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

In this paper, the period distribution of sequences generated by Chebyshev polynomials over the finite field ZN 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 ZN. 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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