Security of public-key cryptosystems based on Chebyshev polynomials over prime finite fields

Abstract

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.