Algebraic Authentication Scheme

Abstract

A zero knowledge proof is a type of authentication scheme, which gives no knowledge beyond the authenticity for identifying an entity. Ring theory plays an important role in designing of a novel algorithm for zero knowledge proof through using of a particular class of non-commutative rings. In this article, we employ the notion of nil 3-Armendariz rings to plan a new algorithm for zero knowledge proof. Our main approach is to build the algebraic structure of the zero knowledge proof depends on the stipulation in the definition of the nil 3-Armendariz rings. The proposed protocol is clarified via numerical simulation example, and its soundness and completeness are evidenced. Finally, we found that the proposed protocol satisfies the completeness, the soundness in the sense that, there is 50% chance of catching a cheating prove, and the proposed protocol has the property of zero knowledge.