Module: Cryptography & Number Theory

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Cryptography & Number Theory
Module Code	CA642 (ITS) / CSC1132 (Banner)
Faculty	Engineering & Computing	School	Computing
Module Co-ordinator	Geoffrey Hamilton
Module Teachers	Renaat Verbruggen
NFQ level	9	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Array

Description

The purpose of this module is to introduce the students to elementary number theory, as required for further study of important cryptographic protocols, and to teach the basics of modern symmetric cryptography. Modern block ciphers and hash functions will be studied in some depth, and modern complex methods of block cipher cryptanalysis (linear and differential) will be covered. Participants will learn to appreciate the significance of cryptography as a means of securing information in the modern world. New ideas and some surprising and novel protocols will be discussed. Students are expected to attend lectures, to undertake a difficult assignment, and partake in external reading and study and homework.

Learning Outcomes

1. understand the significance of cryptography to the modern world and the internet.
2. understand the rationale behind block cipher design.
3. perform the cryptanalysis of a simple block cipher
4. integrate cryptographic algorithms into software projects
5. solve elementary problems in number theory relating to cryptography
6. build on number theoretic basics to further their knowledge of advanced methods of cryptography

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	No Description
Directed learning	3	No Description
Assignment Completion	48	Project work
Independent Study	100	HOme work, home study
Total Workload: 187

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

Classical method of Cryptography
The Caesar cipher. The Vigenere cipher. Rotor machines. The one-time pad.

Modern ciphers and hash functions
Structure of a block cipher. The Fiestel structure. Key and block size length. DES, AES, IDEA, RC5, SAFER, FEAL-4 and other block ciphers. Stream ciphers and LFSRs. One-way hash functions, SHA-1 and its successors.

Cryptanalysis
Cryptanalysis of FEAL-4 using linear and differential cryptanalysis. Meet-in-the-middle attacks.

Key distribution
The key distribution problem. The padlock analogy and the Diffie-Hellman method. An introduction to RSA and related methods.

Smartcards
Smartcard technology. Side channel attacks. Challenge response systems. The surprising applications of an uncloneable one-way function. Mobile phone SIM cards.

Elementary number theory
Finite fields. Modular arithmetic. Efficient algorithms for modular arithmetic. Fermats theorem. Euler's criteria, and the totient function.

Advanced number theory
Primality proving. The Chinese remainder theorem. Quadratic residues and calculating modular square roots and cube roots. The Jacobi symbol.

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Perform the cryptanalysis of a block cipher	25%	Week 6

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

Menezes at al.: 2001, Handbook of Applied Cryptography, CRC Press, http://www.cacr.math.uwaterloo.ca/hac/, 0-8493-8523-7
Kumanduri and Romero: 1998, Number Theory with Computer Applications, Prentice-Hall, New Jersey,
N. Smart: 2009, Cryptography, an Introduction, 3rd, http://www.cs.bris.ac.uk/~nigel/Crypto_Book/,

Other Resources

None