MA3036 - Cryptography and Number Theory (2017/18)
|Module specification||Module approved to run in 2017/18, but may be subject to modification|
|Module title||Cryptography and Number Theory|
|Module level||Honours (06)|
|Credit rating for module||15|
|School||School of Computing and Digital Media|
|Running in 2017/18||No instances running in the year|
This module is an introduction to modern ideas in cryptology and its applications. Increase of storage, manipulation, and transfer of data on computer networks requires effective encryption techniques. This module will provide insight into some of these techniques, algorithms and their development through history. Part of the course is dedicated to the Number Theory relevant to Cryptography. The topics covered in this module are of special interest to students on Computer Science and Communications courses.
Prerequisites: MA1040N Linear Algebra or MA1032N Logic or MA2036N Further Discrete Maths
Assessment: Coursework 50% Examination 50%.
Prior learning requirements
MA1040N Linear Algebra or MA1032N Logic or MA2036N Further Discrete Maths
The principal graduate attribute developed in the module is A3 creative and ethical.
This module aims to equip students with a sound understanding of the concepts of the Number Theory and its application in Cryptography. It is intended that students will undertake mini research tasks in gathering and analyzing data and formulating conjectures. Student will come to appreciate the strength of some results from the Number Theory and their applications in on-line security.
- Factorization of integers;
- Greatest common divisor;
- The Euclidean Algorithm;
- Integer Solutions to ax + by = c;
- Modular Arithmetics;
- Chinese Remainder Theorem;
- Fermat’s Little Theorem and Euler’s generalization;
- Definition and existence of primitive roots;
- Discrete logarithms
- Introduction to cryptography: History and Terminology
- Symmetric Encryption: Monalphabetic Ciphers; Polyalphabetic Ciphers; One-Time Pad; Transposition Ciphers; Product ciphers; Rotor machines; Block Cipher Principles; Data Encryption Standard
- Asymmetric Encryption: RSA public key cryptosystem
Learning and teaching
The module will be taught by a mixture of lectures, workshops and self study practical exercises. The lectures (22 hours) will be used to introduce the various concepts and principles of the module and their strengths in applications. Lectures will be followed by workshops (22 hours).
The workshops will afford students the opportunity to work in small groups on exercises related to previously taught material. The students will be able to present previously completed exercises for comment from the lecturer and other students. In this class time students will also be encouraged to explore and experiment with the concepts and techniques to encourage their own sense of mathematical creativity.
Students will be expected to spend time on unsupervised work, for example, private study of problem sheets and in the preparation of coursework (106 hours). A framework will be put in place to encourage disciplined learning through student self-awareness of progress in volume of work, understanding, attendance and punctuality.
On completing the module, students will be able to:
L1 Provide historical background to cryptography.
L2 Understand strength and weaknesses of different encryption algorithms.
L3 Independently design encryption/decryption algorithms.
L4 Understand proofs of some theorems in the Number Theory.
L5 Apply theoretical results in problem solving.
The assessments are designed to address all the Learning Outcomes of the module. There is a coursework assessing L1 to L5. This assessment will perform both summative and formative assessment functions. At the end of the module there will be an examination assessing L1, L2, L4 and L5.
Practice in examination type questions is provided by the formative in class exercises.
In order to pass the module, a student must achieve an aggregate mark of 40% or more.
· W. Stallings, ‘Cryptography and Network Security: Principles and Practice’, Prentice Hall.
· Paul Garrett, 'Making, Breaking Codes: An Introduction to Cryptography’, Prentice Hall.
· J. Holt, J. Jones, ‘Discovering Number Theory’, W.H. Freeman and Company.
· D. Kahn, ‘The Codebreakers’, McMillan.
· R. Kippenhahn, ‘Code Breaking: History and Exploration’, Constable.
· Simon Singh, 'The Code Book: How to Make It, Break It, Hack It, or Crack It', Delacorte Press .