Statement on the Value of Pure Mathematics in Security

The Heilbronn Institute for Mathematical Research (HIMR) is a strategic partnership between GCHQ and UK universities within which academic mathematicians contribute to problems of national security. HIMR brings pure mathematics to bear on problems of crucial importance to GCHQ’s twin intelligence and cybersecurity missions, thereby helping to protect the United Kingdom and its citizens.

The security protocols used on the internet and in modern e-commerce are built upon ideas from pure mathematics. Perhaps most famously the security of the RSA cryptographic protocol is based on the difficulty of factoring large integers. Other cryptographic schemes are similarly based on hard problems from different parts of pure mathematics such as discrete logarithms, elliptic curves, lattices, error correcting codes and multivariate systems, and many other constructions from number theory, geometry, combinatorics and discrete mathematics. Pure mathematics is crucial in designing and analysing modern security protocols.

HIMR benefits from expertise in other parts of mathematics including probability, statistics, data science and quantum information theory. We are privileged to have had more than 200 mathematicians as members of our Institute since our foundation in 2005.

Part of the mission of HIMR is to support pure mathematics across the UK, and it does so in a variety of ways, including: the employment of fellows (who are encouraged to spend half of their time on publishable research), the development of a mathematical community with expertise in security and coding, and the provision of grants for mathematical events, outreach activities, and research activities.