Abstract
Secure computation (i.e., performing computation while keeping privacy of the inputs) is a fundamental research area in cryptography and a fundamental capability in the theory of computing. Deterministic automata evaluation is a fundamental computation problem, with numerous application areas, including regular expressions, string matching, constant-space computations.
In this paper, we investigate the complexity of achieving secure 2-party deterministic automata evaluation protocols. We show black-box reductions between this problem and the problem of constructing secure 2-party information retrieval protocols, and viceversa. Using previous results, this implies various interesting consequences: completeness of secure deterministic automata evaluation in the class of problems having 2-party and multi-party secure function evaluation protocols (previously, only 2 less natural problems were showed to be complete, or non-constructive characterizations of complete problems were given), and, under standard cryptographic assumptions, a communication-efficient secure protocol for automata evaluation (no such problem was given in the literature) and a time-efficient secure protocol faster than applying Yao’s benchmark general solution.
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This work was supported by the Defense Advanced Research Projects Agency (DARPA) via Air Force Research Laboratory (AFRL), contract number FA8750-14-C-0057. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation hereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, AFRL or the U.S. Government.
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Di Crescenzo, G., Coan, B., Kirsch, J. (2020). Secure Deterministic Automata Evaluation: Completeness and Efficient 2-party Protocols. In: Simion, E., Géraud-Stewart, R. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2019. Lecture Notes in Computer Science(), vol 12001. Springer, Cham. https://doi.org/10.1007/978-3-030-41025-4_4
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