Description
Application to cryptography is probably
one of the greatest hallmarks of applicability of Pure
Mathematics to the ''real world''. This project focuses
on understanding fundamental algorithms that underpin
modern public key cryptography. In particular, we will
study various algorithms which are crucial in ensuring
various aspects of online security and conclude a
detailed analysis of different related protocols and
algorithms used to attack them. Even though the project
focuses on the theoretical aspects of cryptography,
interested students may be able to undertake some coding
and understand developing these algorithms.
Group Project
In the group project, you will learn
several classical algorithms which are mostly based on
modular arithmetic. These include
- Symmetric Key cryptography
- Diffie-Hellman key exchange
- RSA algorithm
- Various integer factoring algorithms
- Digital signature schemes
- Hash functions
Mode of Operation and Evidence of
learning for the Group Project
The project will revolve around learning
through reading, examples and problem solving, with
focus on mathematical rigour and the development of
conceptual understanding. Students will demonstrate
their understanding by understanding several algorithms,
solving relevant problems, exploring further examples
and applications of the material, and clearly
communicating it in both written and oral formats.
Individual project
In the individual phase of the project,
the students will explore more advanced/contemporary
algorithms. Possible choices include:
- Introduction to elliptic curves and
elliptic curve based algorithms
- Lenstra factoring algorithm
- Quadratic Sieve and its number field
version
- More modern algorithms such as X3DH
used in encryption of Signal and Whatsapp messaging.
Mode of Operation and Evidence of
learning for the Individual Project
The project will revolve around learning
through reading, examples and problem solving, with
focus on mathematical rigour and the development of
conceptual understanding. Students will demonstrate
their understanding by understanding several algorithms,
solving relevant problems, exploring further examples
and applications of the material, and clearly
communicating it in both written and oral formats.
Prerequisites
Deeper understanding of Analysis I, Linear Algebra I,
Algebra II is a must. Enrollment of Number Theory III would
be an added bonus especially in the second term.
Resources
Trappe and Washington, Introduction to Cryptography with
Coding Theory. Pearson Educational International, 2006.
Lawrence C. Washington, Elliptic Curves: Number Theory and
Cryptography, Discrete Mathematics and its applications.
2003.
|