Mathematics of Cryptography and Communications

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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.

You will study four core units and four elective units as well as complete a main project under the supervision of a member of staff.

Core course units:

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.
Channels- 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 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Elective course units:

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;
Combinatorics- 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.

Equivalent to at least a British Second Class Honours Degree. English Language Requirements CAE score: (read more) Cambridge English: Advanced (CAE) is part of the Cambridge English suite and is targeted at a high level (IETLS 6.5-8.0). It is an international English language exam set at the right level for academic and professional success. Developed by Cambridge English Language Assessment - part of the University of Cambridge - it helps you stand out from the crowd as a high achiever. 75 (Grade B)