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A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless). In stochastic modeling , as in some computer simulations , the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to ...
The first tests for random numbers were published by M.G. Kendall and Bernard Babington Smith in the Journal of the Royal Statistical Society in 1938. [2] They were built on statistical tools such as Pearson's chi-squared test that were developed to distinguish whether experimental phenomena matched their theoretical probabilities.
However, generally they are considerably slower (typically by a factor 2–10) than fast, non-cryptographic random number generators. These include: Stream ciphers. Popular choices are Salsa20 or ChaCha (often with the number of rounds reduced to 8 for speed), ISAAC, HC-128 and RC4. Block ciphers in counter mode.
The number of floats needed to reach 1 should follow a certain distribution. Random integers are floated to get uniforms on [0,1). Starting with k = 2 31 = 2147483648, the test finds j, the number of iterations necessary to reduce k to 1, using the reduction k = ceiling(k×U), with U provided by
An example would be the TRNG9803 [18] hardware random number generator, which uses an entropy measurement as a hardware test, and then post-processes the random sequence with a shift register stream cipher. It is generally hard to use statistical tests to validate the generated random numbers.
In the asymptotic setting, a family of deterministic polynomial time computable functions : {,} {,} for some polynomial p, is a pseudorandom number generator (PRNG, or PRG in some references), if it stretches the length of its input (() > for any k), and if its output is computationally indistinguishable from true randomness, i.e. for any probabilistic polynomial time algorithm A, which ...
Random numbers have uses in physics such as electronic noise studies, engineering, and operations research. Many methods of statistical analysis, such as the bootstrap method, require random numbers. Monte Carlo methods in physics and computer science require random numbers. Random numbers are often used in parapsychology as a test of precognition.
Mathematics: Random numbers are also employed where their use is mathematically important, such as sampling for opinion polls and for statistical sampling in quality control systems. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms.