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Numbers, Random

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Numbers, Random

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This classic table of random numbers for use in statistical probability experiments, one of the first, was prepared in the precomputer days of 1947 using the specially built electronic equivalent of a 32-place roulette wheel. Fourteen RAND mathematicians, engineers, and computing pioneers participated in the planning, testing, and rerandomizing of the tables and in preparing them for publication. The two tables, one of a million random digits and one of 100,000 Gaussian deviates, were photoreproduced from IBM 856 Cardatype printout. An introduction explains their derivation and statistical properties and gives directions for use. Although large simulation studies now generate their own random numbers, the RAND tables remain useful for smaller-scale work and hand calculations; they are much used in agricultural research. This book was originally published with the same title, Glencoe, IL, The Free Press, 1955 and includes a new foreword by Michael Rich.

Mathematics --- Numbers, Random --- Sampling (Statistics)

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A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary. One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack. There do not seem to be natural examples of functions that are pseudorandom generators. On the other hand, there do seem to be a variety of natural examples of another basic primitive: the one-way function. A function is one-way if it is easy to compute but hard for any efficient adversary to invert on average. The first half of the book shows how to construct a pseudorandom generator from any one-way function. Building on this, the second half of the book shows how to construct other useful cryptographic primitives, such as private key cryptosystems, pseudorandom function generators, pseudorandom permutation generators, digital signature schemes, bit commitment protocols, and zero-knowledge interactive proof systems. The book stresses rigorous definitions and proofs.

Random number generators. --- Computational complexity. --- Data encryption (Computer science) --- Numbers, Random.

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Stochastic programming. --- Mathematical optimization. --- Numbers, Random. --- Random numbers --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Linear programming