Even More Practical Key Exchanges for the Internet using Lattice Cryptography

In 2014, Peikert described the first practical lattice-based key exchange that is provably secure and provides perfect forward security. However, his presentation lacks concrete proposals for parameters. We aim to provide a clear description of how the algorithm can be implemented along with some analysis for potential parameters. Previously in 2015, Singh considered the simpler case, as chosen by Bos, Costello, Naehrig and Stebila in 2014, of cyclotomic rings with power-of-two degree. In this work we focus on the case of cyclotomic rings with degree p− 1 for prime p. This allows for a greater degree of flexibility in choosing lattice dimension, which determines the security level and efficiency of the scheme. We describe the necessary arithmetic setup and then present Peikert’s DiffieHellman-like key exchange along with security, correctness and implementation analysis.