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.