Random number generators: algorithms, testing, applications

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As usual in this journal, the present article is a survey paper which shows Polish readers the state-of-the-art today with the goal of stimulating them to new applications. In the paper, all essential developments in random number generation are treated and the working field of the author, cryptography, is especially mentioned. (In this field, the author has already published with others a major study [K. Górski et al., Generatory losowych ciągów binarnych w kryptografii, Warsaw, 1999; per bibl.].) Among the 70 references to the literature, naturally there are many Polish ones, which is useful for the Polish reader. After two introductory chapters on the application of random numbers and their history, in Chapter 3 the author deals with all known random number generators for uniform and arbitrary distributions, briefly also for stochastic processes. Chapter 4 is especially dedicated to the generation of random bit sequences (number-theoretic methods, shift registers, newer methods), which are of great importance in coding theory and cryptography. Ergodic and chaos theory are referred to. Finally, in Chapter 5 tests of random numbers are treated: traditional and modern ones (spectral, entropy, wavelet tests and such which are named cryptographic). The author recomends that the reader, from the immense number of tests, select a few efficient ones.