# Mathematics

## ECM3726 - Cryptography (2018)

MODULE TITLE CREDIT VALUE Cryptography 15 ECM3726 Dr Gihan Marasingha (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
 Number of Students Taking Module (anticipated) 120
DESCRIPTION - summary of the module content

Cryptography is fundamental to life in the information age. The communications we send and receive daily via the Internet and mobile networks are secured using cryptographic algorithms. Cryptanalysis is the study of tools aimed at deciphering or ‘cracking’ secret messages and cryptosystems. Public-key algorithms have other uses, including authentication and key-exchange.

Underlying these tools is a firm foundation in number theory and the theory of elliptic curves. You will have the opportunity to write cryptographic code in the Python programming language.

Prerequisite modules: ECM3704 Number Theory and ECM2712 Linear Algebra.

AIMS - intentions of the module

This module aims to develop the theory and practice of public-key and symmetric-key cryptography. The tools encountered will be valuable for employment in the security sector or for further study in cryptography or number theory.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 state all definitions pertaining to cryptography;

2 describe cryptographic algorithms and apply them to given problems;

3 implement cryptographic algorithms using a computer programming language;

4 prove relevant theorems and prove the correctness of cryptographic algorithms.

5 describe algorithms to solve unseen problems;

Discipline Specific Skills and Knowledge:

4 understand the application of pure mathematics to practical problems;

5 analyse algorithms;

Personal and Key Transferable / Employment Skills and Knowledge:

6 demonstrate computer programming skills;

7 formulate precise descriptions of complex problems and thereby solve them;

8 use a range of learning resources;

9 manage time effectively.

SYLLABUS PLAN - summary of the structure and academic content of the module

- the complexity of algorithms;

- mono- and polyalphabetic substitution ciphers;

- the Vigenère cipher;

- block cipher modes of operation;

- affine block ciphers;

- the Hill cipher;

- computing with finite fields and the AES cipher;

- classes of cryptanalytic attacks

- Diffie-Hellman key exchange

- the ElGamal public-key cryptosystem;

- cryptanalysis of DLP-based problems:

- Shanks baby-step, giant-step algorithm;

- Pohlig-Hellman

- the RSA cryptosystem;

- trial division, Fermat factorisation;

- Pollard’s p-1 method;

- Pollard’s rho method;

- primality testing (Fermat, Miller-Rabin)

- authentication:

- man-in-the-middle attacks

- digital signatures (ElGamal and RSA);

- forgeries;

- the arithmetic of elliptic curves;

- the elliptic curve method for factorisation;

- elliptic curve cryptography.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures including example classes Guided independent study 117 Reading, working on example sheets, computer programming.

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercise sheets 5 x 10 hours All Model answers provided on ELE.

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours All Via SRS
Coursework – example sheets 20   All Written

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener