Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Postgraduate Module Handbook 2021/2022

Archive Module Description

This page is for the academic year 2021-22. The current handbook year is 2022-23

Department: Mathematical Sciences

MATH30120: Cryptography and Codes

Type Tied Level 3 Credits 20 Availability Available in 2021/22
Tied to G1K509 Mathematical Sciences

Prerequisites

  • Prior knowledge of Elementary Number Theory at undergraduate level.

Corequisites

  • None

Excluded Combination of Modules

  • None

Aims

  • To give a basic introduction to two topics in data transfer which rely on abstract mathematics: Error correcting Codes which are used widely in data transmission over noisy channels, Cryptography which is widely used in banking, internet browsing, and to ensure privacy on mobile networks.

Content

  • Introduction to codes: The Hamming distance, Error detection and correction, equivalence of codes
  • Linear Codes, Dual codes and Decoding Methods
  • Hamming Codes, Golay Codes,
  • Linear Codes over cyclic fields, Cyclic Codes, BCH codes, Reed-Solomon Codes
  • Introduction to open-key cryptography, notion of trapdoor function. The factorisation and discrete logarithm problems
  • Diffie-Hellman key exchange scheme. RSA cryptosystem
  • Elliptic curves over rational numbers and finite fields, Elliptic Curve Diffie-Hellman scheme
  • Lenstra factoring algorithm

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Cryptography and Codes.
  • have an awareness of the abstract concepts of theoretical mathematics in Codes and Cryptography.
  • have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas:
  • Codes: Linear, Hamming, Cyclic, BCH, Reed-Solomon Codes
  • Cryptography: open-key systems
  • Elliptic curves, applications in cryptography.
Subject-specific Skills:
  • In addition students will have specialised mathematical skills in the following areas which can be used in minimal guidance: Abstract Reasoning.
Key Skills:

    Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

    • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
    • Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
    • Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
    • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

    Teaching Methods and Learning Hours

    Activity Number Frequency Duration Total/Hours
    Lectures 42 2 per week for 20 weeks and 2 in term 3 1 Hour 42
    Problems Classes 8 Four in each of terms 1 and 2 1 Hour 8
    Preperation and Reading 150
    Total 200

    Summative Assessment

    Component: Examination Component Weighting: 100%
    Element Length / duration Element Weighting Resit Opportunity
    Written examination 3 Hours 100%

    Formative Assessment:

    Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.


    Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University