Difference between revisions of "MAT5133"

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(Created page with "Introduction to post-quantum Cryptography.")
 
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Introduction to post-quantum Cryptography.
 
Introduction to post-quantum Cryptography.
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'''Sample textbook''':
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[1] Daniel Bernstein, Johannes Buchmann, Erik Dahmen, ''Post-Quantum Cryptography'', Springer, 201-
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'''Catalog entry'''
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''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
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''Contents'':
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(1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms.
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(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.
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(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.
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(4) Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets.
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(5) Functions: Operations of functions, direct image and inverse image.
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(6) Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions.
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(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.
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==Topics List==
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{| class="wikitable sortable"
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! Week !! Topic !! Chapter 1 from the Bernstein-Johannes Buchmann-Dahmen book !! MAT1313, or CS2233/2231, or instructor consent.
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|-
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|  1-3 
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|| [[Introduction to post-quantum cryptography]]
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|| 1
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|| MAT1313 or CS2233/2231, or equivalent.
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|-
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|  2-4 
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|| [[Quantum computing]]
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|| 2
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||
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|-
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|  5-6 
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|| [[Hash-based Digital Signature Schemes]]
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|| 3
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||
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|-
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|  7-8 
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|| [[Code-based cryptography]]
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|| 4
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||
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|-
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|  9-10 
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|| [[Lattice-based Cryptography]]
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|| 5
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||
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|-
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|  11-12 
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|| [[Multivariate Public Key Cryptography]]
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|| 6
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||
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|-
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|  13-end 
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|| [[Homomorphic encryption]]
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|| 7
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||
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|}

Revision as of 10:10, 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) 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
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