Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Coding and Cryptography
Module Code	MS505
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Angela Murphy Semester 2: Angela Murphy Autumn: Angela Murphy
Module Teacher	Angela Murphy
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module introduces students to the reliability of codes and the security of cryptosystems. This module reviews linear algebra, rings and fields. It develops the learning tools and mathematical skills essential for the transmission of data over noisy insecure communication channels. Additionally, this module provides a platform of knowledge that allows participants to engage in cryptographic research.Students will participate in the following learning activities:Lectures; Students will attend three one-hour lectures per week. These lectures are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module.Tutorials; Each student will attend one one-hour tutorial per week. Problem sheets based on lecture content are distributed to the students and they are strongly advised to attempt all tutorial questions in advance of the tutorial. Reading; Students are expected to fully utilise the textbooks recommended below to enhance the learning experience.

Learning Outcomes

1. Design an error-correcting code.
2. Encode and decode binary data over a noisy communication channel.
3. Construct and interpret elliptic curves over finite fields.
4. Compare and contrast some public key cryptosystems,the hard problems on which their security relies and certain attacks on them.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	3 lectures per week
Tutorial	12	1 tutorial per week
Examination	2	end of year exam
Directed learning	18	solving tutorial questions
Independent learning	123	Study over 15 weeks including exam period
Total Workload: 191

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Pre-Requisites..
Modular Arithmetic; Chinese Remainder Theorem; Euler and Fermat's theorems; group theory: primality testing: finite fields..

Error correcting codes.
Bounds on general codes; Linear codes; Hamming codes; Golay codes; Cyclic codes; BCH codes; Reed-Solomon codes; Linear feedback shift registers; The McEliece Cryptosystem..

Elliptic curves.
The Addition Law; Elliptic curves over an extension field; Hasse Bound; Group structure; Factoring with elliptic curves; primality certificates; Elliptic curve cryptosystems; Identity based encryption..

Public Key Cryptography..
RSA algorithm; key generation; implementation; encryption and decryption; attacks on RSA; Primality testing: factoring;Diffie-Hellman Key exchange; methods to solve discrete logarithms such as index calculus; ElGamal public key cryptosystem; RSA signatures; The ElGamal Signature Scheme..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Short answer questions	In-Class test	25%	Week 25

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

Trappe,W,.and Washington,L,.: 2006, Introduction to Cryptography with Coding theory, Pearson International Edition,
MacWilliams,F.J., and Sloane , N.J.A.,: 1988, The theory of error-correcting codes, North Holland, Amsterdam,
Smart, N.,: 2003, Cryptography: An introduction, McGraw Hill Education,
Coding theory and cryptography The essentials: 2000, New York; Marcel Dekker,

Other Resources

1057, website, 0, http://www.certicom.com/,

Array

Programme or List of Programmes

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