A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
NI-MKY Mathematics for Cryptology Extent of teaching: 3P+1C Instructor: Jureček M. Completion: Z,ZK Department: 18106 Credits: 5 Semester: L Annotation:
Students will gain deeper knowledge of algebraic procedures solving the most important mathematical problems concerning the security of ciphers. In particular, the course focuses on the problem of solving a system of polynomial equations over a finite field, the problem of factorization of large numbers and the problem of discrete logarithm. The problem of factorization will also be solved on elliptic curves. Students will further become familiar with modern encryption systems based on lattices.
Lecture syllabus:
1. Ideals in rings, factor rings, rings of polynomials. 2. Finite field extensions and choice of bases in them. 3. Solving algebraic equations over finite fields: relinearization, XL, and XSL algorithms. 4. Solving algebraic equations over finite fields: conversion to the SAT problem and methods solving this problem. 5. Groebner bases, Buchberger algorithm, Faugere F4 algorithm. 6. Factorization: Pollard rho method, p-1 method, Fermat factorization. 7. Factorization: sieve methods. 8. Discrete logarithm: Pohlig-Hellman algorithm, Baby-step giant-step algorithm, Pollard rho method. 9. Discrete logarithm: Index calculus. 10. Elliptic curves over real numbers and Galois fields. 11. ECDLP, elliptic curve factorization. 12. Lattice-based cryptography, GGH encryption system. 13. Orthogonalization and reduction, NTRU encryption system. Seminar syllabus:
Examples of various mathematical structures,, and algorithms will be discussed.Literature:
1. Katz, J. - Lindell, Y. : Introduction to modern cryptography. CRC press, 2014. ISBN 978-1466570269. 2. Hoffstein, J. - Pipher, J. - Silverman, J. H. : An Introduction to Mathematical Cryptography. Springer, 2008. ISBN 978-1441926746. 3. Lidl, R. - Niederreiter, H. : Finite Fields. Cambridge University Press, 2008. ISBN 978-0521065672. 4. Menezes, A. J. - van Oorschot, P. C. - Vanstone, S. A. : Handbook of Applied Cryptography. CRC Press, 1996. ISBN 0-8493-8523-7. Requirements:
Good knowledge of algebra, linear algebra, and basics of number theory (BI-LIN, BI-ZDM, NI-MPI).
Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-MKY/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester NI-PSS.2020 Computer Systems and Networks V 2 NI-ZI.2020 Knowledge Engineering V 2 NI-PB.2020 Computer Security PS 2 NIE-DBE.2023 Digital Business Engineering VO 2 NI-SPOL.2020 Unspecified Branch/Specialisation of Study VO 2 NI-MI.2020 Managerial Informatics V 2 NI-WI.2020 Web Engineering V 2 NI-TI.2023 Computer Science V 2 NI-TI.2020 Computer Science V 2 NI-NPVS.2020 Design and Programming of Embedded Systems V 2 NI-SI.2020 Software Engineering (in Czech) V 2 NI-SP.2020 System Programming V 2 NI-SP.2023 System Programming V 2
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