A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in that it is completely determined by a relatively small set of initial values, called the PRNG's state, which includes a truly random seed. Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom numbers are important in practice for their speed in number generation and their reproducibility, and they are thus central in applications such as simulations (e.g., of physical systems with the Monte Carlo method), in cryptography, and in procedural generation. Good statistical properties are a central requirement for the output of a PRNG, and common classes of suitable algorithms include linear congruential generators, lagged Fibonacci generators, and linear feedback shift registers. Cryptographic applications require the output to also be unpredictable, and more elaborate designs, which do not inherit the linearity of simpler solutions, are needed. More recent instances of PRNGs with strong randomness guarantees are based on computational hardness assumptions, and include the Blum Blum Shub, Fortuna, and Mersenne Twister algorithms.
In general, careful mathematical analysis is required to have any confidence that a PRNG generates numbers that are sufficiently "random" to suit the intended use. John von Neumann cautioned about the misinterpretation of a PRNG as a truly random generator, and joked that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." Robert R. Coveyou of Oak Ridge National Laboratory once titled an article, "The generation of random numbers is too important to be left to chance."
Read more about Pseudorandom Number Generator: Periodicity, Problems With Deterministic Generators, Early Approaches, Mersenne Twister, Cryptographically Secure Pseudorandom Number Generators, BSI Evaluation Criteria, Non-uniform Generators
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