Dr Andrew Lewis-Pye

This course is available on the MSc in Applicable Mathematics. This course is available as an outside option to students on other programmes where regulations permit.

Students must have completed Algorithms and Computation (MA407).

Students should be taking the course MA407 Algorithms and Computation or have taken an equivalent course to provide a basic knowledge of algorithms, and should have experience with proofs and proof techniques used in pure mathematics.

This course provides an introduction, for students with a mathematical background, to the applications of mathematics in information theory, coding theory, cryptography, and related areas. The course will cover mathematical aspects of the following topics: Noiseless coding, the Kraft-McMillan criterion, optimal coding, entropy, Shannon's first theorem; Noisy channels, capacity, system entropy; Error-correcting codes, decoding rules, bounds, construction and properties of linear and cyclic codes; Structure of natural languages, redundancy, the frequency table, making and breaking cryptosystems, historic examples; Public-key cryptography, complexity issues, the RSA system, authentication schemes, the ElGamal system, elliptic curve cryptography.

20 hours of lectures and 9 hours of seminars in the MT. 1 hour of seminars in the LT. 2 hours of lectures in the ST.

N L Biggs, Codes, An Introduction to Information, Communication and Cryptography: G A Jones & J M Jones, Information and Coding Theory; C M Goldie & R G E Pinch, Communication Theory; D J A Welsh, Codes and Cryptography; D T Stinson, Cryptography Theory and Practice.

Exam (90%, duration: 2 hours) in the main exam period.
Coursework (10%) in the MT.