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Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title Cryptography & Number Theory
Module Code CSC1132 (ITS: CA642)
Faculty Computing School Engineering & Computing
NFQ level 9 Credit Rating 7.5
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


WorkloadFull time hours per semester
TypeHoursDescription
Lecture36No Description
Directed learning3No Description
Assignment Completion48Project work
Independent Study100HOme work, home study
Total Workload: 187
Section Breakdown
CRN10621Part of TermSemester 1
Coursework0%Examination Weight0%
Grade Scale40PASSPass Both ElementsY
Resit CategoryRC1Best MarkN
Module Co-ordinatorGeoffrey HamiltonModule TeacherRenaat Verbruggen
Assessment Breakdown
TypeDescription% of totalAssessment Date
AssignmentPerform the cryptanalysis of a block cipher25%Week 6
Formal ExaminationEnd-of-Semester Final Examination75%End-of-Semester
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
RC1: A resit is available for both* components of the module.
RC2: No resit is available for a 100% coursework module.
RC3: No resit is available for the coursework component where there is a coursework and summative examination element.

* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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.

Indicative Reading List

Books:
  • 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/,


Articles:
None
Other Resources

None

<< Back to Module List View 2024/25 Module Record for CA642