Oblivious RAM (ORAM) and private information retrieval (PIR) are classic
cryptographic primitives used to hide the access pattern to data whose storage
has been outsourced to an untrusted server. Unfortunately, both primitives
require considerable overhead compared to plaintext access. For large-scale
storage infrastructure with highly frequent access requests, the degradation in
response time and the exorbitant increase in resource costs incurred by either
ORAM or PIR prevent their usage. In an ideal scenario, a privacy-preserving
storage protocols with small overhead would be implemented for these heavily
trafficked storage systems to avoid negatively impacting either performance
and/or costs. In this work, we study the problem of the best $\mathit{storage\
access\ privacy}thatisachievablewithonly\mathit{small\ overhead}overplaintextaccess.Toanswerthisquestion,weconsider\mathit{differential\ privacy\ access}whichisageneralizationofthe\mathit{oblivious\ access}securitynotionthatareconsideredbyORAMandPIR.Quitesurprisingly,wepresentstrongevidencethatconstantoverheadstorageschemesmayonlybeachievedwithprivacybudgetsof\epsilon = \Omega(\log n).WepresentasymptoticallyoptimalconstructionsfordifferentiallyprivatevariantsofbothORAMandPIRwithprivacybudgets\epsilon = \Theta(\log n)withonlyO(1)overhead.Inaddition,weconsideramorecomplexstorageprimitivecalledkey−valuestorageinwhichdataisindexedbykeysfromalargeuniverse(asopposedtoconsecutiveintegersinORAMandPIR).Wepresentadifferentiallyprivatekey−valuestorageschemewith\epsilon = \Theta(\log n)andO(\log\log n)$
overhead. This construction uses a new oblivious, two-choice hashing scheme
that may be of independent interest.Comment: To appear at PODS'1