Private searching on streaming data is a process
to dispatch to a public server a program, which searches streaming sources of
data without revealing searching criteria and then sends back a buffer
containing the findings. From an Abelian group homomorphic encryption, the
searching criteria can be constructed by only simple combinations of keywords,
for example, disjunction of keywords. The recent breakthrough in fully
homomorphic encryption has allowed us to construct arbitrary searching criteria
theoretically. In this paper, we consider a new private query, which searches
for documents from streaming data on the basis of keyword frequency, such that
the frequency of a keyword is required to be higher or lower than a given
threshold. This form of query can help us in finding more relevant documents.
Based on the state of the art fully homomorphic encryption techniques, we give
disjunctive, conjunctive, and complement constructions for private threshold
queries based on keyword frequency. Combining the basic constructions, we
further present a generic construction for arbitrary private threshold queries
based on keyword frequency. Our protocols are semantically secure as long as
the underlying fully homomorphic encryption scheme is semantically secure
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