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Efficient Oblivious Evaluation Protocol and Conditional Disclosure of Secrets for DFA

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Applied Cryptography and Network Security (ACNS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13269))

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Abstract

In oblivious finite automata evaluation, one party holds a private automaton, and the other party holds a private string of characters. The objective is to let the parties know whether the string is accepted by the automaton or not, while keeping their inputs secret. The applications include DNA searching, pattern matching, and more. Most of the previous works are based on asymmetric cryptographic primitives, such as homomorphic encryption and oblivious transfer. These primitives are significantly slower than symmetric ones. Moreover, some protocols also require several rounds of interaction. As our main contribution, we propose an oblivious finite automata evaluation protocol via conditional disclosure of secrets (CDS), using one (potentially malicious) outsourcing server. This results in a constant-round protocol, and no heavy asymmetric-key primitives are needed. Our protocol is based on a building block called “an oblivious CDS scheme for deterministic finite automata” which we also propose in this paper. In addition, we propose a standard CDS scheme for deterministic finite automata as an independent interest.

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Notes

  1. 1.

    This can be done by adding one special character marking the end of the string.

  2. 2.

    The method in [38] can be used to transform a pattern p to a finite automaton \(LEV_d(p)\) accepts the language \(L_d(p)\) contains all strings with Levenshtein distance at most d from p. It is shown in [39] that a finite automaton for a language \(\varSigma ^*L_d(p)\varSigma ^*\) will not have too many states.

  3. 3.

    In practice, PRF can be used to reduce the size of the common randomness.

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Acknowledgments

Nuttapong Attrapadung was partly supported by JSPS KAKENHI Kiban-A Grant Number 19H01109. Kanta Matsuura was partially supported by JSPS KAKENHI Grant Number 17KT0081.

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Kittiphop Phalakarn & Kanta Matsuura

  2. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Nuttapong Attrapadung

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  1. Kittiphop Phalakarn
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  1. Stevens Institute of Technology, Hoboken, NJ, USA

    Giuseppe Ateniese

  2. Sapienza University of Rome, Rome, Italy

    Daniele Venturi

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Phalakarn, K., Attrapadung, N., Matsuura, K. (2022). Efficient Oblivious Evaluation Protocol and Conditional Disclosure of Secrets for DFA. In: Ateniese, G., Venturi, D. (eds) Applied Cryptography and Network Security. ACNS 2022. Lecture Notes in Computer Science, vol 13269. Springer, Cham. https://doi.org/10.1007/978-3-031-09234-3_30

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