Journal
IEEE TRANSACTIONS ON COMPUTERS
Volume 59, Issue 10, Pages 1392-1401Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TC.2010.148
Keywords
Chaos; Chebyshev polynomials; period distribution; public-key cryptography; security analysis
Funding
- National Natural Science Foundation of China [60973114, 60703035]
- Natural Science Foundation of CQ CSTC [2009BA2024, 2008BB2193]
- State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University [2007DA10512709207]
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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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