Mathematical Coding and Cryptology
Subject code: SIP 7026
Lecturers
A/Prof Bob Clarke, Dr Sue Barwick
University of Adelaide
Mode of delivery
On-line delivery with possible
twice a week lectures at University of Adelaide North Terrace campus.
Assumed knowledge
To be advised
Aim/Learning Objectives
Aims:
This course aims to give students an introduction to the two
areas of cryptology and coding theory.
Objectives:
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.
Content
The fundamental objective of Cryptology is to enable two people Alice
and Bob to communicate over an insecure channel (such as a telephone line or a
computer network) in such a way that an eavesdropper cannot understand what is
being said. Classical cryptosystems required Alice and Bob to share a key which
they could use both to encrypt a message before sending it, and to decrypt a
received message. The prior communication of this key is difficult in practice.
In 1976, work by Diffie and Hellman revolutionised modern cryptology. They
developed a public key system which removed the need for Alice and Bob to share
a private key. This course covers classical cryptosystems, public key
cryptosystems, digital signature schemes and the cryptosystems DES and AES used
as standards by the USA government and many financial institutions.
The birth of Coding Theory
was inspired by the classical paper of Shannon in
1948. Since then a great deal of research has been devoted to 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, for example returning pictures from deep space, storage of
data on CDs and design of identification numbers such as student numbers.
Coding theory is also of great mathematical interest, it illustrates the power
and beauty of modern algebra and has applications to many other areas of
mathematics.
The first part of the subject concentrates on linear codes,
with topics including syndrome decoding, perfect codes and cyclic codes.
The Hamming and Golay codes, and others, are discussed.
The second part is an introduction to contemporary cryptology,
including both symmetric and public key systems.
Examples of cryptosystems studied include the Data Encryphon Standard
and the RSA algorithm.
The course concludes with a selection of
topics from authentication, identification and digital signatures.
Assessment
Details of the actual assessment used in a given year
can be found in the study guide provided at the start of the semester.
Resources
All the materials necessary for the course will be availabe on-line. The
lecture notes are based on the following books:
Cryptology:
Douglas R. Stinson,
Cryptography: theory and practice, (1995)
Coding Theory:
Raymond Hill, A first course in coding theory, (1988)
A bibliography for further reading on the subject will be provided.