Coding theory and cryptography

2022/2023
Programme:
Financial mathematics, First Cycle
Year:
3 year
Semester:
second
Kind:
optional
Group:
B2
ECTS:
5
Language:
slovenian
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Prerequisites

Completed courses Algebra 1, Introduction to programming and Probability 1.

Content (Syllabus outline)

Coding theory. Information and entropy. Shannon's theory. Error-correcting codes. Bounds on the size of codes. Linear, Hamming, cyclic and Reed-Muller codes. Cryptography. Classical cryptography. Symmetric-key cryptosystems. RSA cryptosystem and public-key cryptography. Digital signatures. Hash functions. Key distribution and key agreement schemes. Identification, authentication, secret sharing schemes. Zero-knowledge proofs.

Readings

D. R. Stinson: Cryptography : Theory and Practice, 3rd edition, Chapman & Hall/CRC, Boca Raton, 2005.
J. Talbot, D. Welsh: Complexity and Cryptography, Cambridge Univ. Press, Cambridge, 2006.
D. Welsh: Codes and Cryptography, Oxford Univ. Press, Oxford, 1988.

Objectives and competences

Students learn the basics of coding theory and cryptography.

Intended learning outcomes

Knowledge and understanding:
Mathematical procedures that enable reliable and secure communication.

Application:
Coding theory and cryptography are used in digital communications and for providing information security.

Reflection:
Basic techniques of modern cryptography are based on mathematical concepts and procedures that provide the maximum level of security known.

Transferable skills:
The students will acquire skills of critical thinking and analysys of the communication channels and computer systems with respect to information security.

Learning and teaching methods

Lectures, exercises, homework, consultations

Assessment

Type (examination, oral, coursework, project):
2 midterm exams instead of written exam, written exam
oral exam
grading: 1-5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Primož Potočnik:
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. On the nullspace of arc-transitive graphs over finite fields. Journal of algebraic combinatorics, ISSN 0925-9899, 2012, vol. 36, no. 3, str. 389-401. [COBISS-SI-ID 16162137]
POTOČNIK, Primož. B-groups of order a product of two distinct primes. Mathematica slovaca, ISSN 0139-9918, 2001, vol. 51, no. 1, str. 63-67. [COBISS-SI-ID 10617433]
POTOČNIK, Primož, VERRET, Gabriel. On the vertex-stabiliser in arc-transitive digraphs. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2010, vol. 100, iss. 6, str. 497-509. [COBISS-SI-ID 15680601]
Arjana Žitnik:
JURIŠIĆ, Aleksandar, TERWILLIGER, Paul, ŽITNIK, Arjana. The Q-polynomial idempotents of a distance-regular graph. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2010, vol. 100, iss. 6, str. 683-690. [COBISS-SI-ID 15688537]
KAVČIČ, Urška, MUCK, Tadeja, LOZO, Branka, ŽITNIK, Arjana. Readability of multi-colored 2D codes. Technics tehnologies education management, ISSN 1840-1503, 2011, vol. 6, no. 3, str. 622-630, ilustr. [COBISS-SI-ID 2673008]
CONDER, Marston D. E., PISANSKI, Tomaž, ŽITNIK, Arjana. GI-graphs: a new class of graphs with many symmetries. Journal of algebraic combinatorics, ISSN 0925-9899, 2014, vol. 40, iss. 1, str. 209-231. [COBISS-SI-ID 16969561]