Difference between revisions of "MAT5133"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
Line 14: Line 14:
  
 
''Contents'':
 
''Contents'':
−
(1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms.
+
(1) Introduction to post-quantum cryptography.
−
(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.
+
(2) Quantum computing.
−
(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.
+
(3) Hash-based Digital Signature Schemes.
−
(4) Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets.
+
(4) Code-based cryptography.
−
(5) Functions: Operations of functions, direct image and inverse image.
+
(5) Lattice-based Cryptography
−
(6) Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions.
+
(6) Multivariate Public Key Cryptography.
−
(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.
+
(7) Homomorphic encryption.
  
  
Line 63: Line 63:
 
|  13-end   
 
|  13-end   
 
|| [[Homomorphic encryption]]  
 
|| [[Homomorphic encryption]]  
−
|| 7
+
||  
 
||  
 
||  
 
|}
 
|}

Revision as of 10:14, 22 March 2023

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) Introduction to post-quantum cryptography. (2) Quantum computing. (3) Hash-based Digital Signature Schemes. (4) Code-based cryptography. (5) Lattice-based Cryptography (6) Multivariate Public Key Cryptography. (7) Homomorphic encryption.




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
Retrieved from "https://mathresearch.utsa.edu/wiki/index.php?title=MAT5133&oldid=4854"