MAT-30038 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

Programme/Approved Electives for 2024/25

Available as a Free Standing Elective

Co-requisites

None

Prerequisites

MAT-20025 Abstract Algebra.

Barred Combinations

None.

Description for 2024/25

Number Theory studies the properties of the natural numbers and the integers. It is one of the oldest and most beautiful areas of Pure Mathematics, and also one of the most active areas of modern research. Recently, ideas from Number Theory have been applied to problems in Cryptography, such as the design of ciphers and secret sharing schemes. This module will trace the development of the subject from ancient problems to these modern applications.

This module aims to introduce students to Number Theory, which is one of the oldest and most beautiful branches of Pure Mathematics, and also illustrate how some concepts from Number Theory have had unexpected applications to modern problems in cryptography.

Intended Learning Outcomes

evaluate single linear congruences or systems of simultaneous linear congruences, either determining a solution or providing a mathematical proof that none exist: 1,3
state the definition of a primitive root modulo a natural number, and apply this definition to solve theoretical problems concerning the enumeration and properties of primitive roots: 1,3
select and apply suitable algorithms to address number-theoretic problems such as primality testing, integer factorisation, or the discrete logarithm problem: 1,2,3
explain and evaluate the construction and properties of a variety of cryptographic systems such as secret sharing schemes, symmetric and asymmetric (public key) ciphers, or signature schemes: 2,3
appraise the strengths and weaknesses of different cryptographic systems, and make judgements on appropriate techniques to attack poorly implemented systems: 2,3

Study hours

Lectures: 30 Hours
Examples Classes: 6 Hours
Unseen examination : 2 hours
Independent Study: 92 Hours
Preparation of Coursework: 20 Hours

School Rules

None.

Description of Module Assessment