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MATH3401: CRYPTOGRAPHY AND CODES III

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Type	Open
Level	3
Credits	20
Availability	Available in 2024/2025
Module Cap
Location	Durham
Department	Mathematical Sciences

Prerequisites

Elementary Number Theory II (MATH2617)

Corequisites

None.

Excluded Combinations of Modules

Cryptography (COMP3731).

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 mathematicalskills 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 theapplication of the theory to practical examples.
Assignments for self-study develop problem-solving skills andenable students to test and develop their knowledge andunderstanding.
Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total
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
Preparation 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 assignments to be submitted.

More information

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