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The database community, at least for the last decade, has been grappling with querying encrypted data, which would enable secure database as a service solution. A recent breakthrough in the cryptographic community (in 2009) related to Fully Homomorphic Encryption (FHE) showed that arbitrary computation on encrypted data is possible. Successful adoption of FHE for query processing is, however, still a distant dream, and numerous challenges have to be addressed. One challenge is how to perform algebraic query processing of encrypted data, where they produce encrypted intermediate results and operations on encrypted data can be composed.
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