Secret-Key PIR (SK-PIR) + SKE ⇒ DEPIR

Secret-Key PIR (SK-PIR) together with SKE implies DEPIR.

Statement

Migrated verbatim from CIMR25 - Secret-Key PIR from Random Linear Codes § Notes:

  • But I could preprecess the database and store the state encrypted on the server, then I could run a 2 round protocol where I download the encrypted state
    • This gives a sk 2-round DEPIR with communication and computation

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:

  • ORIGINAL UNCITED CONSTRUCTION by the wiki editor (‘But I could preprecess the database and store the state encrypted on the server…’). Attributable to no paper. Must not be merged into the graph as a literature reduction; sources[] deliberately empty.
  • SUSPECTED IMPRECISION (recorded, not fixed): O(s + n/s) communication is minimised at s = sqrt(n), giving O(sqrt(n)) — sublinear, but far from the polylog(N) that ‘doubly efficient’ normally denotes. Calling the result a ‘DEPIR’ is at best a stretch.
  • SUSPECTED IMPRECISION: downloading the encrypted state each query makes per-query communication at least |state|, which conflicts with the sublinear-communication requirement unless the cost is amortised over many queries — the text does not say.
  • The security of the encrypted-server-state step is not argued; the SKE hypothesis is inferred from ‘store the state encrypted’, not stated.
  • Typos: ‘prepreprocessing’, ‘preprecess’.
  • Mixes n (used here) with the N of the abstract for database size.