Analysis of BCNS and Newhope Key-exchange Protocols

Abstract

Lattice-based cryptographic primitives are believed to offer resilience against attacks by quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key-exchange protocols based on hard problems in lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. In this work we present an analysis of Ring-LWE based key-exchange mechanisms and compare two implementations of Ring-LWE based key-exchange protocol: BCNS and NewHope. This is important as NewHope protocol implementation outperforms state-of-the art elliptic curve based Diffie-Hellman key-exchange X25519, thus showing that using quantum safe key-exchange is not only a viable option but also a faster one. Specifically, this thesis compares different reconciliation methods, parameter choices, noise sampling algorithms and performance.