PMCRYPTO - MSc Cryptography

The School of Computing and Digital Media is committed to provide a preparation for you which

meets the current market needs in an important discipline that helps ensure the security of our

modern connected world while satisfying the highest criteria for academic quality. At Masters Level,

this means teaching courses in areas at the forefront of modern technological development.

Cryptography, information security and the mathematics that underpin them are at the heart of the

modern world keeping businesses and consumers safe from the threats of data loss, theft and

corruption. This course meets a key need enabling you to specialize your knowledge but also to

benefit from the cross fertilization available from related disciplines and modules across the School

and through its Cybersecurity Research Centre.

The topics covered in this course will give you opportunities to find employment in a sector

Section A: Version Control

Course Leader Graham Taylor-Russell

Course Code PMCRYPTO HECoS Code 100400 – Applied Mathematics

Last Revised on

(automated) 20/05/2025 10:50 Last Revised by (automated) Costel Rusu

identified as having a skills shortage in the UK and beyond. While many traditional industries (even including some parts of the IT Sector such as software testing) are vulnerable to automation and AI techniques, information security is one area that has a clear need for growth in qualified graduates throughout the next decade. You will be introduced in a supported way to ideas that find widespread application and will be given the preparation needed to succeed in a fast changing environment; as well as receiving a grounding in the underlying mathematics of the tools that are most widely used your course will emphasise the related skills and personal development attributes you will need to progress through employment in a fast changing technical environment. Social, ethical and professional issues also find strong emphasis as the ability to engage in these areas will be a necessary facet in your future careers in these disciplines. Learning will be supported by a blend of face-to-face activities supplemented by (e)-resources. Workshop classes that follow lectures will support your mastery of complex skills in a small group environment and labs and software (e.g. Maple and Python) will enable you to apply theory to practical situations and investigate the way algorithms operate in practice. The University Learning Centre with its range of books and journals in the cybersecurity subject will complement the module specific resources and particularly the major project that is the culmination of the course

To provide solid theoretical foundations for understanding the current major applications of

cryptography to modern day problems. You will encounter the mathematical theory (mainly from

number theory and other branches of abstract algebra) necessary to appreciate algorithms in both

symmetric and asymmetric cryptography.

To provide a historical overview of the development of the subject while principally focusing

on the problems of the modern technological age.

To see cryptography within a wider context of information security where systems, standards

and human factors have an important role alongside theoretical algorithms.

To prepare you to work in technological areas across the range of cybersecurity areas.

To develop practical skills such as programming that will benefit you in a range of

employment situations.

To strengthen self-reflection enabling you to undertake continued professional development

in your chosen careers

To strengthen your abilities to undertake research, enabling you to contribute where appropriate

to consultancy projects of the research centres of the School and to undertake higher degrees.

To promote and strengthen your appreciation of the social, ethical and legal issues related to

cryptography and the ways in which these may affect your future professional practice.

After completing the course graduates are anticipated to be able to demonstrate the following:

LO1: A detailed understanding of key mathematics underpinning cryptography including:

(a) Number theory for cryptography; properties of natural numbers; integer factorization; quadratic congruences; divisors and discrete logarithms.

(b) Discrete mathematics for cryptography; sets, rings and fields; gcds and their properties, inverses;elliptic curves over finite fields.

(c) Algorithms and complexity

LO2: An ability to apply mathematics to the delivery of cryptographic security including:

(a) Algorithms for asymmetric cryptographic based on mathematical trapdoor functions (RSA, El Gamel, Elliptic Curve)

(b) The limitations and risks associated with algorithms

LO3: An understanding of the historical development of cryptography and how the subject may evolve in the context of future technological developments including inter alia:

(a) Classical algorithms for cryptography

(b) The development of symmetric and asymmetric cryptography including AES

(c) 21st century paradigms (quantum computing, blockchain etc.) and the way these will affect future developments in information security and associated disciplines..

LO4: Detailed appreciation of the social, legal and ethical context of modern cryptography including:

(a) Information Security and Privacy Legislation;

(b) Information Security protocols;

(c) Risk Identification and Management.

LO5: Development and demonstration of key skills that will underpin research and employment follow completion of the course through:

(a) Programming in Python and Maple; experience of industry standard software appropriate for optional choices in statistics and forecasting (e.g. R) and in artificial intelligence.

(b) Managing an extended self-directed investigation.

ULO. Demonstrate confidence, resilience, ambition and creativity and will act as inclusive, collaborative and socially responsible practitioners/professionals in their discipline.

