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

In this paper, a definition of Chebyshev polynomials over GF(q)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.

Research highlights
► A definition of Chebyshev polynomials over GF(q) is introduced.
► A public-key encryption algorithm based on such polynomials is analyzed.
► The security of the algorithm and the discrete logarithm problem are discussed.