Random number generation

Random number generation produces values intended to be unpredictable or to follow a specified probability distribution. It can use physical processes or deterministic algorithms.

Pseudorandom number generator: A deterministic algorithm that produces sequences designed to resemble random numbers. It can generate random-looking sequences quickly, but its output is determined by its initial state.
Probability distribution: A mathematical description of the possible values of a random variable and their probabilities. A generator's target distribution specifies how often its different outputs should occur.
Cryptography: The study and practice of securing information through mathematical methods. Cryptographic systems rely on unpredictable keys, nonces, and other values.
True random number generator: A generator whose output derives from a physical process treated as nondeterministic. It contrasts with deterministic generators, though physical sources still require careful measurement and testing.
NIST SP 800-90B: A National Institute of Standards and Technology publication on entropy sources for random bit generation. It sets methods for assessing entropy sources used in security-sensitive generators.
Cryptographically secure pseudorandom number generator: A pseudorandom generator designed to resist prediction by an adversary. It extends algorithmic generation with requirements suited to secret keys and security protocols.
Uniform distribution: A probability distribution that assigns equal probability across its possible outcomes. Many generators aim for uniform values before transforming them into other distributions.
Monte Carlo method: A computational method that uses random sampling to estimate quantities or solve problems. Repeated random trials make otherwise difficult calculations tractable.
Deterministic algorithm: An algorithm that produces the same output whenever it receives the same input and state. A deterministic generator cannot create unpredictability from nothing; it expands an initial state into a sequence.
FIPS 140: A U.S. government standard defining security requirements for cryptographic modules. Its validation regime includes requirements affecting random-bit generation in cryptographic modules.

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