Group authenticated key exchange schemes via learning with errors

Abstract

We propose a novel passively secure group key exchange GKE scheme via learning with errors LWE. Then, we extend it to a GKE scheme via ring-learning with errors. We show the security analysis of our GKE schemes based on the LWE assumption and the security property of secure sketch in the random oracle model. One of our innovative points is a simple and practical robust extractor that serves as the key derivation function. Based on our GKE scheme, we build a group authenticated key exchange scheme and then prove its security under the LWE assumption and the secure property of secure sketch in the random oracle model. The proposed scheme not only provides authenticated key exchange security and mutually authenticated security but also needs only two round communications to negotiate a shared session key. Copyright © 2015John Wiley & Sons, Ltd.