## MA3CEC-Cryptography and Error Correcting Codes

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA1LA Linear Algebra or MA1LANU Linear Algebra and MA1FM Foundations of Mathematics or MA0FMNU Foundations of Mathematics
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4CEC Cryptography and Error Correcting Codes
Current from: 2021/2

Module Convenor: Dr Basil Corbas

Type of module:

Summary module description:

To introduce and examine two of the most important and exciting contemporary applications of pure mathematics. Namely, Public Key Cryptography and Error Correcting Codes.

Aims:
To introduce and examine two of the most important and exciting contemporary applications of pure mathematics.

Assessable learning outcomes:
By the end of the module students are expected to be able to:
Implement the RSA public key cryptosystem and use it to encode, decode and authenticate documents.
Construct error correcting codes capable of correcting a specific number of errors.
Understand the principles used to apply the error correcting codes.
Calculate probabilities of correct transmission of messages after the application of error correcting codes.

The course provides a striking illustration of how abstract mathematical ideas can have vital applications in everyday life.

Outline content:
Modern cryptography, based on the concept of Public Key, makes possible the transmission of vast amounts of data in a secure way. The main topic is a detailed exposition of the RSA cryptosystem and how it can be used, not only for the secret transmission of messages, but also to provide digital signatures and authentication.
Error Correcting Codes help correct errors created by random noise in modern digital equipment. Without them, most digital electronic equipment we take for granted (l ike computers, CD or DVD players and so on), wouldnâ€™t be able to function. They are based on some extremely fascinating mathematical ideas and this course provides a basic introduction to the concepts involved.

Brief description of teaching and learning methods:
Lectures supported by problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 4 Guided independent study: 76 Total hours by term 0 100 0 Total hours for module 100

Summative Assessment Methods:
 Method Percentage Written exam 100

Summative assessment- Examinations:
2 hours.

Summative assessment- Coursework and in-class tests:
One examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September.