International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 14 December 2012

Joshua Baron, Karim El Defrawy, Kirill Minkovich, Rafail Ostrovsky, Eric Tressler
ePrint Report ePrint Report
In this paper we consider the problem of secure pattern matching that allows

single-character wildcards and substring matching in the malicious (stand-alone) setting.

Our protocol, called 5PM, is executed between

two parties: Server, holding a text of length $n$, and

Client, holding a pattern of length $m$ to be matched

against the text, where our notion of matching is more general and includes non-binary alphabets, non-binary Hamming distance and non-binary substring matching.

5PM is the first secure expressive pattern matching protocol designed to optimize round complexity by carefully specifying the entire protocol round by round. In the malicious model, 5PM requires $O((m+n)k^2)$ bandwidth and $O(m+n)$ encryptions, where $m$ is the pattern length and $n$ is the text length. Further, 5PM can hide pattern size with no asymptotic additional costs in either computation or bandwidth. Finally, 5PM requires only two rounds of communication

in the honest-but-curious model and eight rounds in the malicious model. Our techniques reduce

pattern matching and generalized Hamming distance problems to a novel linear algebra formulation that allows for generic solutions based on any additively homomorphic encryption. We believe our efficient algebraic techniques are of independent interest.

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