A Review On Random Number Generators

Random numbers are useful for a variety of purposes these days, such as generating data encryption keys, simulating and modeling complex phenomena and for selecting random samples from larger data sets. They have also been used aesthetically, for example in literature and music, and are of course ever popular for games and gambling. There are two main approaches to generating random numbers: Pseudo-Random Number Generators (PRNGs) and True Random Number Generators (TRNGs). The approaches have quite different characteristics and each has its pros and cons. In this article we base on Pseudo-Random Number Generators-generating random numbers by using mathematical methods. PRNGs are efficient, meaning they can produce many numbers in a short time, and deterministic, meaning that a given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known.. Prom the random number data listing method, mid-square method, Fibonacci generator to linear,nonlinear congruential generator, feedback shift register generator, chaos generator,combined generator and etc, random number generators develop over the past tens of years.Every RNG has its deficiencies. No RNG is appropriate for all tasks. For example, several good RNGs from the toolbox of stochastic simulation are unsuited for crypto-graphical applications, because they produce predictable output streams. On the other hand, cryptographic RNGs are usually (but not always) too slow for doing Monte Carlo simulations.So it seems to be very important how to test a random number generator is good or not. The popular statistical tests are parameter test, uniform test, independence test, goodness-of-fit test and etc. Although many of these tests have become the standard methods, we are also confused that after passing how many tests a RNG can be accepted. As Neumann said, testing a random numbers is harder than producing them.And random number generator test suites solve this issue in a way. Nowadays the popular test suites are Classical Tests by Donald Knuth, Diehard by George Marsaglia, Crypt-X by Helen Gustafson,Edward and Dawson,William Caelli and Lauren Nielsen,NIST of National Institute of Standards and Technology and Test U01 by Pierre L'Ecuyer.With the improvement of the computational ability of the computer,people begin to pay attention to the advantages of combined generators. The advantages of Combined generators are reducing auto-correlation, improving independence and uniformness, enlarging the period of RNG. Now let's discuss a new random number generator T, firstly we consider four known random number generators : A, B, C, E, the random numbers are {a_i}, {b_i}, {c_i}, {e_i} respectively. If a_i> b_i, then t_i = c_i, otherwise t_i = e_i. We will take a example of this method as below:RNG A:RNG B:RNG C:RNG E:The above four RNGs will produce 10000 random numbers respectively, then generate {t_i}, i = 1,2,…, 10000, by using the combined method we've given. The following is the tests of {a_i},{b_i},{c_i},{e_i},{t_i},i = 1,2,…, 10000. (a_i > b_i,i.e.t_i = c_i,5042 pairs in total.)Parameter Tests: Take a as 0.05,if |u_i|≤1.960,RNG passes the mean test; if |u₂|≤1.960,RNG passes the second-order test;if |u₃|≤1.960,RNG pases the variance test.Uniform test:X² test (V₁)(m = 500).K S test (V₂):Serial test (V₃)(m = 4):Takeαas 0.05,if |V₁|≤551.950,RNG passes the x² test; if |V₂|≤0.158433,RNG passes the KS test; if |V₃|≤24.996,RNG passes the serial test.Correlation coefficient test I (W₁)(j = 15):Correlation coefficient test II (W₂)(j = 15):Contingency Table test (W₃)(m=10,=8):...