New Algorithms for Lattice-Based Cryptography

Given the potential for functional quantum computing to be available in the next few decades - and the insecurity of current number theoretic encryption schemes against quantum computing - it is pertinent to develop a new standard for post quantum-cryptography. The National Institute of Standards and Technology (NIST) announced a call for competition in 2016 and the cryptographic community have responded with many proposals.

This project is based in one of the major areas: lattice cryptography. A process that often appears in lattice based crypto-schemes is that of sampling from discrete Gaussian distributions over lattices. This is a hard distribution to sample from efficiently and previous sampling algorithms have given a lower bound on the standard deviation. The project aims to investigate the use of new methods for sampling from such distributions, with the goal of developing an efficient algorithm for sampling beyond such a lower bound.

To achieve this requires the knowledge of various areas of mathematics, including number theory to study the fundamental structures of lattices and functional analysis for the convergence. This research aligns with EPSRC research areas of Number theory and Theoretical Computer Science.