Completed courses Algebra 1 and Introduction to programming.

# Coding theory and cryptography

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.

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.

Students learn the basics of coding theory and cryptography.

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.

Lectures, exercises, homework, consultations

2 midterm exams instead of written exam, written exam

Oral exam

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

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]