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 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.