Subjects(version: 867)
Course, academic year 2019/2020

Probability and Cryptography - NMMB407
Title: Pravděpodobnost a kryptografie Department of Algebra (32-KA) Faculty of Mathematics and Physics from 2018 to 2019 winter 6 winter s.:4/0 Ex [hours/week] unlimited unlimited taught Czech, English full-time http://dostanou moje poznamky na konci semestru
Guarantor: Mgr. Michal Kupsa M Mgr. MMIB Mathematics > Algebra, Probability and Statistics NMIB051 NMIB051
 Annotation - ---CzechEnglish
Last update: T_KA (14.05.2013)
Selected topics of Probability and Statistics, and their applications in Cryptography.
 Course completion requirements - ---CzechEnglish
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

Students have to pass final oral exam.

 Literature - ---CzechEnglish
Last update: T_KA (14.05.2013)
• G.Grimmet a D.Stirzaker (2001) Probability and Random Processes. Oxford Univ. Press.
• J.M. Stoyanov (1987) Couterexamples in Probability. J.Wiley & Sons.
• D.A. Levin, Y. Peres a E.L. Wilmer (2008) Markov Chains and Mixing Times. AMS.
• T.M. Cover a J.A. Thomas (1991) Elements of Information Theory. J.Wiley & Sons.
• V. Shoup (2009) Computational Introduction to Number Theory and Algebra. Cambridge University Press.

 Requirements to the exam - ---CzechEnglish
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures.

 Syllabus - ---CzechEnglish
Last update: T_KA (14.05.2013)
• Conditional stochastic independence and information theoretical quantities.
• Generating functions and random walk. Bonferroni inequalities. Finite de Finetti theorems.
• Markov chains, classification of states, mixing times.
• Efficient parameter estimations in exponential families. Cramér-Rao bound.
• Introduction to the large deviation theory. Sanov theorem.
• Information geometry and statistics. Stein lemma. Testing random generators.
• Probability in authentication and secret sharing. Hash functions and randomness.

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