Trapdoor pseudorandom generators ⇔ PRG

Trapdoor pseudorandom generators is equivalent to PRG.

Statement

Migrated verbatim from pseudorandom-generator § Trapdoor pseudorandom generators:

The pseudorandomness of a trapdoor PRG is equivalent to the pseudorandomness of $(\mathsf{Gen},\mathsf{Eval})$ treated as a PRG with keyspace $(\mathcal{K}\times \mathcal{T}).$ Beyond that, a trapdoor PRG should be

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Equivalence is between the pseudorandomness PROPERTIES, not the objects (‘the pseudorandomness of a trapdoor PRG is equivalent to the pseudorandomness of (Gen,Eval) treated as a PRG with keyspace K x T’) — property-level equivalence needs its own encoding.
• No citation.
• ‘trapdoor-pseudorandom-generator’ has no page.