Paper 2020/076

Wyner-Ziv reconciliation for key exchange based on Ring-LWE

Charbel Saliba and Laura Luzzi and Cong Ling

Abstract

We consider a key encapsulation mechanism (KEM) based on ring-LWE where reconciliation is performed on an $N$-dimensional lattice using Wyner-Ziv coding. More precisely, we consider Barnes-Wall lattices and use Micciancio and Nicolosi's bounded distance decoder with polynomial complexity $\mathcal{O}(N \log^2(N))$. We show that in the asymptotic regime for large $N$, the achievable key rate is $\Theta(\log N)$ bits per dimension, while the error probability $P_e$ vanishes exponentially in $N$. Unlike previous works, our scheme does not require a dither.