Pseudorandom generator

A pseudorandom generator, or pseudorandom number generator (PRNG), is an algorithm that produces a sequence of numbers that appear to be random but are actually generated in a deterministic manner. Unlike true random number generators, which derive randomness from physical processes (like thermal noise or radioactive decay), PRNGs use mathematical functions to generate sequences of numbers based on an initial value known as a "seed.

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A pseudorandom generator is a deterministic, efficiently computable function

G : {0, 1}^{n} \to {0, 1}^{m (n)}

with

m (n) > n

, whose output on a uniform seed is computationally indistinguishable from a uniform

m (n)

-bit string. Its security is relative to a specified class of tests.

For example, suppose a generator maps 128 seed bits to 256 output bits. Its range contains at most

2^{128}

strings out of

2^{256}

possibilities. Enumerating the range would distinguish it almost perfectly, but requires infeasible work at this size. A secure construction must resist efficient tests that avoid enumeration as well. Merely copying the seed twice fails immediately: a test compares the two halves. Useful generators enable randomized algorithms or cryptographic protocols to expand a limited supply of random seed material.^[ref]