Pseudorandomness and Random Number Generation

  1. Classical Pseudorandom Number Generators
    1. Linear Congruential Generators
      1. LCG Formula and Operation
        1. Parameter Selection
          1. Hull-Dobell Theorem
            1. Full Period Conditions
            2. Strengths and Weaknesses
              1. Simplicity and Speed
                1. Correlation Problems
                  1. Predictability Issues
                  2. Spectral Test for LCGs
                    1. Lattice Structure Analysis
                      1. Quality Assessment
                    2. Lagged Fibonacci Generators
                      1. Additive Lagged Fibonacci
                        1. Multiplicative Lagged Fibonacci
                          1. Parameter Selection
                            1. Period and Statistical Properties
                            2. Linear-Feedback Shift Registers
                              1. Structure and Operation
                                1. Characteristic Polynomials
                                  1. Maximal-Length LFSRs
                                    1. Applications in Communications
                                    2. Generalised Feedback Shift Registers
                                      1. Structure and Variants
                                        1. Improvements over LFSRs
                                          1. Twisted GFSR
                                          2. Mersenne Twister
                                            1. Algorithm Overview
                                              1. Period Length
                                                1. State Space and Initialization
                                                  1. Statistical Properties
                                                    1. Widespread Use and Limitations
                                                      1. Not Cryptographically Secure
                                                        1. Memory Requirements
                                                      2. Xorshift Generators
                                                        1. Basic Principle
                                                          1. Variants
                                                            1. Xorshift*
                                                              1. Xorshift+
                                                                1. Xoroshiro
                                                                2. Statistical Properties
                                                                  1. Performance Characteristics

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                                                                2. Statistical Testing of Random Number Generators

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                                                                4. Cryptographically Secure Pseudorandom Number Generators