How to construct random functions

A constructive theory of randomness for functions, based on computational complexity, is developed, and a pseudorandom function generator is presented. This generator is a deterministic polynomial-time algorithm that transforms pairs (g, r), where g is any one-way function and r is a random k -bit string, to polynomial-time computable functions ƒ r: 1, …, 2 k → 1, …, 2 k. These ƒ r 's cannot be distinguished from random functions by any probabilistic polynomial-time algorithm that asks and receives the value of a function at arguments of its choice. The result has applications in cryptography, random constructions, and complexity theory.