Pseudorandomness and Random Number Generation

  1. Applications of Random Number Generation
    1. Cryptography
      1. Key Generation
        1. Nonces and Initialization Vectors
          1. Padding Schemes
            1. Challenge-Response Protocols
              1. Digital Signatures
                1. Salt Generation
                2. Simulation and Modeling
                  1. Monte Carlo Methods
                    1. Numerical Integration
                      1. Financial Modeling
                        1. Physics Simulations
                          1. Chemistry Simulations
                          2. Stochastic Processes
                            1. Markov Chains
                              1. Random Walks
                                1. Queuing Theory
                              2. Computer Programming and Software
                                1. Data Structures
                                  1. Skip Lists
                                    1. Hash Tables
                                      1. Randomized Trees
                                      2. Randomized Algorithms
                                        1. Quicksort
                                          1. Load Balancing
                                          2. Shuffling and Sampling
                                            1. Fisher-Yates Shuffle
                                              1. Reservoir Sampling
                                                1. Random Permutations
                                              2. Gaming and Entertainment
                                                1. Procedural Content Generation
                                                  1. AI Behavior Randomization
                                                    1. Online Gaming Security
                                                      1. Fairness Verification
                                                      2. Statistical Sampling and Research
                                                        1. Population Sampling
                                                          1. A/B Testing
                                                            1. Survey Randomization
                                                              1. Clinical Trial Randomization

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                                                            5. Theoretical Foundations of Pseudorandomness

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                                                            7. Practical Implementation and Considerations