Private Compound Wildcard Queries Using Fully Homomorphic Encryption

Fully homomorphic encryption (FHE) brings a paradigm shift in cryptographic engineering by enabling us to resolve various unsolved problems. Among them, this work solves the problem to design a private database query (PDQ) protocol that supports compound queries with wildcard conditions on encrypted databases using FHE. More precisely, we consider a setting where clients outsource an encrypted database using FHE to a remote server, and later request results of compound queries including a wildcard search condition-given a set of attribute values {A
₁
; A
₂
; ...; A
_n
} and a search pattern W, retrieve a set of all attribute values A
_i
's in which the pattern W occurs. To this end, we first develop an algorithm for testing whether an encrypted string contains an encrypted pattern without revealing any information of the pattern, taking auxiliary encryptions as additional inputs. Then, using this algorithm, we design PDQ protocols on encrypted databases, which support compound queries using wildcard search conditions. Finally, we demonstrate proof-of-concept implementation results of our protocols by exploiting single-instruction-multiple-data operations and multi-threading techniques.