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.

Delivery

36 hours of lectures and tutorials

Assessment

Ongoing assessment 30%, exam 70%.

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)

Linkage past

Prerequisite is MATHS 1007A/B Mathematics I (Pass Div I) or both MATHS 1007A/B Mathematics I (Pass Div II) and MATHS 2004 Mathematics IIM (Pass Div I). Assumed knowledge: students who have not completed either PURE MTH 2000 Discrete Mathematics II or PURE MTH 2002 Algebra II should see the Level III Mathematics Coordinator.

Linkage present

No present linkages have been noted.

Linkage future

This course is not a prerequisite for any specific course. Students wishing to learn more about the topics of Coding and Cryptology will need the material on finite fields taught in PURE MTH 3012 Fields and Geometry; and will also find the course PURE MTH 3003 Number Theory and PURE MTH 3007 Groups and Rings useful.

Restrictions

None.

Recommended text

None.