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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. ==Definition== Let 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''. A function with is a ''pseudorandom generator'' against with ''bias'' if, for every in , the statistical distance between the distributions and is at most , where is the uniform distribution on . The quantity is called the ''seed length'' and the quantity is called the ''stretch'' of the pseudorandom generator. A pseudorandom generator against a family of adversaries with bias is a family of pseudorandom generators , where is a pseudorandom generator against with bias and seed length . In most applications, the family represents some model of computation or some set of algorithms, and one is interested in designing a pseudorandom generator with small seed length and bias, and such that the output of the generator can be computed by the same sort of algorithm. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Pseudorandom generator」の詳細全文を読む スポンサード リンク
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