Abstract
The notion of covert computation, an enhanced form of secure multiparty computation, allows parties to jointly compute a function, while ensuring that participating parties cannot distinguish their counterparties from a random noise generator, until the end of the protocol, when the output of the function is revealed, if favorable to all parties. Previous works on covert computation achieved super-constant round protocols for general functionalities [5, 16], with efficiency at least linear in the size of the circuit representation of the computed function. Indeed, [9] showed that constant-round covert computation of any non-trivial functionality with black-box simulation is impossible in the plain model.
In this work we construct the first practical constant-round covert protocol for a non-trivial functionality, namely the set-intersection functionality, in the Random Oracle Model. Our construction demonstrates the usefulness of covert subprotocols as building blocks in constructing larger protocols: We show how to compile a concurrently covert protocol for a single-input functionality, e.g. string equality, into an efficient secure and covert protocol for a corresponding multi-input functionality, e.g. set intersection.
Our main contributions are summarized as follows:
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We upgrade the notion of covert computation of [5] to concurrent covert computation.
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We provide a general compiler that converts concurrent covert protocols for single-input functionalities to concurrent covert protocols for corresponding multi-input counterparts of these functionalities, at linear cost, in the Random Oracle Model.
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To demonstrate the usefulness of our compiler, we construct a concurrently covert string equality protocol and then apply our compiler to achieve a two-message concurrent covert protocol for Set Intersection (SI) with a linear cost in the Random Oracle Model.
This work was done in part while the authors were visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF award #CNS-1523467.
C. Cho—A part of work was performed while visiting University of California, Irvine
D. Dachman-Soled—Work supported in part by NSF CAREER award #CNS-1453045 and by a Ralph E. Powe Junior Faculty Enhancement Award.
S. Jarecki—Work supported in part by NSF CAREER award #CNS-0747541.
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Cho, C., Dachman-Soled, D., Jarecki, S. (2016). Efficient Concurrent Covert Computation of String Equality and Set Intersection. In: Sako, K. (eds) Topics in Cryptology - CT-RSA 2016. CT-RSA 2016. Lecture Notes in Computer Science(), vol 9610. Springer, Cham. https://doi.org/10.1007/978-3-319-29485-8_10
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