Number theory and cryptography 1000-1S06TLK
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
Course coordinators
Term 2023: | Term 2024: |
Type of course
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. W. Narkiewicz, Classical problems in number theory
5. W. Sierpiński, Elementary theory of numbers
6. A. Enge, Elliptic curves and their application to cryptography
7. H. L. Montgomery, Topics in multiplicative number theory