posted 28 Jul 2025
Mathematical Foundations of Cryptography
§ Overview
The aim of the course is to teach the mathematical foundations behind the commonly used cryptographic algorithms and systems used in modern computation and communications.
As such, it is useful to begin with a discussion over some relevant topics in number theory and abstract algebra to develop a foundation on which we build cryptographic schemes.
§ Contents
Algebraic Structures
Basic group and field structures.
Modular Arithmetic
Addition, multiplication, and multiplicative inverses under a cyclic group.
Greatest Common Divisor
Finding a solution to the Diophantine equation in .
Fast Powering
Many cryptographic schemes rely on exponentiation, and we want to do it fast and secure.
Totient Function and Euler's Theorem
The totient function has some nice properties under a cyclic group, making it attractive for cryptosystems such as RSA.