials, period distribution, public-key cryptography, security analysis.
CITATION
Kwok-Wo Wong, Fei Chen, Xiaofeng Liao, "On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$", IEEE Transactions on Computers, vol. 59, no. , pp. 1392-1401, October 2010, doi:10.1109/TC.2010.148