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# Coding and Cryptology III

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## Description

The fundamental objective of cryptology is to enable communication over an insecure channel in such a way that an eavesdropper cannot understand what is being said. Classical cryptosystems required participants to share a common key. The new public key systems removed the need to share a private key. Coding theory is concerned with finding efficient schemes by which digital information can be coded for reliable transmission through a noisy channel. Error correcting codes are widely used in applications such as transmission of pictures from deep space, storage of data on CDs and design of identification numbers.

## Objective

This course aims to give students an introduction to the two areas of cryptology and coding theory. At the end of this course students should: have a knowledge of classical cryptosystems and the techniques used to break them; understand the ideas of public key cryptosystems and digital signature schemes, and be able to use the algorithms for RSA and ElGamal; understand the ideas involved in error correcting codes; understand linear codes, syndrome decoding and perfect codes. understand the basic properties of cyclic codes, including the decoding algorithm.

## Content

Topics covered in Cryptography are: classical cryptosystems; cryptanalysis: the different types of attack on these systems; Shannon's theory of perfect secrecy; unconditional and computational security; perfect secrecy. Public key cryptography: the RSA method and the El-Gamal cryptosystem and the mathematical problems on which they are based; digital signature schemes; the DES and AES cryptosystems. Topics covered in Codes are: maximum likelihood decoding, symmetric channels, minimum distance of a code, error correcting capabilities of a code; Linear Codes: the generator and parity check matrix, the dual of a code; bounds on codes; syndrome decoding. Perfect codes: sphere packing bound, Hamming codes. Cyclic codes.

Year Semester Level Units
2013 2 3 3
 Naomi BengerLecturer for this course

## Delivery

36 hours of lectures and tutorials

## Assessment

Ongoing assessment 30%, exam 70%.

PREREQUSITE: MATHS 1012 Mathematics IB. ASSUMED KNOWLEDGE: PURE MTH 2106 Algebra.

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