Data security and availability for operational use are frequently seen asconflicting goals. Research on searchable encryption and homomorphic encryptionare a start, but they typically build from encryption methods that, at best,provide protections based on problems assumed to be computationally hard. Bycontrast, data encoding methods such as secret sharing provideinformation-theoretic data protections. Archives that distribute data usingsecret sharing can provide data protections that are resilient to maliciousinsiders, compromised systems, and untrusted components. In this paper, we create the Serial Interpolation Filter, a method forstoring and interacting with sets of data that are secured and distributedusing secret sharing. We provide the ability to operate over set-oriented datadistributed across multiple repositories without exposing the original data.Furthermore, we demonstrate the security of our method under various attackermodels and provide protocol extensions to handle colluding attackers. TheSerial Interpolation Filter provides information-theoretic protections from asingle attacker and computationally hard protections from colluding attackers.
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