Permutation Polynomials over Finite Fields and their application to Cryptography

The 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

Coding Theory-Based Cryptopraphy: McEliece Cryptosystems in Sage

Unlike RSA encryption, McEliece cryptosystems are considered secure in the presence of quantum computers. McEliece cryptosystems leverage error-correcting codes as a mechanism for encryption. The open-source math software Sage provides a suitable environment for implementing and exploring McEliece cryptosystems for undergraduate research. Using our Sage implementation, we explored Goppa codes, McEliece cryptosystems, and Stern’s attack against a McEliece cryptosystem

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler