# ASYMMETRIC CRYPTOGRAPHY - 2022/3

Module code: COMM045

## Module Overview

The module introduces general concepts of asymmetric (a.k.a. public key) cryptography and covers main algorithms and protocols in this field. The module will introduce mathematical foundations that are essential for the functionality and security of asymmetric cryptographic algorithms and then focus on the security definitions and constructions of concrete algorithms for authentication, confidentiality and integrity. The theoretical part of the module will focus on provable security of asymmetric cryptographic algorithms and introduce the concept of cryptographic reductions. In labs students will develop and test their understanding of the material and learn how to implement and use existing algorithms from asymmetric cryptography.

### Module provider

Computer Science and Electronic Eng

GRANGER Robert (CS & EE)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 125

Laboratory Hours: 10

Captured Content: 15

Semester 1

None

## Module content

• Number-theory and modular arithmetic (incl. algorithms for gcd, modular inverse and exponentiation computations, prime numbers, operations in cyclic groups, group order, discrete logarithm problem and algorithms, integer factorization problem and algorithms)

• Public-key / asymmetric encryption (incl. schemes such as RSA, ElGamal, Goldwasser-Micali, Rabin, Paillier, homomorphic properties and provable security of public-key encryption (e.g. IND-CPA and IND-CCA security, RSA problem, Diffie-Hellman problems), key lengths)

• Digital signatures (incl. schemes such as RSA, ElGamal, Schnorr, DSS, Hash-and-Sign paradigm, one-time signatures (e.g. Lamport, Merkle), provable security of digital signatures (e.g. EUF-CMA security))

• Key establishment protocols (incl. key transport/distributions, key exchange/agreement protocols, Diffie-Hellman key exchange, key derivation functions, attacks on key establishment protocols, provable security of key establishment protocols (e.g. AKE-security notion), extensions to multi-party key establishment)

• Advanced cryptographic techniques (e.g. signcryption, Shamir’s secret sharing, identification/zero-knowledge protocols)

## Assessment pattern

Assessment type Unit of assessment Weighting
Examination 3-HOUR OPEN-BOOK INVIGILATED EXAM 100

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate that they have achieved the module's learning outcomes.

The summative assessment for this module consists of an individual open-book 3-hour invigilated exam with a set of questions that students are required to answer. This addresses LO1 and LO2.

For formative assessment and feedback, each two-hour lab will start with a short quiz which tests understanding of that week's material, with solutions explained. A set of exercises - including implementation tasks - and solutions will be available prior to the lab to further develop and test understanding, and there will be additional unseen tutorial-style exercises and solutions to improve understanding of and facility with the mathematical foundations and their applications. This addresses LO1, LO2 and LO3.

## Module aims

• The aim of this module is to equip students with background knowledge and practical experience of modern asymmetric cryptographic algorithms and protocols. The module will explain the underlying theory and show practical application of asymmetric cryptographic algorithms

## Learning outcomes

 Attributes Developed 1 Understand cryptographic principles, challenges and goals that arise in the context of public-key cryptography KC 2 Understand the functionality and security of widely used asymmetric cryptographic algorithms, including their advantages and disadvantages and the underlying mathematical theory KCT 3 Experience practical application of asymmetric cryptographic algorithms KPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Help students understand the nature of public key cryptography, including main principles, challenges and goals

• Explain most significant concepts and algorithms in asymmetric cryptography

• Explain security requirements and functionality of asymmetric cryptographic algorithms

• Enable students to apply existing asymmetric cryptographic algorithms in practice

The learning and teaching methods include:

• Lectures (15 hours) in the form of detailed lecture slides and topic-based captured content videos.

• Labs (10 hours) consisting of a one-hour flipped learning class with a quiz and answers, highlighting important parts of the lecture and taking questions, and one hour on additional exercises delivered in the manner of a tutorial to improve understanding of and facility with the mathematical foundations and their applications.

• Independent study (125 hours), with students expected to expend the remaining workload on studying the lectures, reading the textbook chapters and watching the further topic videos, preparing for the labs, working through the additional lab exercises and solutions, and preparing for the exam.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.