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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.

MI-MKY.16 Mathematics for Cryptology Extent of teaching: 3P+1C

Instructor: Completion: Z,ZK

Department: 18106 Credits: 5 Semester: L

Annotation:
Students become familiar with parts of mathematics necessary for deeper understanding of the methods used in symmetric and asymmetric cryptography. They learn the mathematical principles on which security of encryption systems, cryptanalysis methods, cryptography over elliptic curves, and quantum cryptography are based.

Lecture syllabus:

1. General Algebra: Group, ring, eld, vector space.

2. Extension of nite elds and choice of their bases.

3. (2) Algebraic equations: Grobner bases.

4. (2) Solving algebraic equations over nite elds.

5. Discrete logarithm: Die-Hellman key exchange, ElGamal encryption system.

6. Discrete logarithm: Babystep-giantstep algorithm, Pollard's rho method.

7. Discrete logarithm: Pohlig-Hellman algorithm.

8. Elliptic curves over real numbers and Galois elds.

9. Factoring using elliptic curves, the MOV algorithm.

10. Quantum computing: foundations of quantum mechanics, qubit and operations with it.

Seminar syllabus:
Examples of various mathematical structures will be discussed.

Literature:

1. Hoffstein, J. - Pipher, J. - Silverman, J. H. An Introduction to Mathematical Cryptography. Springer, 2008. ISBN 978-1441926746.

2. Lidl, R. - Niederreiter, H. Finite Fields. Cambridge University Press, 2008. ISBN 978-0521065672.

3. Menezes, A.J. - van Oorschot, P. C. - Vanstone, S. A. Handbook of Applied Cryptography. CRC Press, 1996. ISBN 0-8493-8523-7.

4. Nielsen, M. A. - Chuang, I. L. Quantum Computation and Quantum Information. Cambridge University Press, 2011. ISBN 978-1107002173

Requirements:
Good knowledge of algebra, linear algebra and basics of number theory (BI-LIN, BI-ZDM, MI-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

MI-ZI.2016 Knowledge Engineering V 2

MI-ZI.2018 Knowledge Engineering V 2

MI-WSI-SI.2016 Web and Software Engineering V 2

MI-WSI-ISM.2016 Web and Software Engineering V 2

MI-PSS.2016 Computer Systems and Networks V 2

MI-SP-TI.2016 System Programming V 2

MI-NPVS.2016 Design and Programming of Embedded Systems V 2

MI-PB.2016 Computer Security PO 2

MI-SP-SP.2016 System Programming V 2

MI-WSI-WI.2016 Web and Software Engineering V 2

MI-SPOL.2016 Unspecified Branch/Specialisation of Study VO 2

NI-TI.2018 Computer Science V 2

Page updated 20. 4. 2024, semester: L/2023-4, L/2020-1, L/2022-3, L/2021-2, Z/2019-20, Z/2022-3, Z/2020-1, Z/2023-4, L/2019-20, Z/2021-2, Z/2024-5, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška

MI-MKY.16	Mathematics for Cryptology			Extent of teaching:	3P+1C
Instructor:				Completion:	Z,ZK
Department:	18106	Credits:	5	Semester:	L

1.		General Algebra: Group, ring, eld, vector space.
2.		Extension of nite elds and choice of their bases.
3.		(2) Algebraic equations: Grobner bases.
4.		(2) Solving algebraic equations over nite elds.
5.		Discrete logarithm: Die-Hellman key exchange, ElGamal encryption system.
6.		Discrete logarithm: Babystep-giantstep algorithm, Pollard's rho method.
7.		Discrete logarithm: Pohlig-Hellman algorithm.
8.		Elliptic curves over real numbers and Galois elds.
9.		Factoring using elliptic curves, the MOV algorithm.
10.		Quantum computing: foundations of quantum mechanics, qubit and operations with it.

1.		Hoffstein, J. - Pipher, J. - Silverman, J. H. An Introduction to Mathematical Cryptography. Springer, 2008. ISBN 978-1441926746.
2.		Lidl, R. - Niederreiter, H. Finite Fields. Cambridge University Press, 2008. ISBN 978-0521065672.
3.		Menezes, A.J. - van Oorschot, P. C. - Vanstone, S. A. Handbook of Applied Cryptography. CRC Press, 1996. ISBN 0-8493-8523-7.
4.		Nielsen, M. A. - Chuang, I. L. Quantum Computation and Quantum Information. Cambridge University Press, 2011. ISBN 978-1107002173