Mathematics, Statistics and Operational Research (although this only deals with L6 qualifications)

https://www.qaa.ac.uk/docs/qaa/sbs/sbs-mathematics-statistics-and-operational-research-23.pdf?sfvrsn=5c71a881_12

• The two core modules delivering mathematical theory and designed specifically for the course (MA7009 and MA7010) will emphasise learning by practice and the assessment includes time constrained tests and/or a final examination that summatively covers all learning outcomes. Other strands of assessment in these modules consists either of one or more shorter tests that support consolidation of knowledge or of a portfolio derived from workshop investigations where students use mathematical software to explore concepts in number theory and related areas. The Number Theory for Cryptography module (MA7010) also tests the acquisition of programming skills in Python (a Pass/Fail component that does not contribute to the module mark) and in MAPLE (or an alternative platform such as Python) via the portfolio of investigations.

• The third new module in the spring semester (MA7011) has a time constrained test to assess knowledge of the algorithms and methods midway through the module (reducing the bunching of examinations at the end of the semester) supplemented by a written essay/report on modern developments that ensures students demonstrate the ability to research, write and present arguments before being required to do so in the major project/dissertation module..

• The other modules (shared with related courses) will be assessed by up to three components; typically, these will enable the student to display a working knowledge of technologies alongside the practical ability to use the supporting tools. With full time students taking three modules each with 2-3 assessment components in 15 weeks the programme will require intensive effort by students but as much as possible material delivered early in the module is assessed before the final summative component.

• The dissertation/major project will assess the theoretical knowledge, the analytical and technical skills and decision-making potential of the students, allowing them to demonstrate the ability to develop analysis and/or solutions for business, industry and government.

While the course does not have any compulsory work based learning element, students may have opportunities to contribute to projects undertaken within the Cybersecurity Research Centre where mathematical skills in cryptography are required.

They may also have the opportunity to act as Success Coaches and give similar mentoring support to undergraduate students.

Where a student is able to obtain a suitable placement they may request that this be accredited through the School of Computing and Digital Media’s generic work placement module(s) with the credit replacing an option module they would otherwise take.

Part-time students will take the same programme as FT students but at a slower rate. Where practical core modules will be studied first. CS7064 and MA7011 are designed to be taken concurrently – where this is not practical for a PT student CS7064 should be taken first.

To obtain the degree award of MSc Cryptography the students need to pass 180 credits including all core modules and the MSc dissertation project module (CT7P01 MSc Project).

Passing 120 credits from the course structure including at least one of the MA7 coded core modules entitles the students to the PGDip Cryptography award.

Passing 60 credits from the course structure including at least one of the MA7 coded core modules entitles the students to the PGCert Cryptography award.

The course includes two semesters of formal scheduled teaching for full-time study (and up to four semesters for part-time study) where you will acquire the knowledge and skills for developing and understanding the theory and its applications. The taught modules are followed by one further semester (potentially extending to two semesters in PT mode) undertaking the dissertation/major project where you will apply the knowledge and skills learned to deliver a significant piece of self-managed work. During your study you will be encouraged to reflect on your learning and to develop strategies for professional and personal development. This is achieved through a range of methods:

· Students are encouraged to maintain blogs/log books to reflect on what they have learned each week, and to maintain a personal development portfolio;

· In some of the modules the work undertaken in practical workshop tasks forms part of the formal assessment and contributes to the final module mark so increasing the engagement in the students in the practical work;

· Formative feedback is provided during each semester and students are able to discuss draft coursework in tutorials and workshops in order to refine and enhance their work before final submission.

It is expected that after the formal scheduled teaching element students will be able to propose project topics which better place them within the professional context as well as better utilize the knowledge and skills gained while studying.

· Students are encouraged to engage in the seminars and workshops organized by the school’s research centres where the topics are consonant with their course of study.

Cryptography and cyber security are identified as areas of skills shortage where a growing number of entrants are needed to reflect increased risks in the modern cyber enabled world. New technologies such as blockchain will offer opportunities for new skills to be developed and applied across the regional, national and international economy.

The programme of modules is designed to ensure that graduates are not only competent technical practitioners able to understand the underlying mathematics and algorithms but are also equipped to appreciate the social context that will be essential for many successful careers in this area.

Students will be expected to acquire and enhance their skills in complementary areas such as python programming, a skill that will open up potential career opportunities in areas outside the cyber and information security specialisms. Opportunities such as these will be enhanced by the structure of the final major project with its proven track record of developing employment related skills on other programmes in the School of Computing and Digital Media.

Cryptography applies in many areas of industry where extensive data processing, electronic communications or software development takes place. As a result, this cryptography qualification will provide wider employment opportunities than a traditional computer, software or network engineering degree.

Knowledge of cryptographic solutions will enhance your employment opportunities with large businesses, including online retailers, banks and companies in the financial technology industry, corporate enterprises, electronic entertainment vendors and network service providers.

You will be required to have:

• a 2.1 undergraduate degree (or equivalent) in mathematics, computer science, data science, software engineering, computing, ICT, physics or economics. Please note your undergraduate degree must have included at least basic training in maths and computing.

Programming skills with one of the popular languages, such as Java or Python, would also be a great advantage.

Applicants with a 2.2 at undergraduate level may also be considered and will be required to attend an interview.