Permutation Polynomials over Finite Fields and their application to Cryptography
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AbstractThe aim of the paper is the study of Permutation Polynomials over finite fields and their application to cryptography. In this paper, I will begin by a brief review of finite fields, define permutation polynomials over finite fields and their properties. I will present old results such as Hermite-Dickson’s Theorem as well as some most recent ones. After introducing cryptog- raphy, I will give a historical overview, by explaining some cryptosystems such as RSA and ElGamal. Finally, I will present some cryptographical protocols based on Permutation Polynomials over Finite Fields.
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