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