# KC6007 - Mathematical Cryptology

## What will I learn on this module?

Mathematical Cryptology concerns the creation and analysis of secret messages using mathematical techniques. You will learn about both classical and contemporary cryptology from the time of Julius Caesar until the present day. Mathematical techniques have been at the heart of many of these approaches and, on this module, you will be able to see, for example, how modular algebra can be a powerful cryptographic tool. Large prime numbers are another useful tool at the heart of modern cryptology and you will learn how to formulate an efficient approach to determining whether a large number is prime or composite.

By the end of the module, you should have developed an awareness of different approaches to deciphering various forms of ciphertext and should have an ability to appraise which cryptographical techniques are robust.

Outline Syllabus
Classical Cryptology: Encryption and decryption using direct standard alphabets and alphabets created using classical techniques from the shift cipher to polygraphic ciphers.

Contemporary Cryptology: Encryption and decryption using techniques based on Boolean functions and exploring the mathematical theorems and approaches at the heart of modern cryptology practices.

### How will I learn on this module?

You will learn through a series of lectorials and classes will be scheduled in our modern computer laboratories enabling you to apply the techniques presented in the lecture part of the session and, in this way, deepen your understanding of the material and develop your practical skills. This, in turn, develops your confidence to explore the subject area further as an independent learner outside of the classroom. Initially, computer programs will be provided to assist you in deciphering hidden messages but you will progress and develop your own approach, using Matlab, to decipher messages.

Formative feedback is available weekly in the classes as you get to grips with new cryptologic techniques and solve problems. In addition, we operate an open door policy where you can meet with your module tutor to seek further advice or help if required. Your ability to select appropriate techniques and use the appropriate computational approach to decipher messages is assessed in a lab based class assignment whereas your ability to appraise various cryptographic techniques and develop appropriate mathematical theory is tested in a formal exam at the end of the module.

General feedback on assessments will be given in class and individual feedback will be written on scripts. An opportunity to discuss work further will be available on an individual basis when work is returned and also through the open door policy.

### How will I be supported academically on this module?

Direct contact with the teaching team during the lectorials will involve participation in both general class discussions as well as one to one discussions during the hands-on part of the lectorial. This gives you a chance to get immediate feedback pertinent to your particular needs in this session. Further feedback and discussion with the teaching team are also available at any time through our open door policy. In addition, all teaching materials, selected Matlab scripts, and supplementary material (such as interesting articles) are available through the e-learning portal.

### What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

### What will I be expected to achieve?

Knowledge & Understanding:
1. Use appropriate methods to identify the encryption method used to encipher a message.
2. Identify large prime numbers efficiently.

Intellectual / Professional skills & abilities:
3. Where practically possible, decipher a message using appropriate tools and techniques.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4. Critically appraise the use of cryptology in various scenarios.

### How will I be assessed?

SUMMATIVE
1. Coursework (30%) – 3
2. Examination (70%) – 1, 2, 3, 4

FORMATIVE
Formative assessment will be available on a weekly basis in the lectorials through normal lecturer-student interactions, allowing them to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on student work and errors in understanding will be addressed reactively using individual discussion. Solutions for laboratory tasks will be provided after the students have attempted the questions, allowing students to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.

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### Module abstract

‘Mathematical Cryptology’ concerns the creation and analysis of secret messages using mathematical techniques. You will learn about both classical and contemporary cryptology from the time of Julius Caesar until the present day. You will get the answer to questions such as ‘How is my money kept safe when I buy things online?’ or ‘How can I sign an electronic document without my signature being forged?’. The module is ‘hands-on’ and is taught through a series of lectorials which combine formal lectures and hands on experience using computer software. Formative feedback is available weekly in the classes as you get to grips with new cryptologic techniques and solve problems. Assessment is via a lab-based class assignment (where you will decipher a hidden message) worth 30% of the module mark, and a formal examination worth the remaining 70%.

The module has been designed to give you an education in how cryptological techniques have developed over the last two millennia as well as an ability to, both, create hidden messages and reveal hidden messages.

### Course info

UCAS Code G100

Credits 20

Mode of Study 3 years full-time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2022

## Mathematics BSc (Hons)

All information on this course page is accurate at the time of viewing.

Courses starting in 2021 are offered as a mix of face to face and online learning. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to flex accordingly to ensure the health and safety of our students and staff.

Contact time is subject to increase or decrease in line with additional restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors, potentially to a full online offer, should further restrictions be deemed necessary in future.

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