An interactive proof via some generalized reduced rings

Algebra is one of the important fields of mathematics. It concerns in the study and manipulates of mathematical symbols. It also concerns with study of abstractions such as groups, rings and fields. Ring theory is the most attractive category of algebra in the area of cryptography. Recently, many algebraic cryptosystem protocols based on non-commutative algebraic structures such as; authentication, key exchange, and encryption-decryption processes are adopted. In this paper, we employ the algebraic structure called nil Armendariz (NA) rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is implemented and illustrated through numerical example, and its soundness and completeness are proved.