Cryptography and Error Correcting

Summary module description:

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.
Understand how Rabbin?s public key cryptosystem operates
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.

Additional outcomes:
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 (like computers, CD or DVD players and so on), wouldn?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.

Summative Assessment Methods:
Written exam 100%

Other information on summative assessment:
One examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convener will apply the following penalties for work submitted late, in accordance with the University policy.
where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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.

Length of examination:
2 hours.

Requirements for a pass:
A mark of 40% overall.