application of algebraic-ring in key exchange protocol

In this article, we present a non-interactive key exchange protocol with a faster run time, which is based on a module-lwe. the structure of protocol is designed just by relating the error vectors of both sides, without any use of a reconciliation mechanism. the idea is that as error vectors get closer to each other the success probability of the protocol increases. the innovation in this scheme is the use of high-order bits in the keys computed by both sides. compared to the existing lattice-based key-exchange protocols, this scheme leads to lower computational complexity and longer parameters.