Mathematics & Cryptography

Complexity. Innovation. Seemingly unsolvable challenges.
We apply the latest technologies in a variety of ways.

Mathematics & Cryptography

Our mathematicians work in a wide range of fields, using a variety of techniques across many disciplines to solve complex real-world problems and applying their skills collaboratively in multi-disciplinary teams.  The strongest requirement for any mathematician at GCHQ is the ability to generate creative ideas to address these problems, and a willingness to learn new concepts; your career could involve working in many different areas.

Working at GCHQ, you will enjoy the opportunity to influence decisions made by government, the armed forces and law enforcement agencies. Mathematical expertise sits at the heart of our technical capability and you’ll be applying your analytical skills in areas such as large datasets, cryptography, internet security and mobile communications.

Underpinning much of our work is our high performance computing environment.  We are involved in solving some of GCHQ’s hardest computational problems by writing highly-optimised implementations of algorithms on a variety of computers with specialised architectures.

We have produced some samples of the entrance tests that form part of the assessment for a role as a mathematician at GCHQ so that you will be familiar with the format when you apply.

Sample GCHQ Mathematics Aptitude Test
Sample GCHQ Mathematics Applications Test

mathematics & cryptography roles

What our people say

What do you most enjoy about working at GCHQ?

I am interested in my work

My manager is considerate of my life outside work

I am treated with respect by the people I work with

I am proud when I tell others I am part of GCHQ

I understand how the work of GCHQ makes a difference to the UK

EXPLORE MATHEMATICS & CRYPTOGRAPHY ROLES & RESPONSIBILITIES

Mathematics & Cryptography R&D

With a 1st or 2:1 degree in Maths, you’ll be working alongside some of the UK’s leading mathematical thinkers.

We devise the UK’s cryptography and provide consultation on its application in government systems.  This may involve designing and implementing bespoke algorithms or protocols for use in constrained or difficult environments, or securing systems that will require protection for many years in the future. To do this effectively, we need to apply a range of cryptanalytic techniques to understand potential weaknesses. This involves combining ideas from probability and statistics, group theory, combinatorics, complexity theory and efficient algorithm implementation with an enthusiasm for problem solving.

Of course, strong cryptographic primitives alone do not necessarily make something secure; we need to understand how cryptographic technologies are used in everyday life, and analyse weaknesses at a product, protocol, system or hardware level by fusing the cryptanalytic techniques mentioned above with computer security skills.

Cryptographic Security R&D

We devise the UK’s cryptography and provide consultation on its application in government systems.  This may involve designing and implementing bespoke algorithms or protocols for use in constrained or difficult environments, or securing systems that will require protection for many years in the future.  We need to understand how cryptographic technologies are used in everyday life, working closely with vendors and their products.

Public key cryptography is the cornerstone on which the modern digital world is built. We lead UK research in this area to help protect the UK and to advise government on algorithm design and use. For this, we must understand mathematical problems in integer factorisation, discrete logarithms and elliptic curves, so we are interested in a variety of pure mathematical research topics, with a focus on number theory.

Quantum resistant algorithms, designed to resist attack from a hypothetical quantum computer, will form the core of the next generation of cryptography.  We are involved in the evaluation of new protocols, bringing an understanding of quantum systems engineering principles to bear on cryptographic thinking.

Data Science and Information Processing

We carry out research into designing and applying state-of-the-art machine learning and graph analysis techniques to discover patterns in large data stores or high volume data sets, and build statistical models to enhance processing or pattern detection for cyber defence.  Similar approaches are takento develop real-time analytics for streaming data, or tools for automated analysis of various media.

We often receive data in new, unrecognised or corrupted formats and need to be able to analyse it to extract the underlying information.  A combination of mathematical analysis and a willingnessto generate and test new ideas, building on limited knowledge, is required for this type of work.

Meet our team
Find your perfect role at GCHQ

Departments and Roles at GCHQ