QUANTITATIVE MODELLING AND CRYPTOGRAPHY

 SHE Level 3 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M3G121115 Module Leader Salma Mohamed School School of Computing, Engineering and Built Environment Subject Cyber Security and Networks Trimester A (September start)

Pre-Requisite Knowledge

Mathematics for Computing (M1I322951) or equivalent

Summary of Content

The module covers selected topics in the area of discrete mathematics with particular emphasis on mathematical modelling as a problem solving tool. The module will cater for a wide range of mathematical ability and there is a strong emphasis on enhancing student's personal study skills. The ideas and techniques developed in this module are selected to underpin the advanced studies and research undertaken by students in the areas of network reliability and security.

Syllabus

Network Algorithms -definition of a network -modelling with networks -matchings: Hall's theorem and applications -linear programming Introduction to Cryptography -substitution and transposition ciphers -required cryptosystem properties: One-Time Pad -sequential and block encryption modes: Electronic Code Book (ECB), Cipher block Chaining (CBC), Cipher Feedback (CFB) -symmetric cryptographic systems: DES and AES. -Public Key systems: RSA, Diffie-Hellman -cryptanalysis strategies -implementing cryptosystems Probability and Applications -discrete and continuous distributions: Uniform, Normal and Exponential -an introduction to Queuing Theory: The standard models -finate state markov models -random Number Generators: strengths and weaknesses -sampling distributions Statistics -populations and samples -simple Hypothesis Testing (proportion and mean) -Confidence Intervals -bivariate data: correlation, best fit -time series

Learning Outcomes

On completion of this module the student should be able to:-model network problems using graph theory-solve network problems using linear programming -describe the operation of standard codes and crypto-systems-describe the properties of cryptosystems-develop and apply simple finite state Markov chains-apply elementary statistical tests and interpret the results-calculate using random variables

Teaching / Learning Strategy

Three hours lecture and two hours of tutorial per week. Directed study will require the completion or extension of the applications covered in tutorials. Students will be given activities to explore in their own time, in particular directed study on the use of publicly available software. Students will be given the opportunity to undertake formative self-assessment tests on each topic area. The whole of week 12 is set aside for preparation for the final assessment. Feedback will be supplied through the marking and supplied solutions to self-assessment tests; in tutorials though discussions with tutor; and through individual comments on the marked coursework. Directed study will require the undertaking of specified tutorial material; the completion or extension of the applications covered in tutorials; and the opportunity for the student to dig deeper through identified 'advanced' topics (either supplied, or obtainable from identified sources such as the World Wide Web - 'advanced' topics are not assessable).

Newman, M.E.J, Networks: An Introduction, OUP (2010). ISBN-13: 978-0-19-920665-0 . Griffiths, D., Head First Statistics, Pragma (2008). ISBN-13: 978-056527587 Schafer, G., Security in Fixed and wireless Networks: An introduction to securing data communications, John Wiley and Sons (2003). ISBN-13: 0-470-86370-6 Mao, W., Modern Cryptography : Theory and Practice, Mao, Prentice Hall, (2004). ISBN-13: 978-0130669438 Klima, R.E. & Sigma, N.P. Cryptology: Classical & Modern with Maplets, Chapman Hall/CRC (2012). ISBN:9781439872413

Transferrable Skills

Traditional Academic Skills - specialist knowledge, ability to apply knowledge, logical thinking, problem-solving, ability to use numerical data. Personal Development Skills - self-discipline, self-reliance, independence desire to go on learning, ability to reflect Enterprise or Business Skills - ability to prioritise tasks, time management.

Module Structure

Activity Total Hours
Tutorials (PT) 12.00
Lectures (FT) 36.00
Tutorials (FT) 24.00
Independent Learning (PT) 138.00
Independent Learning (FT) 126.00
Assessment (FT) 14.00
Assessment (PT) 14.00
Lectures (PT) 36.00

Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 70.00 35% Unseen written exam
Coursework 1 0.00 30.00 35% Coursework