SubjectsSubjects(version: 867)
Course, academic year 2019/2020
Probability and Cryptography - NMMB407
Title: Pravděpodobnost a kryptografie
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:4/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://dostanou moje poznamky na konci semestru
Guarantor: Mgr. Michal Kupsa
Class: M Mgr. MMIB
Classification: Mathematics > Algebra, Probability and Statistics
Incompatibility : NMIB051
Interchangeability : NMIB051
Annotation -
Last update: T_KA (14.05.2013)
Selected topics of Probability and Statistics, and their applications in Cryptography.
Course completion requirements -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

Students have to pass final oral exam.

Literature -
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 -
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 -
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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