The University of Southampton
Courses

# 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

TypeHours
Tutorial6
Preparation for scheduled sessions18
Follow-up work18
Lecture36
Revision10
Total study time150

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

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

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

### Assessment

#### Summative

MethodPercentage contribution
Continuous Assessment 20%
Final Assessment  80%

#### Repeat

MethodPercentage contribution

#### Referral

MethodPercentage contribution