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Algebraic structures, cryptography and data security

ОК.33

Обов’язкова дисципліна для ОП

First

2023/2024

5 Semester

4

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. Sridharan S., Balakrishnan R. Discrete Mathematics: Graph Algorithms, Algebraic Structures, Coding Theory, CRC Press, 2020. 4. Klesov, O.I. Elementary number theory and elements of cryptography. К.: TViMS, 2016. 5. Aho Alfred, Hopcroft John, Ullman Jeffrey. The design and analysis of computer algorithms. Addison-Wesley Publishing Company, 1974. 6. Knuth D. The Art of Computer Programming: In 3 Volumes, 1968-2022. 7. Welschenbach M. Cryptography in C and C++. APress, 2001. 8. Goldwasser S., Bellare M. Lecture Notes on Cryptography. https://cseweb.ucsd.edu/~mihir/papers/gb.pdf 9. Marynych O.V. Alhebraichni struktury, kryptohrafiia ta zakhyst informatsii: Elektronnyi navchalnyi posibnyk. https://do.csc.knu.ua/marynych/wp-content/uploads/sites/2/2023/12/AlgStructCrypto.pdf

Lectures - 42 hours, seminars - 14 hours, consultations - 2 hours, independent work - 46 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