In this paper, a new definition of Chebyshev polynomials over prime finite fields is introduced. Our approach uses a finite field trigonometry and reveals some aspects concerning the security of a recently proposed public-key encryption algorithm based on those polynomials. Particularly, we show that recovering the corresponding plaintext from a given ciphertext involves the discrete logarithm problem.

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Conference 2008 IEEE International Symposium on Information Theory, ISIT 2008
Lima, J.B., De Souza, R.M.C. (R. M. Campello), & Panario, D. (2008). Security of public-key cryptosystems based on chebyshev polynomials over prime finite fields. In IEEE International Symposium on Information Theory - Proceedings (pp. 1843–1847). doi:10.1109/ISIT.2008.4595307