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Mathematics of Cryptography and Communications (MSc)

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Course overview

This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory. During the course critical awareness of problems in information transmission, data compression and cryptography is raised, and the mathematical techniques which are commonly used to solve these problems are explored.

The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography and our academic staff include several leading researchers in these areas. Students on the programme have the opportunity to carry out their dissertation projects in cutting-edge research areas and to be supervised by experts.

The transferable skills gained during the MSc will open up a range of career options as well as provide a solid foundation for advanced research at PhD level.

Key facts

Key facts about the course
Qualification Master of Science
Duration 1 year full-time
Department and Faculty Mathematics, Faculty of Science
Partner institution(s) --
Course director Dr Teo Sharia 
+44 (0)1784 414331
Contact for more information Ms Jenny Lee
+44 (0)1784 443093

Fees / funding

Please visit the Fees and funding pages for the latest information about tuition fees and the different sources of funding which may be available to you.

How to apply

Applications for entry to all our full-time postgraduate degrees can be made online.

Further information on making an application, including the documentation that you will need to submit with the application is available in the How to apply section of this site.

If you are interested in applying to Royal Holloway, why not arrange a visit to our campus to see for yourself what academic and student life is like here. More information on arranging visits is available on our Open days pages.


Entry requirements

Entry criteria:

UK Upper Second Class Honours degree (2:1), or equivalent, in Mathematics.

Exceptionally, at the discretion of the course director, qualifications in other subjects
(for example, physics or computer science) or degrees of lower classification may be considered.

English language requirements:

IELTS 6.5 overall and a minimum of 5.5 in all other subscores. For equivalencies, please see here

Applicants come from a diverse range of backgrounds and we accept a broad range of qualifications but a solid foundation in mathematics is needed.

Students from overseas should visit the International pages for information on the entry requirements from their country and further information on English language requirements. Royal Holloway offers a Pre-Master’s Diploma for International Students and English language pre-sessional courses, allowing students the opportunity to develop their study skills and English language before starting their postgraduate degree.


Why choose this course?

  • You will be provided with a solid mathematical foundation and a knowledge and understanding of the subjects of cryptography and communications preparing you for research or professional employment in this area.
  • The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.
  • You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.
  • After completing the course former students have a good foundation for the next step of their career both inside and outside academia.

Department research and industry highlights

The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry.

Course content and structure

You will study eight courses as well as complete a main project under the supervision of a member of staff.

Core courses:

Advanced Cipher Systems
Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed as well as methods for obtaining confidentiality and authentication.

In this unit, you will investigate the problems of data compression and information transmission in both noiseless and noisy environments.

Theory of Error-Correcting Codes
The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Public Key Cryptography
This course introduces some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves. Several important public key cryptosystems are studied, such as RSA, Rabin, ElGamal Encryption, Schnorr signatures; and modern notions of security and attack models for public key cryptosystems are discussed.

Main project
The main project (dissertation) accounts for 33.3% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.


Additional courses:

Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory
‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms
In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics
In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory
You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory
Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.


On completion of the course graduates will have:

  • a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications
  • the appropriate background in information theory and coding theory enabling them to understand and be able to apply the theory of communication through noisy channels
  • the appropriate background in algebra and number theory to develop an understanding of modern public key cryptosystems
  • a critical awareness of problems in information transmission and data compression, and the mathematical techniques which are commonly used to solve these problems
  • a critical awareness of problems in cryptography and the mathematical techniques which are commonly used to provide solutions to these problems
  • a range of transferable skills including familiarity with a computer algebra package, experience with independent research and managing the writing of a dissertation.

View the full course specification for Mathematics of Cryptography and Communications (MSc) in the Programme Specification Repository


Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 66.7% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 33.3%.

Employability & career opportunities

Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security manager at London Underground.


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