A reconciliation approach to key generation based on Module-LWE

We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice
$E_{8}$
, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus
$q$
with comparable error probability and similar requirements in terms of bandwidth. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.