# Coding and Cryptography

## Course summary

Course code: MATH1137
Level: 6
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Stephen Lakin

## Specification

### Pre and co requisites

Linear Algebra and Applications.

### Aims

Some of the most exciting and relevant applications of mathematics in the modern world, especially with our increasing reliance on technology, can be found in coding theory and cryptography. A rapidly-developing subject, the transmission and security of data often relies heavily on mathematical techniques.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Apply mathematical techniques to coding and cryptography,
2. Use a variety of codes and ciphers.

### Indicative content

Introduction to coding theory. Parity checking, error detection and correction, code bounds. Examples of simple codes such as Hamming codes and Hadamard codes. Linear codes, polynomial codes and cyclic codes, including historical and modern examples. Modern applications such as Reed-Solomon codes.

Introduction to cryptography. Historical ciphers, including substitution ciphers, stream ciphers (e.g. linear shift register) and block ciphers (e.g. DES/AES). Public-key cryptography, including the mathematical theory behind the ciphers (e.g. RSA, elliptic curves). Privacy, authentication, integrity and non-repudiation. Digital signatures and PKI infrastructures. Future developments, including quantum computing and quantum cryptography.

Employability skills and the relevance to modern industry will be built into the course material.

### Teaching and learning activity

The material will be delivered through a flexible mix of lectures, tutorials and independent study.

### Assessment

Summative assessment:
Coursework - 50%
Coursework covering both learning outcomes. May include selected tutorial exercises and/or an investigation into certain codes.

Examination - 50%
Examination covering both learning outcomes (1-2)

Formative assessment: weekly tutorial exercises