On the Efficiency of FHE-Based Private Queries - 2018


Personal query processing is a terribly engaging downside within the fields of each cryptography and databases. During this work, we tend to limit our attention to the efficiency facet of the problem, particularly for basic queries with conditions on various combinations of equality. While not loss of generality, these conditions can be thought to be a Boolean perform, and this Boolean perform will then be evaluated at ciphertexts produced by a totally homomorphic encryption (FHE) theme while not decryption. From the efficiency perspective, the remaining concern is to efficiently test the equality perform while not severely downgrading the performance of FHE-primarily based querying solutions. To this end, we tend to initial analyze the multiplicative depth needed for an equality check algorithm with respect to the plaintext space inhabited by general FHE schemes. The first reason for this approach is that given an equality take a look at algorithm, its efficiency is measured in terms of the multiplicative depth required to construct its arithmetic circuit expression. Indeed, the implemented equality check algorithm dominates the entire performance of FHE-primarily based query solutions, aside from the performance of the underlying FHE theme. Then, we measure the multiplicative depth considering an FHE scheme that takes an extension field as its plaintext house and that supports the depth-free evaluation of Frobenius maps. According to our analysis, when the plaintext space of an FHE scheme is a field of characteristic 2, the equality take a look at algorithm for '-bit messages needs very cheap multiplicative depth dlog'e. Furthermore, we tend to design a group of personal query protocols for conjunctive, disjunctive, and threshold queries primarily based on the equality take a look at algorithm. Similarly, applying the equality test algorithm over F two l , our querying protocols require the minimum depths. More specifically, a multiplicative depth of [log l] + [log (one + ?)] is needed for conjunctive and disjunctive queries, and a depth of [log l] + two[log (one+? )] is needed for threshold conjunctive queries, when their question conditions have p attributes to be compared. Finally, we tend to give a Communication-efficient version of our solutions, though with additional computational costs, when an higher sure d (zero = d = one) on the selectivity of a database is given. Consequently, we cut back the Communication cost from n to approximately [dn] ciphertexts with [log n] additional depth when the database consists of n tuples.

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