Infopaket

Algebraic structures, cryptography and data security

Обов’язкова дисципліна для ОП

First

2021/2022

5 Semester

5

PLO16. Understand the concept of information security, principles of safe software design, ensure the security of computer networks given incompleteness and uncertainty of the source data.

Full-time form

In order to successfully master the course "Algebraic Structures, Cryptography and Data Security" students must be fluent in the standard course "Algebra and Geometry". In particular, be able to perform basic operations with matrices and polynomials, know the basic concepts of the theory of linear spaces (linear dependence, basis, linear operator) and the theory of binary relations (equivalence, partial order, factorization using equivalence relations). Students must also have basic programming skills.

The aim of the course "Algebraic Structures, Cryptography and Data Security" is to acquaint students with the basic types of abstract algebraic structures (groups, rings, fields and their extensions) and the basics of number theory, with the goal towards further use in cryptography and information security. The discipline consists of two modules: "Module 1. Algebraic structures and basics of number theory" and "Module 2. Basic algorithms of cryptography, public key cryptosystems, cryptography over elliptic curves".

1. Apostol T. Introduction to Analytic Number Theory. Springer-Verlag, 1976. 2. Fraleigh J. A First Course in Abstract Algebra, 7th ed. Addison-Wesley Publishing, 2003. 3. Avdoshin S.M., Nabebin A.A. Diskretnaya matematika: modulyarnaya algebra, kriptogra-fiya, kodirovaniye. M.: DMK Press, 2017. 4. Klesov O.Í. Yelementarna teoríya chisel ta yelementi kriptografíí̈. K.: TVíMS, 2016. 5. Kostrikin A.I. Sbornik zadach po algebre, M: Fizmatlit 2001. 6. Akho Al'fred V., Khopkroft Dzhon, Ul'man Dzheffri D. Struktury dannykh i algoritmy: Uch.pos. – SPb.: Izdatel'skiy dom «Vil'yams», 2010. 7. Knut D. Iskusstvo programmirovaniya: V 3 t.– M.: Mir; Tom 1, 1976; Tom 3, 1978. 8. Kostrikin A.I. Vvedeniye v algebru, M: Fizmatlit, 2000. 9. Vel'shenbakh M. Kriptografiya na S i S++ v deystvii. M.: Triumf, 2003. 10. Marinich O.V. Algebraí̈chní strukturi, kriptografíya ta zakhist ínformatsíí̈: Yelektronniy navchal'niy posíbnik. http://do.unicyb.kiev.ua/marynych/wpcontent/uploads/2020/09/AlgStructCrypto.pdf

Lectures - 42 hours, seminars - 26 hours, consultations - 2 hours, independent work - 62 hours. The course includes 2 content modules. The discipline finishes with an exam in the 5th semester.

Intermediate assessment: The maximal number of available points is 60. • Test work no. 1: 15/9 points. • Test work no. 2: 15/9 points. • Laboratory work : 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

Ukrainian