On the security of public-key algorithms based on chebyshev polynomials over the finite field zN

Xiaofeng Liao; Fei Chen; Kwok-Wo Wong

doi:10.1109/TC.2010.148

On the security of public-key algorithms based on chebyshev polynomials over the finite field z_N

Xiaofeng Liao
, Fei Chen
, Kwok-Wo Wong

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

49 Citations (Scopus)

Abstract

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. © 2006 IEEE.

Original language	English
Article number	5487511
Pages (from-to)	1392-1401
Journal	IEEE Transactions on Computers
Volume	59
Issue number	10
DOIs	https://doi.org/10.1109/TC.2010.148
Publication status	Published - 2010

Research Keywords

Chaos
Chebyshev polynomials
period distribution
public-key cryptography
security analysis

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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 \$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. {\textcopyright} 2006 IEEE.",

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AU - Wong, Kwok-Wo

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AB - 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 $Z-N$. Then, we modify the original algorithm to make it suitable for practical purpose. Its security under some existing models is also discussed in detail. © 2006 IEEE.

KW - Chaos

KW - Chebyshev polynomials

KW - period distribution

KW - public-key cryptography

KW - security analysis

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JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

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