Numbers are one of the most fundamental concepts in mathematics and indeed in everyday life. Their study dates back thousands of years to Chinese, Babylonian, Greek, Indian, and Persian thinkers. In the second half of the twentieth century, amazing and far-reaching applications to the emerging information technology industry were found. Nowadays their theory provides the basis for all security on the internet and other communication channels, keeping your messages and bank details safe, for example. Surprising new applications continue to be discovered!
In the first half of the module you’ll learn the core results of number theory such as the Chinese Remainder Theorem and Fermat’s Little Theorem and gain technical skills in working with prime numbers, modular arithmetic, and Diophantine equations. In the second half of the module you’ll see how these core results and techniques are applied in cryptography, the science of protecting information. More specifically, you’ll learn about: classical cryptosystems and their weak point, the “key distribution problem”, the public key ciphers and computational security, and the challenge coming from quantum computing.
Lecture 44, PC 4, Revision 4, Independent Study 98, Assessment Preparation 50
Spring
Problem sheets worth 30%.
Examination (2-hours) worth 70%.
Reassessment Method: Like-for-like Including composite form of reassessment for failed portfolio– written single problem sheet
On successfully completing the module, students will be able to:
1) Apply key concepts of number theory and cryptography,
2) Execute some fundamental computational methods and algorithms in number theory and cryptography,
3) Evidence a conceptual understanding of how to approach and solve problems in elementary number theory and cryptography,
4) Evaluate arguments, hypotheses, and conclusions drawn from the domain of number-theoretic and cryptographic problems, examples, and theorems,
5) Communicate their work and knowledge of number theory and cryptography accurately and using sound arguments.
University of Kent makes every effort to ensure that module information is accurate for the relevant academic session and to provide educational services as described. However, courses, services and other matters may be subject to change. Please read our full disclaimer.