MAT5133
Introduction to post-quantum Cryptography.
Sample textbook:
[1] Daniel Bernstein, Johannes Buchmann, Erik Dahmen, Post-Quantum Cryptography, Springer, 201-
Catalog entry
Prerequisite: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
Contents: (1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. (2) Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems. (3)Sets and boolean algebras: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory. (4) Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets. (5) Functions: Operations of functions, direct image and inverse image. (6) Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions. (7) Introduction to computability. Classical models of computation (recursive functions, and Turing models). Limitations of computation (the Halting Problem, the busy beaver problem, fast-growing functions). Contemporary models of computation.
Topics List
| Week | Topic | Chapter 1 from the Bernstein-Johannes Buchmann-Dahmen book | MAT1313, or CS2233/2231, or instructor consent. |
|---|---|---|---|
| 1-3 | Introduction to post-quantum cryptography | 1 | MAT1313 or CS2233/2231, or equivalent. |
| 2-4 | Quantum computing | 2 | |
| 5-6 | Hash-based Digital Signature Schemes | 3 | |
| 7-8 | Code-based cryptography | 4 | |
| 9-10 | Lattice-based Cryptography | 5 | |
| 11-12 | Multivariate Public Key Cryptography | 6 | |
| 13-end | Homomorphic encryption | 7 |
