Syllabus
- 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.
Annotation
Selected topics of Probability and Statistics, and their applications in Cryptography.