M0170 Cryptography

Faculty of Science
Spring 2006
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Paseka, CSc.
Timetable
Fri 12:00–13:50 N21
  • Timetable of Seminar Groups:
M0170/01: Fri 14:00–14:50 N21, J. Paseka
Prerequisites
Mathematical analysis I. and II., Linear algebra and geometry I. and II. , Fundamentals of mathematics, Algebra I, Probability and Statistics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The basic aim of the lecture is the introduction of the student to establish the mathematical basics of the cryptography theory. Some applications, especially in computer science, of the cryptography theory are mentioned.
Syllabus
  • Introduction. A very abstract summary. History. Outline of the course. Cryptosystems and their application in computer science. Basic principles. Breaking a cryptosystem. Perfect secrecy. The one time-pad and linear shift-register sequences. The one time-pad. The insecurity of linear shift register sequences. One-way functions. Informal approach; the password problem. Using NP-hard problems as cryptosystems. The Data Encryption Standard (DES). The discrete logarithm. Public key cryptosystems. The idea of a trapdoor function. The Rivest-Shamir-Adleman (RSA) system. A public-key system based on the discrete logarithm. Authentication and digital signatures. Authentication in a communication system. Using public key networks to send signed messages. Two-party protocols. Multi-party protocols. Randomized encryption.
Literature
  • Welsh, Dominic.: Codes and Cryptography.Oxford University Press,M New York 1989. ISBN
  • Porubský, Š. a Grošek, O. Šifrovanie. Algoritmy, Metódy, Prax. Grada, Praha 1992. ISBN 80-85424-62-2
  • MENEZES, A. J., Paul van OORSCHOT and Scott A. VANSTONE. Handbook of applied cryptography. Boca Raton: CRC Press, 1997, xiii, 780. ISBN 0-8493-8523-7. info
  • SCHNEIER, Bruce. Applied cryptography : protocols, algorithms, and source code in C. New York: John Wiley & Sons, 1996, xxiii, 758. ISBN 0471128457. info
  • SALOMAA, Arto. Public-key cryptography. 2nd ed. Berlin: Springer, 1996, x, 271. ISBN 3540613560. info
Assessment methods (in Czech)
Zkouška je ústní. Je nutná aktivní účast na cvičeních nebo zpracování písemného referátu, který bude následně přednesen na některém ze cvičení. Téma bude stanoveno po dohodě s vyučujícím.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~paseka
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2004, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, autumn 2021, Autumn 2023.
  • Enrolment Statistics (Spring 2006, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2006/M0170