Quantum Safe Construction of Authentication and Key Exchange Based on Module Lattices

An authenticated mobile key exchange is necessary for post quantum secure communication over a public channel. It allows two entities to create a secure and unique session key for every communication session. We feel a need to design two party efficient and secure authenticated key agreement. We have also observed all the protocols given above are based on learning with error assumption over a finite ring. The ”Module Learning with Errors” assumption is the more appropriate choice among ”Learning with Errors” and ”Ring Learning with Errors” for designing practical password-authenticated key exchange protocols. With the help of ”Module Learning with Errors” assumption, and by lowering the number of ring polynomials, several implementations of the protocols can be realized. Therefore, this paper contains quantum safe, efficient, and practical ”Module Learning with Errors” assumption based authenticated key agreement protocol. The protocol’s security analysis is presented within the framework of the random oracle model.