Title :
On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$
Author :
Liao, Xiaofeng ; Chen, Fei ; Wong, Kwok-Wo
Author_Institution :
Dept. of Comput. Sci. & Eng., Chongqing Univ., Chongqing, China
Abstract :
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.
Keywords :
Chebyshev approximation; chaos; polynomials; public key cryptography; statistical distributions; Chebyshev polynomials; finite field ZN; public-key algorithms; Chebyshev approximation; Galois fields; Polynomials; Public key; Zinc; Chaos; Chebyshev polynomials; period distribution; public-key cryptography; security analysis.;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.2010.148
