# Coding theory and cryptography 2

2024/2025
Programme:
Computer Science and Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
B
ECTS:
6
Language:
slovenian, english
Course director:
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Prerequisites

There are no prerequisites.

Content (Syllabus outline)

The course is divided into core part, which treats the basics concepts and theoretical foundations and of coding theory and cryptography, and optional parts that include selected applications.
Core part:1. Data compression (symbol coding, Shannon's theory, Huffman coding, arithmetic coding, dictionary methods) 2. Cryptography (Basic concepts: symmetric cryptosystems, block ciphers, stream ciphers, asymmetric cryptosystems, hash functions, message authentication codes, digital signatures. Theoretical foundations: pseudorandom generators, one-way functions, their relations and uses in security analysis.) 3. Error-correcting codes (Shannon’s theorem, upper and lower bounds on the number of codewords, linear codes)

For the optional part the lecturer selects some of the following topics: selected cryptosystems, selected cryptographic protocols, efficient computation over finite fields, zero knowledge proof systems, secret sharing schemes, selected error-correcting codes (turbo codes, low density parity-check codes, Goppa codes), probabilsictic models of data

1. J. Justesen, T. Høholdt A course in error-correcting codes, Zürich : European Mathematical Society, cop. 2004.
2. D. R. Stinson: Cryptography : theory and practice, 3rd ed., Boca Raton : Chapman & Hall/CRC, cop. 2006.
3. D. Welsh: Codes and cryptography, Oxford : Clarendon Press, cop. 1989, 1995.
Objectives and competences

Students acquire competency to analyze communication channels with respect to security of information, reliability of transmission and computational complexity.

Intended learning outcomes

Knowledge and understanding: Applications of coding to achieve efficiency, security and reliability of communication. Strengths and weaknesses of symbol coding, stream coding, and dictionary methods. Comparison and applications of symmetric and asymmetric cryptosystems. Degrees of cryprographic security. Properties and use of linear codes. Good theoretical foundations in coding theory and cryptography and understanding of security analysis of cryptosystems. Knowledge of selected cryptosystems, protocols and codes in use.
Application: Data security.
Reflection: Strengths and weaknesses of different methods.
Transferable skills: Learning mathematical foundations of an applied area.

Learning and teaching methods

Lectures, seminar, recitation classes, coursework, consultations and independent work by the students.

Assessment

Type (examination, oral, coursework, project):

Continuous assessment (homework, midterm exams, project work)
Final (written or oral exam)

Grading: 6-10 pass, 5 fail (according to the rules of University of Ljubljana)

Lecturer's references

Sergio Cabello:
CABELLO, Sergio, PADRÓ, Carles, SÁEZ, Germán. Secret sharing schemes with detection of cheaters for a general access structure. Designs, codes and cryptography, ISSN 0925-1022, 2002, vol. 25, no. 2, str. 175-188. [COBISS-SI-ID 13352281]
CABELLO, Sergio, ROTE, Günter. Obnoxious centers in graphs. SIAM journal on discrete mathematics, ISSN 0895-4801, 2010, vol. 24, no. 4, str. 1713-1730. [COBISS-SI-ID 15762265]
CABELLO, Sergio, GIANNOPOULOS, Panos, KNAUER, Christian, MARX, Dániel, ROTE, Günter. Geometric clustering: fixed-parameter tractability and lower bounds with respect to the dimension. ACM transactions on algorithms, ISSN 1549-6325, 2011, vol. 7, no. 4, article 43 (27 str.). [COBISS-SI-ID 16028761]
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]