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

For academic year: 2024/25 Last Updated: 21 November 2024

MAT-30038 - Number Theory and Cryptography
Coordinator: Paul Truman Room: MAC2.16 Tel: +44 1782 7 33246
Lecture Time: See Timetable...
Level: Level 6
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2024/25

None

Available as a Free Standing Elective

No

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.

Aims
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

1: Assignment weighted 15%
Number Theory Assignment


2: Assignment weighted 15%
Cryptography Assignment


3: Exam weighted 70%
2-hour unseen examination


The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. Details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 21 November 2024