Post-quantum cryptography using multivariate polynomial systems

Multivariate public-key cryptography (MPKC) is one of the four most common branches of post-quantum cryptography, describing cryptosystems based on solving systems of multivariate polynomials. An important step in the cryptanalysis of MPKC system is finding a Gröbner basis for the system. My research focusses on adapting generic Gröbner Basis algorithms to families of multivariate polynomial systems with specific structures. I am currently looking at multivariate linearised polynomials, which have not been studied in great detail.

Additionally I am exploring applications of the HHL quantum algorithm for solving systems of multivariate polynomials, in particular Boolean systems.

This project is linked to the EPSRC Cyber Security research theme

It is part of the nature of Cyber Security - and a key reason for the urgency in developing new research approaches - that it now is a concern of every section of society, and so the successful CDT will have a very broad impact indeed. We will ensure impact for:

* The IT industry; vendors of hardware and software, and within this the IT Security industry;

* High value/high assurance sectors such as banking, bio-medical domains, and critical infrastructure, and more generally the CISO community across many industries;

* The mobile systems community, mobile service providers, handset and platform manufacturers, those developing the technologies of the internet of things, and smart cities;

* Defence sector, MoD/DSTL in particular, defence contractors, and the intelligence community;

* The public sector more generally, in its own activities and in increasingly important electronic engagement with the citizen;

* The not-for-profit sector, education, charities, and NGOs - many of whom work in highly contended contexts, but do not always have access to high-grade cyber defensive skills.

Impact in each of these will be achieved in fresh elaborations of threat and risk models; by developing new fundamental design approaches; through new methods of evaluation, incorporating usability criteria, privacy, and other societal concerns; and by developing prototype and proof-of-concept solutions exhibiting these characteristics. These impacts will retain focus through the way that the educational and research programme is structured - so that the academic and theoretical components are directed towards practical and anticipated problems motivated by the sectors listed here.