ELEC6242 Cryptography

Module Overview

This module covers the mathematics, techniques, and applications of modern cryptography. We will look at the history of code making and code breaking, and draw lessons for the future from the mistakes and successes of the past. We will also give a gentle introduction to the mathematics underlying modern cryptosystems.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

The historic struggle between code-makers and code-breakers
The broad categories of codes and ciphers, and appropriate uses for each

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

Perform simple mathematics appropriate to public-key encryption, and to cryptosystems based on polynomials over the binary numbers

Transferable and Generic Skills

Having successfully completed this module you will be able to:

Use graduate-level literature to investigate areas of mathematics previously unfamiliar to you

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

Attack classical ciphers such as Vigenère, and LFSR-based stream ciphers
Select appropriate ciphers, cipher modes, and protocols for simple applications

Syllabus

Cryptography background - Vocabulary - History - Steganography - Simple codebreaking - Information: confusion and diffusion, entropy - One-time pads and their failures (Venona). Mathematical background - Finite Abelian Groups - Finite Fields. - Groups based on integer multiplication - Discrete logarithms - Groups based on elliptic curve Public and private key cryptography, shared secrets Public key cryptosystems - RSA, ElGamal - Authentication - Signatures - Deniability - Identity-based cryptography Private key cryptosystems Stream ciphers: LFSR, RC4, and later. Block ciphers: Feistel, Rijndael, and later Cryptographic modes: ECB, CBC, GCM. Cryptographic protocols, including TLS. “Random numbers” and their weaknesses Elementary cryptanalysis Weaknesses in implementations Hardware Quantum cryptography

Learning and Teaching

Type	Hours
Follow-up work	18
Revision	10
Completion of assessment task	12
Preparation for scheduled sessions	18
Tutorial	6
Lecture	36
Wider reading or practice	50
Total study time	150

Resources & Reading list

David Kahn (1997). The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet.

Ross J Anderson (2008). A Guide to Building Dependable Distributed Systems.

Bruce Schneier (1995). Applied Cryptography: Protocols, Algorithms and Source Code in C.

Assessment

Summative

Method	Percentage contribution
Cryptanalysis Investigation	20%
Examination (2 hours)	80%

Repeat

Method	Percentage contribution
Examination	100%

Referral

Method	Percentage contribution
Examination (2 hours)	100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisites: (ELEC1201 and MATH2047) OR (COMP1202 AND COMP2210) OR COMP6238