Completed courses Algebra 2 and Introduction to programming.
Coding theory and cryptography
2025/2026
Programme:
Mathematics, First Cycle
Year:
3 year
Semester:
second
Kind:
optional
Group:
B2
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
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 ed. - Boca Raton : Chapman & Hall/CRC, cop. 2006.
- J. Talbot, D. Welsh: Complexity and cryptography : an introduction, Cambridge : Cambridge University Press, cop. 2006.
- D. Welsh: Codes and cryptography, Oxford : Clarendon Press, cop. 1989, 1995.
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
2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
Tilen Marc:
MARC, Tilen, STOPAR, Miha, HARTMAN, Jan, BIZJAK, Manca, MODIC, Jolanda. Privacy-enhanced machine learning with functional encryption. V: SAKO, Kazue (ur.). Computer Security - ESORICS 2019 : 24th European Symposium on Research in Computer Security : proceedings. Part 1, ISSN 0302-9743, 2019, str. 3-21. [COBISS-SI-ID 18935897]
MARIA BERMUDO MERA, Jose, KARMAKAR, Angshuman, MARC, Tilen, SOLEIMANIAN, Azam. Efficient lattice-based inner-product functional encryption. V: HANAOKA, Goichiro (ur.), SHIKATA, Junji (ur.), WATANABE, Yohei (ur.). Public-Key Cryptography – PKC 2022 : 25th IACR International Conference on Practice and Theory of Public-Key Cryptography: proceedings. Part II, ISSN 0302-9743, 2022, str. 163-193. [COBISS-SI-ID 105762051]
KNAUER, Kolja, MARC, Tilen. On tope graphs of complexes of oriented matroids. Discrete & computational geometry, ISSN 0179-5376, 2020, vol. 63, iss. 2, str. 377-417. [COBISS-SI-ID 18935385]
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]
