## QUANTITATIVE METHODS AND CRYPTOGRAPHY

 SHE Level 3 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M3G124460 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 -linear programming Introduction to Cryptography -substitution and transposition ciphers -required cryptosystem properties: One-Time Pad -sequential and block encryption modes: -symmetric cryptographic systems: DES and AES. -Public Key systems: RSA, Diffie-Hellman -implementing cryptosystems -cryptanalysis strategies Probability and Applications -discrete and continuous distributions: Uniform, Normal and Exponential -an introduction to Queuing Theory: The standard models -finite state Markov models -random Number Generators -sampling distributions Statistics -populations and samples -simple Hypothesis Testing (proportion and mean) -Confidence Intervals -bivariate data: correlation, best fit

### Learning Outcomes

On successful completion of this module a student should be able to:Critically analyse the operation of standard codes and crypto-systemsCreate and critically analyse simple mathematical models in the area of networking and securityApply elementary statistical tests and interpret the results

### Teaching / Learning Strategy

Three hours lecture and two hours of tutorial per week. 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 Mao, W., Modern Cryptography: Theory and Practice, Prentice Hall, (2004). ISBN-13: 978-0130669438 -360b7 Martin K,. Everyday Cryptography, OUP (2012) ISBN-13: 978-0199695591 Piper F., Cryptography: A Very Short Introduction, (2002). ISBN-13: 978-0192803153

### Transferrable Skills

General Cognitive Skills C1 Logical thinking and problem solving. C2 Critical analysis. -709 C3 Effective information management, retrieval and research skills for independent enquiry and learning. Communication & Numeracy -709 D1 Communication skills (Electronic, written, oral and listening) necessary to make effective presentation of a technical nature (information, ideas, problems and their solution) to a range of audiences. D2 Numeracy in both understanding and presenting cases involving a quantitative dimension. Autonomy, accountability and working with others E1 Awareness of my strengths and weaknesses E2 Creativity, innovation and independent thinking. -709 E3 Appreciating and desiring the need for reflection and planning for self-learning and improving performance as the foundation for CPD and life-long learning. E6 Ability to prioritise tasks and time management (organising and planning work).

### Module Structure

Activity Total Hours
Tutorials (PT) 12.00
Independent Learning (PT) 134.00
Tutorials (FT) 24.00
Lectures (FT) 36.00
Independent Learning (FT) 122.00
Assessment (FT) 18.00
Assessment (PT) 18.00
Lectures (PT) 36.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 70.00 35% Unseen written exam
Coursework 1 n/a 30.00 35% Quantitative modelling exercises