## COMP3223 Cryptography

### 10 creditsClass Size: 220

Module manager: Dr Toni Lassila
Email: T.Lassila@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2024/25

### Pre-requisites

 COMP1511 Introduction to Discrete Mathematics

This module is not approved as a discovery module

### Module summary

This module provides a thorough introduction to cryptography and its applications. We cover the mathematical foundations of cryptography and discuss modern cryptosystems in detail. This includes both symmetric and public-key systems like AES and RSA and their usage and applications in digital signatures and complex cryptographic protocols like digital money and electronic voting.

### Objectives

On completion of this module, students should be able to:
-Know and apply fundamental cryptographic techniques and algorithms.
-Understand and apply the principles of modern symmetric and public-key cryptosystems and further cryptographic primitives such as hash functions.
-Apply appropriate known cryptographic techniques for a given scenario.
-Understand the dangers of inventing one’s own cryptographic methods.
-Explain how key exchange protocols work and how they fail.
-Explain how Public Key Infrastructure supports digital signing and encryption and discuss the limitations/vulnerabilities.
-Discuss the importance of modular arithmetic and prime numbers in cryptography and explain their use in cryptographic algorithms.
-Explain the role of random numbers in security, beyond just cryptography (e.g., password generation, randomized algorithms)
-Describe quantum cryptography and the impact of quantum computing on cryptographic algorithms.
-Describe likely attacker types against a particular system.
-Describe risks to privacy and anonymity in commonly used applications.
-Describe real-world applications of cryptographic primitives and protocols.
-Discuss cryptographic protocols and their properties.

Learning outcomes
1. Understand and apply in practice the fundamental principles of cryptography and information security.

2. Analyse and evaluate the strengths and weaknesses of cryptosystems.

3. Apply mathematical analysis to understand how symmetric and asymmetric cryptosystems are constructed.

4. Make appropriate use of the academic literature on cryptography.

5. Understand the future developments of cryptosystems and their security implications and use this information to advise their professional career.

### Syllabus

Cryptographic goals. Cryptanalysis of classical ciphers, Modern symmetric cryptosystems: DES, AES and its operation modes.
Mathematical foundations of public-key cryptography: modular arithmetic, Extended Euclidean Algorithm, efficient exponentiation, prime number generation, Chinese Remainder Theorem, Miller-Rabin test.
Public-key cryptography: RSA, Elgamal, Diffie-Hellman key exchange. Digital signatures, Hash functions, Quantum cryptography and the impact of quantum computing.
Different types of attacks, Classification of cryptosystems in terms of security, Cryptographic design principles, Applications and cryptographic protocols: digital money, secure elections

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 10 1.00 10.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Formative assessment will be provided as part of the two pieces of coursework.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Exercises 20.00 In-course Assessment Exercises 20.00 Total percentage (Assessment Coursework) 40.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 60.00 Total percentage (Assessment Exams) 60.00

The exam will be a Computer-Based Exam This module will be reassessed by examination only.