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Secure pattern matching based on bit parallelism

Non-interactive protocols for non-deterministic string matching automata evaluation

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Abstract

In this paper, we consider the problem of secure pattern matching that uses evaluation of non-deterministic string matching automata (NSMA). Our solution is based on a class of hardware-based pattern matching algorithms called bit-parallel pattern matching, which simulates the behavior of NSMAs. The properties of this class of algorithms allow our constructions to handle any fixed-length pattern in a non-interactive way with only two rounds of communication. Our secure protocol is able to handle the Hamming distance computation and substring and subpattern matching for any finite alphabet. It is also possible to use this protocol for keyword, text, and live text search. Security of our protocol is proved in the semi-honest model. Then, in order to strengthen security of the solution and retain its efficiency, we design a variant of the protocol which is proved to be secure with one-sided simulation in the malicious model. As a proof of concept, we also present another protocol that shows how our basic idea can be extended to other scenarios of pattern matching such as secure computation outsourcing.

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Notes

  1. This is a fictitious column which affects only the result of comparing P to the prefixes of T of at most \(m-1\) characters, i.e., only initial sequences of T shorter than P which cannot contain P. Setting the cells of this column to 1 will result in those locations being correctly triggered as a mismatch, and for simplicity, we use 1s for both match/mismatch searches and searches with user-defined distances. An alternative approach is to use special processing for the first \(m-1\) characters of T without maintaining this column. In either case, the first \(m-1\) locations of T are not expected to be included in the computation output.

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Acknowledgements

The first author would like to thank Professor Yehuda Lindell for his priceless comments in Crypto Stack Exchange community, Babak Siabi, and Professor Salman Niksefat for useful comments and discussions regarding secure multi-party computation. Portions of this work were supported by Grants CNS-1223699 and CNS-1319090 from the US National Science Foundation and FA9550-13-1-0066 from the US Air Force Office of Scientific Research. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the funding agencies.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Mohammad Hasan Samadani & Mehdi Berenjkoob

  2. Department of Computer Science and Engineering, University at Buffalo (SUNY), Buffalo, NY, USA

    Marina Blanton

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  1. Mohammad Hasan Samadani
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  2. Mehdi Berenjkoob
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  3. Marina Blanton
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Corresponding author

Correspondence to Marina Blanton.

Additional information

M. H. Samadani: Portions of this work were done while the first author was visiting University of Notre Dame, IN, USA.

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Samadani, M.H., Berenjkoob, M. & Blanton, M. Secure pattern matching based on bit parallelism. Int. J. Inf. Secur. 18, 371–391 (2019). https://doi.org/10.1007/s10207-018-0410-8

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