DKG + HE ⇒ TPKE

DKG together with HE implies TPKE.

Statement

Migrated verbatim from decisional-composite-residuosity § Known Results:

DCR → threshold encryption (via Paillier with distributed key generation) — standard

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:

GENUINELY CONJUNCTIVE while the parent record is marked conjunctive:false - both hypotheses are needed together on this link.
threshold-encryption and distributed-key-generation have no wiki pages; identifiers invented.
Uncited (Fouque-Poupard-Stern / Damgard-Jurik would be the standard sources); the ’- standard’ label is misapplied.
This link is inferred from a parenthetical construction sketch; the page never states it as a theorem.
via Paillier with distributed key generation chains two construction steps.
Marked standard where Fouque-Poupard-Stern / Damgard-Jurik are attributable.
threshold-encryption and distributed-key-generation have no pages.