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This makes p − 1 = ab r easy to factor, making it practical to establish the period of very large generators. The modified procedure is called complementary-multiply-with-carry (CMWC), and the setup is the same as that for lag-r MWC: multiplier a, base b, and r + 1 seeds, x 0, x 1, x 2, ..., x r−1, and c r−1.
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 ...
While /dev/urandom is still intended as a pseudorandom number generator suitable for most cryptographic purposes, the authors of the corresponding man page note that, theoretically, there may exist an as-yet-unpublished attack on the algorithm used by /dev/urandom, and that users concerned about such an attack should use /dev/random instead. [7]
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A random seed (or seed state, or just seed) is a number (or vector) used to initialize a pseudorandom number generator. A pseudorandom number generator's number sequence is completely determined by the seed: thus, if a pseudorandom number generator is later reinitialized with the same seed, it will produce the same sequence of numbers.
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The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto (松本 眞) and Takuji Nishimura (西村 拓士). [1] [2] Its name derives from the choice of a Mersenne prime as its period length.
Noam Nisan (1992) showed that this derandomization can actually be achieved with a pseudorandom generator of seed length () that fools all ()-space machines. Nisan's generator has been used by Saks and Zhou (1999) to show that probabilistic log-space computation can be simulated deterministically in space O ( log 1.5 n ...