Pseudorandom generator

In theoretical computer science and cryptography, a pseudorandom generator (PRG) for a class of statistical tests is a deterministic procedure that maps a random seed to a longer pseudorandom string such that no statistical test in the class can distinguish between the output of the generator and the uniform distribution. The random seed is typically a short binary string drawn from the uniform distribution.

Many different classes of statistical tests have been considered in the literature, among them the class of all Boolean circuits of a given size. It is not known whether good pseudorandom generators for this class exist, but it is known that their existence is in a certain sense equivalent to (unproven) circuit lower bounds in computational complexity theory. Hence the construction of pseudorandom generators for the class of Boolean circuits of a given size rests on currently unproven hardness assumptions.

Let ${\displaystyle {\mathcal {A}}=\{A:\{0,1\}^{n}\to \{0,1\}^{*}\}}$ be a class of functions. These functions are the statistical tests that the pseudorandom generator will try to fool, and they are usually algorithms. Sometimes the statistical tests are also called adversaries.

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