Private query processing on inverted index

A private query criteria Q
_k
is a Boolean logic expression in Λ, V and ¬ of an input set K. A private query processing protocol takes as input a private query criteria Q
_k
and a public data set d
_c
and outputs a document d ε d
_c
such that Q
_K
(d) = 1. This paper studies private query processing protocols in the context of inverted index programs and makes the following 3-fold contributions: 1) in the first fold, a new notion of private query processing protocols defined over inverted index programs within the Mapping-Reducing-Filtering framework is introduced and formalized; Our formalization is general and can be applied to the other scenarios such as private searching on streams, data processing on large clusters and compressing term positions in web indexes as well; 2) in the second fold, a new implementation of private query processing protocols based on (m, n)-Bloom filters with storages and additively homomorphic public-key encryptions is proposed. The idea behind our implementation is that a map function Map is activated to generate a matrix M of form (document
_j
: word
_{j, 1}
, ..., word
_{j, n}
, j = 1, ..., m). The reduce function Reduce is then invoked to generate an inverted index M̂ of form (keyword
_i
, document
_{i, 1}
, document
_{i, αi}
). Finally, a (m, n)-Bloom-Filter with storage is activated to generate matched documents according to the specified query criteria; 3) in the third fold, we show that the proposed query processing protocol on the inverted index is semantically secure assuming that the underlying additively homomorphic public-key encryption is semantically secure. To the best of our knowledge, this is the first semantically secure query processing protocol defined over the inverted index programs and we expect more applications to be deployed within this framework.