Uniform random numbers : theory and practice

Series Foreword by Yu-Chi Ho. Preface. 1: Introduction. 2: Preliminaries from Number Theory. 2.1. Modular Arithmetic. 2.2. Geometry of Numbers. 2.3. Uniform Distribution of Sequences. 3: Linear Congruential Generators. 3.1. Lattice Structure. 3.2. Spectral Test. 3.3. Implementing Long-Period LCGs. 4: Beyond Linear Congruential Generators. 4.1. LCGs Using Polynomial Arithmetic. 4.2. LCGs Using Multiplicative Inversion. 4.3. Random Sequences in Cryptography. 5: Statistical Tests. 5.1. Description of Test Procedures. 5.2. Tests Using Non-Uniform Random Variate Generation. 6: Derandomization. 6.1. Low-Discrepancy Sequences. 6.2. K-wise Independent Random Variables. A: Sample C Routines. References Index.