This book discusses the theory and practice of random number generators that are useful for computer simulation and computer security applications. Random numbers are ubiquitous in computation. They are used in randomized algorithms to perform sampling or choose randomly initialized parameters or perform Markov Chain Monte Carlo (MCMC). They are also used in computer security applications for various purposes such as cryptographic nuances or in authenticators. In practice, the random numbers used by any of these applications are from a pseudo-random sequence. These pseudo-random sequences are generated by RNGs (random number generators). This book discusses the theory underlying such RNGs, which are used by all programmers. However, few try to understand the theory behind them. This topic is an active area of research, particularly when the generators are used for cryptographic applications. The authors introduce readers to RNGs, how they are judged for quality, the mathematical and statistical theory behind them, as well as provide details on how these can be implemented in any programming language. The book discusses non-linear transformations that use classical linear generators for cryptographic applications and how to optimize to make such generators more efficient. In addition, the book provides up-to-date research on RNGs including a modern class of efficient RNGs and shows how to search for new RNGs with good quality and how to parallelize these RNGs.

Presents the theoretical basis and intuition of various random number generators without overly detailed proofs Enables readers to design, develop, modify, or experiment with new random number generators Provides comprehensive coverage of random number generation for both simulation and cryptographic applications

Autorentext

Lih-Yuan Deng, PhD, is a Professor in the Department of Mathematical Sciences at the University of Memphis. His research focuses on random number generators and has published several papers on the topic, as well as in other areas of statistics and data science.

Nirman Kumar, PhD, is currently a Consulting Member of Technical Staff at Oracle America, Inc. Prior to this, he was an Assistant Professor of Computer Science at the University of Memphis. His research work has focused on theoretical computer science and machine learning and he has several publications in the areas of computational geometry, randomized algorithms, and machine learning.

Henry Horng-Shing Lu, PhD, is a Professor in the Institute of Statistics at the National Yang Ming Chiao Tung University. His research focuses on statistics, image science, and bioinformatics with publications on related topics for scientific and industrial applications.

Ching-Chi Yang, PhD, is an Assistant Professor in the Department of Mathematical Sciences at the University of Memphis. His research focuses on statistical applications and has published several papers in the areas of statistical dimensional analysis.

Inhalt

Introduction.- Classical Random Number Generators for Computer Simulation.- Searching for Large Order MRG's.- Methods to Improve Basic Generators and Statistical Justifications.- Family of Efficient MRGs.- Quality Assessment for Random Number Generators.- Spectral Test for Judging MRG Quality.- Parallel RNG Methods.- MRGs with Many Non-zero Terms and its Efficient Implementation.- Empirical Tests on RNG.- Review of Secure Random Number Generators.- Secure RNG for Security Applications.- Review of Classical Ciphers.- Modern Software and Hardware Stream Ciphers.- Design of Secure Random Number Generators.- General Design Principle of New Class of Secure RNGs.- Specific Classes of Secure and Efficient RNGs.- Design and Implementation of R packages.