Privacy-preserving range queries allow encrypting data while still enabling queries on ciphertexts if their corresponding plaintexts fall within a requested range. This provides a data owner the possibility to outsource data collections to a cloud service provider without sacricing privacy nor losing functionality of ltering this data. However, existing methods for range queries either leak additional information (like the ordering of the complete data set) or slow down the search process tremendously by requiring to query each ciphertext in the data collection. We present a novel scheme that only leaks the access pattern while supporting amortized polylogarithmic search time. Our construction is based on the novel idea of enabling the cloud service provider to compare requested range queries. By doing so, the cloud service provider can use the access pattern to speed-up search time for range queries in the future. On the one hand, values that have fallen within a queried range, are stored in an interactively built index for future requests. On the other hand, values that have not been queried do not leak any information to the cloud service provider and stay perfectly secure.
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