Key Exchange and Encryption Schemes Based on Non-commutative Skew Polynomials

Abstract

In this paper we introduce a new key exchange algorithm (Diffie-Hellman like) based on so called (non-commutative) skew polynomials. The algorithm performs only polynomial multiplications in a special small field and is very efficient. The security of the scheme can be interpretated in terms of solving binary quadratic equations or exhaustive search of a set obtained through linear equations. We give an evaluation of the security in terms of precise experimental heuristics and usual bounds based on Groebner basis solvers. We also derive an El Gamal like encryption protocol. We propose parameters which give 3600 bits exchanged for the key exchange protocol and a size of key of 3600 bits for the encryption protocol, with a complexity of roughly 2²³ binary operations for performing each protocol. Overall this new approach based on skew polynomials, seems very promising, as a good tradeoff between size of keys and efficiency.