Towards an operad-based cryptography: Applications of commutative operads

Abstract

In this paper we show the use of commutative operads in public-key cryptography. Commutative operads were introduced by S.N. Tronin in 2006. They are a special case of algebraic operads and a natural generalization of commutative algebraic theories. We consider some cryptographic protocols based on commutative operads. For the protocol of the creation a common secret key, we describe and investigate its implementation and cryptographic security in particular cases.