Public-key encryption based on Chebyshev polynomials over GF(q)

Authors:
J. B. Lima;D. Panario;R. M. Campello de Souza
Affiliations:
Polytechnic School of Pernambuco, University of Pernambuco, Rua Benfica, 455, CEP 50750-470, Recife, Brazil;School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada;Department of Electronics and Systems, Federal University of Pernambuco, C.P. 7800, Recife, Brazil
Venue:
Information Processing Letters
Year:
2010

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Abstract

In this paper, a definition of Chebyshev polynomials over GF(q) is introduced. Based on such polynomials, a generalization of a recently proposed public-key encryption algorithm that uses Chebyshev polynomials over prime finite fields is presented. Since our approach uses a finite field trigonometry, it is also possible to analyze some security aspects of the mentioned algorithm in the extension field scenario. The security of the algorithm relies in part on the difficulty of computing discrete logarithms over finite fields.