Master of Mathematics in Combinatorics and Optimization - Cryptography in Waterloo Canada | University of Waterloo

Combinatorics examines finite systems and their characteristics. Contemporary scientific progress frequently utilizes combinatorial models to represent real-world phenomena, with computational advancements enabling practical exploration. Given that computers operate on discrete information, combinatorics has become essential to computer science. Optimization, or mathematical programming, focuses on finding maximum and minimum values of functions within given constraints. The rise of computing power propelled optimization's development as a mathematical discipline, enriching both combinatorics and traditional analysis. These optimization problems originate from engineering, physical sciences, management fields, and diverse mathematical domains. The MMath program includes approximately one year of graduate-level coursework followed by either a research project or thesis under faculty guidance.

Traditional cryptography employed algorithms reliant on confidential keys, which required secure pre-communication exchange. (In well-designed systems, security should depend solely on the key, with the algorithm presumed known to adversaries.) A revolutionary cryptosystem emerged in 1976—asymmetric or public-key cryptography. These systems distinctly separate encryption and decryption functions, allowing public sharing of one key while keeping the other private. This innovation removes the necessity for secure key exchange before communication. Such systems rely on computationally difficult mathematical challenges like integer factorization. Identifying suitable complex problems and developing associated public-key systems has created a vibrant research field. The Centre for Applied Cryptographic Research (CACR) at Waterloo conducts both theoretical and applied investigations into cryptography, security, and privacy. Current cryptographic research in the C&O department encompasses elliptic/hyperelliptic curve cryptography, pairing-based systems, quantum-resistant cryptography, and cryptographic protocol development and analysis.