Number Theory and Cryptography
General data
Course ID: | 1000-1D06TLK |
Erasmus code / ISCED: |
11.124
|
Course title: | Number Theory and Cryptography |
Name in Polish: | Teoria liczb i kryptografia |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Master seminars for Mathematics |
ECTS credit allocation (and other scores): |
6.00
|
Language: | English |
Type of course: | Master's seminars |
Short description: |
The seminar covers a variety of number-theoretic topics with particular emphasis on those that are related to cryptography. |
Full description: |
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 |
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 |
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 methods and 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) |
Classes in period "Academic year 2023/24" (in progress)
Time span: | 2023-10-01 - 2024-06-16 |
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MO TU W TH SEM-MGR
FR |
Type of class: |
Second cycle diploma seminar, 60 hours
|
|
Coordinators: | Jacek Pomykała, Bartosz Źrałek | |
Group instructors: | Jacek Pomykała, Bartosz Źrałek | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Pass/fail
Second cycle diploma seminar - Pass/fail |
Classes in period "Academic year 2024/25" (future)
Time span: | 2024-10-01 - 2025-06-08 |
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MO TU W TH FR |
Type of class: |
Second cycle diploma seminar, 60 hours
|
|
Coordinators: | Piotr Achinger, Masha Vlasenko | |
Group instructors: | Piotr Achinger, Masha Vlasenko | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Pass/fail
Second cycle diploma seminar - Pass/fail |
Copyright by University of Warsaw.