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Random Cycle Bit Generator (RCB) 2016 R. Cookman [35] RCB is described as a bit pattern generator made to overcome some of the shortcomings with Mersenne Twister and short periods/bit length restriction of shift/modulo generators. Middle-Square Weyl Sequence RNG (see also middle-square method) 2017 B. Widynski [36] [37]
To generate a sequence of n-digit pseudorandom numbers, an n-digit starting value is created and squared, producing a 2n-digit number. If the result has fewer than 2n digits, leading zeroes are added to compensate. The middle n digits of the result would be the next number in the sequence and returned as the result. This process is then ...
It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...
ACORN (random number generator) ... Middle-square method; MIXMAX generator; Multiply-with-carry pseudorandom number generator; N. Naor–Reingold pseudorandom function;
Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance.
For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 21 random samples (a little over two million), etc ...
If one has a pseudo-random number generator whose output is "sufficiently difficult" to predict, one can generate true random numbers to use as the initial value (i.e., the seed), and then use the pseudo-random number generator to produce numbers for use in cryptographic applications.
The performance of the BBS random-number generator depends on the size of the modulus M and the number of bits per iteration j. While lowering M or increasing j makes the algorithm faster, doing so also reduces the security. A 2005 paper gives concrete, as opposed to asymptotic, security proof of BBS, for a given M and j. The result can also be ...