CS276 Lecture 14 (draft)

Summary

Today we show how to construct a pseudorandom function from a pseudorandom generator.

1. Construction of Pseudorandom Functions

Lemma 1 (Generator Evaluated on Independent Seeds) Suppose that is a pseudorandom generator. Fix a parameter , and define as

Then is a pseudorandom generator.

Let be a length-doubling pseudorandom generator. Define such that equals the first bits of , and define such that equals the last bits of .

The the GGM pseudorandom function based on is defined as follows: for key and input :

Theorem 2 If is a pseudorandom generator and is computable in time , then is a secure pseudorandom function.