M0170 Cryptography

Faculty of Science
Autumn 2023
Extent and Intensity
2/1/0. 5 credit(s). 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
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M0170/01: Thu 16:00–16:50 M3,01023, 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 the mathematical basics of cryptography theory. Some applications, especially in computer science, of the cryptography theory are mentioned.
Learning outcomes
Absolving the discipline student obtains following basic knowledge and skills:
* Understanding of basic principles of cryptography, the formulation of perfect security.
* Understanding of nature and variations of the perfect encryption system one-time pad.
* Practical calculation procedures in solving equations resulting from the use of linear shift-registers.
* Understanding the concepts of computational complexity, integrity and authenticity.
* Understanding and explanation of the nature of asymmetric encryption system.
* Applications of cryptographic techniques in solving specific problems from security and data encryption.
Particularly, after passing the course, the student will be able:
* to define and interpret the basic notions used in the basic parts of cryptography and to explain their mutual context;
* to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
* to use effective techniques utilized in basic fields of cryptography;
* to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
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
  • Porubský, Š. a Grošek, O. Šifrovanie. Algoritmy, Metódy, Prax. Grada, Praha 1992. ISBN 80-85424-62-2
  • Welsh, D., Codes and Cryptography, Oxford University Press, New York 1989.
  • BUCHMANN, Johannes A. Introduction to cryptography. 2nd ed. New York: Springer, 2004, xvi, 335. ISBN 038721156X. info
  • 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
Teaching methods
Lectures: theoretical explanation with practical examples.
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework.
Students will be asked to participate actively in seminars or to do written homework that will be lectured at some seminar. The theme will be chosen after the negotiation with the lecturer.
Assessment methods
Lecture with a seminar. Examination is oral with a written preparation. The success at the examination is based on providing an exposition with respect to a chosen chapter.
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
In the case of not passing up to now the course Coding we recommend to enroll in that course. The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2004, Spring 2006, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, autumn 2021.
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