Pseudorandom Generator - Definition

Definition

Let Fn = {f: {0, 1}n → T} be a class of functions. A function G: {0, 1}s → {0, 1}n, where s < n, is a pseudorandom generator against Fn with bias ε if for every f in Fn, the statistical distance between the distributions f(G(X)), where X is sampled from the uniform distribution on {0, 1}s, and f(Y), where Y is sampled from the uniform distribution on {0, 1}n, is at most ε.

The quantity s is called the seed length and the quantity n - s is called the stretch of the pseudorandom generator. Functions from the class Fn are sometimes called adversaries.

A pseudorandom generator against a family of adversaries F = {Fn} with bias ε(n) is a collection of pseudorandom generators {Gn: {0, 1}s(n) → {0, 1}n}, where Gn is a pseudorandom generator against Fn with bias ε(n).

In most applications, the family F represents some model of computation, and one is interested in desigining a pseudorandom generator that is computable in the same or some closely related model.

Read more about this topic:  Pseudorandom Generator

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