Infopaket

Mathematical foundations of information security

ДВС.1.01

Вибіркова дисципліна для ОП

Second

2023/2024

5 Semester

4

PLO5. Know and apply corresponding mathematical concepts, methods of domain, system and object-oriented analysis to mathematical modelling and developing of software. Choose a programming paradigm guided by convenience of implementing methods and algorithms for solving problems in the field of information security. PLO13. Know and apply methods of design algorithms, create corresponding software and data structures.

Full-time form

1. Know: basic concepts of discrete mathematics, classes of time complexity and explore of complexity of algorithms, discrete probabilistic distributions, main algebraic structures and main concepts of number theory. 2. Be able to: explore of problem, build mathematical models corresponding areas, estimate durability of systems by using of result of analysis. 3. Have basic skills: be able to use integrated environment of software designing.

The purpose of the discipline is to master the basic concepts of symmetric and asymmetric cryptographic systems of both classical and nonclassical types and which are based on applications of probability theory, algorithm complexity theory, theory of groups, rings and fields, number theory and algorithms used in these theories. Such algorithms include algorithms for testing numbers for simplicity, modular arithmetic algorithms and numerical algorithms in groups, algorithms for calculating a discrete logarithm, and so on.

1. Vasilenko A.N. Theoretical-number algorithms in cryptography. - М.: МCCME - 2003.- 328 p. 2. Venbo Mао. Modern Cryptography. – Sankt-Peter.: ``Viljams''. - 2005.- 763 p. 3. Coblenc N. Course of number theory and cryptography. - М.: Printed TVP. - 2001.- 260 p. 4. Korobejnikov A.G., Datychin Yu. А. Mathematical foundations of cryptology. – Sankt-Pet.: Verlag ITMO - 2004.- 110 p. 5. Rifbko B.J. Fionov А.N. Cryptografical methods information security. - М: Goriachaja linia. -- Telecom. - 2005. - 229 p. 6. Stallings William. Ochrona danych w sieci i intersieci. - Warszawa: Wydawnictwo Naukowo Techniczne. - 1997. - 474s.

Lectures, laboratory classes, independent work, tests, homework, defense of laboratory work, exam.

- Semester assessment: 1. Test 1: LO 1.1, LO1.2 - 10 points / 6 points. 2. Test 2: LO1.3 - 10 points / 6 points. 3. Homework 1-7: LO1.1, LO1.2, LO1.3-10 points / 6 points. 4. Protection of laboratory work 1 (project): LO2.1, LO3.1, LO4.1, LO4.2 - 11 points / 6 points. 5. Protection of laboratory work 2 (project): LO2.1, LO3.1, LO4.1, LO4.2 - 8 points / 5 points. 6. Protection of laboratory work 3 (project): LO2.1, LO3.1, LO4.1, LO4.2 - 11 points / 6 points. In one of the forms of control, the student has the right to replace it with a certificate with the possibility of obtaining 9 points. To exercise this right, the student must, by 1st of January of the current year, write and attach to the classroom a statement with his personal signature. Final assessment (in the form of an exam): - maximum number of points: 40 points; - learning outcomes which shall be assessed: LO1.1, LO1.2, LO1.3, LO2.1.

Ukrainian