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Is every pseudorandom generator a one-way function, even if the output length has no extra restrictions?

se flag
Wan

Intuitively, if we can invert a PRG, then we can easily distinguish it with random distribution by checking g(inverse(y)) = y. So every PRG is a OWF?

Unlike the problem "Is every pseudorandom generator a one way function?", i can prove that if the output length is large enough (for example |g(x)| >= 2|x|) then the PRG must be a OWF, but it seems that such a restriction is not necessary.

cn flag
Why was this closed when the linked "duplicate" only deals with the case explicitly excluded here?
fgrieu avatar
ng flag
@Maeher: One reason is historical: the fragments _", even if the output length has no extra restrictions"_ in the title and _"Unlike … necessary"_ in the body of the question have been added after the close. Indeed the question is no longer a dupe. However I hesitated reopening, because I don't find the statement clear enough. It lacks the (modified) definition of PRG and OWF considered. Also it lacks the proof for standard PRG with use of the hypothesis on output length. Apr 13, 2023 update: but I did reopen it because it was asked.
mangohost

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