Elements of Cryptography and Coding Theory

Course profile: academic

Form of study: stationary

Course type: obligatory

Academic discipline: Mathematics, field of study in the arts and science: mathematics

Year: 2, semester: 3

Prerequisities: Algebra I, Elementary Number Theory, Linear Algebra II

lecture 15 h. exercise class 30 h.

Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.

ECTS credits: 4

Balance of student workload:

attending lectures15x1h = 15h

attending exercise classes 7x4h + 2h(preliminary teaching) = 30h

preparation for classes 7x3h = 21h

completing notes after exercises and lectures 7x3h = 21h

consultations 5x1h = 5h

small projects: preparation and defense 40h = 40h

final work: preparation and take 10h + 2h = 12h

Quantitative description

Direct interaction with the teacher: 53 h., 2 ECTS

Practical exercises: 117 h., 4 ECTS

Learning outcomes:

Knowledge of elements of finite field algebra, linear algebra and number theory, which are needed to describe error-correcting codes and cryptosystems, among other things, knowledge of base-b representation (especially binary and hexadecimal expansions), ability of conversion between two different base-b representations, ability of the use of the extended Euclidean algorithm, ability of the use of modular exponentiation, ability to find inverses of the ring Z/mZ, ability to solve systems of linear congruences.K_W04, K_W05, K_W06, K_U01, K_U02, K_U03

Knowledge of chosen cryptosystems (symmetric ones and asymmetric ones): ability to encript and decript messages.K_U29, K_U25, K_U17, K_U11

Knowledge of basic definitions and properties of block codes. K_U29, K_U25, K_U17, K_U06

Knowledge of notions: linear codes, encoding and decoding information..K_U29, K_U25, K_U17, K_U16