Number Theory and Cryptography 1000-1D06TLK
The seminar covers a variety of number-theoretic topics with particular emphasis on those that are related to cryptography. The topics include:
1. Divisibility in integral domains
2. Quotient structures
3. Bilinear group structures
4. Computational problems
5. Arithemtic and multiplicative functions
6. Primality in unique decomposition domains
7. Decomposition bases
8. Congruence theory. modular arithmetic
9. Lattices and their application to the factorization problem
10. Classical conjectures in number theory
11. Derandomization problem
12. Factorization methods and algorithms
Type of course
Course coordinators
Term 2024: | Term 2023: |
Learning outcomes
Ability to study mathematical literature
leading to an understanding of the deep applications of number theory in
modern cryptography.
Ability to deliver a prepared lecture and answer questions from seminar participants.
Assessment criteria
For students completing the monographic seminar-
passing the seminar is based on the delivered lecture and active participation in classes.
For students who attend the MA seminar, passing the seminar is based on:
1) preparing and delivering a lecture,
2) approval of the subject of the master's thesis (1st year students) or submission of thesis (2nd year students)
Bibliography
1. E. Bach, J. Shallit, Algorithmic Number Theory
2. S. Y. Yan, Number Theory for Computing
3. R. Crandall, C. Pomerance, Prime numbers - a computational perspective
4. P. Ribenboim, The little book of bigger primes
5. W. Narkiewicz, Classical problems in number theory
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: