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On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$
October 2010 (vol. 59 no. 10)
pp. 1392-1401
Xiaofeng Liao, Chongqing Univeristy, Chongqing
Fei Chen, Chongqing Univeristy, Chongqing
Kwok-Wo Wong, The City University of Hong Kong
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.

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Index Terms:
Chaos, Chebyshev polynomials, period distribution, public-key cryptography, security analysis.
Xiaofeng Liao, Fei Chen, Kwok-Wo Wong, "On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$," IEEE Transactions on Computers, vol. 59, no. 10, pp. 1392-1401, Oct. 2010, doi:10.1109/TC.2010.148
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