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SP800-90 series on Random Number Generation, NIST; Random Number Generation in the GNU Scientific Library Reference Manual; Random Number Generation Routines in the NAG Numerical Library; Chris Lomont's overview of PRNGs, including a good implementation of the WELL512 algorithm; Source code to read data from a TrueRNG V2 hardware TRNG
For a specific example, an ideal random number generator with 32 bits of output is expected (by the Birthday theorem) to begin duplicating earlier outputs after √ m ≈ 2 16 results. Any PRNG whose output is its full, untruncated state will not produce duplicates until its full period elapses, an easily detectable statistical flaw. [36]
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 ...
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.
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.
Thus, a multiply-with-carry generator is a Lehmer generator with modulus p and multiplier b −1 (mod p). This is the same as a generator with multiplier b, but producing output in reverse order, which does not affect the quality of the resultant pseudorandom numbers.
KISS (Keep it Simple Stupid) is a family of pseudorandom number generators introduced by George Marsaglia. [1] [2] [3] Starting from 1998 Marsaglia posted on various newsgroups including sci.math, comp.lang.c, comp.lang.fortran and sci.stat.math several versions of the generators.
Cryptographically Secure Random number on Windows without using CryptoAPI; Conjectured Security of the ANSI-NIST Elliptic Curve RNG, Daniel R. L. Brown, IACR ePrint 2006/117. A Security Analysis of the NIST SP 800-90 Elliptic Curve Random Number Generator, Daniel R. L. Brown and Kristian Gjosteen, IACR ePrint 2007/048. To appear in CRYPTO 2007.