Pseudorandomness and Random Number Generation

  1. Theoretical Foundations of Pseudorandomness
    1. Computational Complexity Theory
      1. P vs. NP Problem
        1. BPP Complexity Class
          1. Relevance to Pseudorandomness
            1. Derandomization
            2. One-Way Functions
              1. Definition and Properties
                1. Candidate One-Way Functions
                  1. Integer Factorization
                    1. Discrete Logarithm Problem
                      1. Subset Sum Problem
                      2. Existence and Implications
                      3. Hard-Core Predicates
                        1. Definition and Importance
                          1. Extracting Hard Bits
                            1. Goldreich-Levin Theorem
                            2. Pseudorandom Generators
                              1. Formal Definition
                                1. Security Notions
                                  1. Construction from One-Way Permutations
                                    1. Seed Expansion
                                      1. Computational Indistinguishability
                                      2. Pseudorandom Functions
                                        1. Definition and Properties
                                          1. Security Notions
                                            1. Distinguishing from Random Functions
                                              1. GGM Construction
                                              2. Pseudorandom Permutations
                                                1. Definition and Properties
                                                  1. Strong PRPs
                                                    1. Luby-Rackoff Construction
                                                      1. Feistel Networks
                                                        1. Applications in Block Ciphers

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                                                      4. Cryptographically Secure Pseudorandom Number Generators

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                                                      6. Applications of Random Number Generation