Probability and Cryptography - NMIB051
| Title: |
Pravděpodobnost a kryptografie |
| Guaranteed by: |
Department of Algebra (32-KA) |
| Faculty: |
Faculty of Mathematics and Physics |
| Actual: |
from 2018 |
| Semester: |
winter |
| E-Credits: |
6 |
| Hours per week, examination: |
winter s.:3/1, C+Ex [HT] |
| Capacity: |
unlimited |
| Min. number of students: |
unlimited |
| 4EU+: |
no |
| Virtual mobility / capacity: |
no |
| State of the course: |
cancelled |
| Language: |
Czech |
| Teaching methods: |
full-time |
| Teaching methods: |
full-time |
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| Annotation -
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Last update: T_KA (03.05.2011)
Selected topics of Probability and Statistics, and their applications in Cryptography.
Last update: T_KA (03.05.2011)
Vybrané kapitoly teorie pravděpodobnosti a statistiky, a jejich aplikace v kryptografii.
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| Literature -
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Last update: T_KA (03.05.2011)
- 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.
Last update: T_KA (03.05.2011)
- 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.
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| Syllabus -
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Last update: T_KA (03.05.2011)
- 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.
Last update: T_KA (04.05.2011)
- Podmíněná stochastická nezávislost a informačně-teoretické veličiny.
- Generující funkce a náhodná procházka. Bonferroniho nerovnosti. Konečné de Finettiho věty.
- Markovské řetězce, klasifikace stavů, rychlost konvergence.
- Nestranné odhady parametrů v exponenciálních rodinách. Cramér-Raova mez.
- Úvod do teorie velkých odchylek. Sanovova věta.
- Informační geometrie a statistika. Steinovo lemma. Testování náhodných generátorů.
- Pravděpodobnost v autentifikaci a sdílení tajemství. Hašování a náhodnost.
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