Unkeyed DEPIR ⇒ DEPIR

Unkeyed DEPIR implies DEPIR.

Statement

Migrated verbatim from doubly-efficient-pir § Doubly-efficient PIR:

The three main variants of DEPIR are: secret-key, public-key, and unkeyed. Note that any unkeyed DEPIR is trivially a PK-DEPIR which is trivially an SK-DEPIR. The latter keyed variants of DEPIR were introduced by BIPW17.

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:

• NODE COLLAPSE: unkeyed-depir has no page and pk-depir is an ALIAS of content/Primitives/doubly-efficient-pir.md, so hypothesis and conclusion resolve to the same slug — this edge becomes a self-loop.
• ‘trivially’ is asserted with no argument and no citation; BIPW17 in the same sentence covers only the introduction of the keyed variants.
• COMPOSITE CHAIN in one sentence: unkeyed ⇒ PK-DEPIR ⇒ SK-DEPIR. Must be split into two reductions.
• None of the three variants has its own page; DEPIR, SK-DEPIR and PK-DEPIR are all aliases of this single page, so all three nodes collapse to one slug in the current wiki.
• ‘trivially’ asserted with no argument and no citation (the BIPW17 citation in the same sentence covers only the introduction of the keyed variants).