SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Number theory and Cryptography - OB1310504
Title in English: Teorie čísel a kryptografie
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: winter
E-Credits: 2
Examination process: winter s.:
Hours per week, examination: winter s.:0/1 C [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Additional information: http://class.pedf.cuni.cz/Jancarik/DesktopDefault.aspx?tabindex=1&tabid=23&portalsekce=2
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Jarmila Novotná, CSc.
doc. RNDr. Antonín Jančařík, Ph.D.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)
Introduction to the history of cryptography, cryptoanalysis and number theory.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)

To acquaint students with history of cryptography and cryptoanalysis and the foundations of the theory of numbers (primality tests and factorization), including specific applications in cryptology - RSA.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)

Koblitz, N. A Course in Numer Theory and Cryptography, Springer-Verlag, 1998, ISBN 0-387-94293-9

Piper, F., Murény, S. Kryptografie, Praha: Dokořán, 2006, ISBN 80-7363-074-

Rosen, H. Elementary Number Theory and Its Applications, Addison-Wesley, 2000, ISBN: 0201870738

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)

Seminar

Requirements to the exam - Czech
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)

Zápočet bude uělen za průběžné plnění úkolů v průběhu semestru. Většina úkolů se bude skládat ze zašifrovávání a rozšifrovávání textů a tématických referátů.

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (12.03.2010)

Main topics:

Divisibility and Euclidean algorithm

The final fields

Primes and pseudoprimes

Primality tests

Factorizations

RSA

 
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