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Number theory and cryptography

General data

Course ID:	1000-1S06TLK
Erasmus code / ISCED:	11.124 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Number theory and cryptography
Name in Polish:	Teoria liczb i kryptografia (sem. mono. wspólnie z 1000-1D06TLK)
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Seminars for Mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective 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. 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

Classes in period "Academic year 2023/24" (in progress)

Time span:	2023-10-01 - 2024-06-16	Selected timetable range: weekly course term Navigate to timetable MO TU W TH SEM-MON FR
Type of class:	Monographic seminar, 60 hours more information
Coordinators:	Jacek Pomykała, Bartosz Źrałek
Group instructors:	Jacek Pomykała, Bartosz Źrałek
Students list:	(inaccessible to you)
Examination:	Course - Grading Monographic seminar - Grading

Classes in period "Academic year 2024/25" (future)

Time span:	2024-10-01 - 2025-06-08	Selected timetable range: weekly course term Navigate to timetable
Type of class:	Monographic seminar, 60 hours more information
Coordinators:	Piotr Achinger, Masha Vlasenko
Group instructors:	Piotr Achinger, Masha Vlasenko
Students list:	(inaccessible to you)
Examination:	Course - Grading Monographic seminar - Grading

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