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On Garbling Schemes with and Without Privacy

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Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

Garbling schemes allow to construct two-party function evaluation with security against cheating parties (SFE). To achieve this goal, one party (the Garbler) sends multiple encodings of a circuit (called Garbled Circuits) to the other party (the Evaluator) and opens a subset of these encodings, showing that they were generated honestly. For the remaining garbled circuits, the garbler sends encodings of the inputs. This allows the evaluator to compute the result of function, while the encoding ensures that no other information beyond the output is revealed. To achieve active security against a malicious adversary, the garbler in current protocols has to send O(s) circuits (where s is the statistical security parameter).

In this work we show that, for a certain class of circuits, one can reduce this overhead. We consider circuits where sub-circuits depend only on one party’s input. Intuitively, one can evaluate these sub-circuits using only one circuit and privacy-free garbling. This has applications to e.g. input validation in SFE and allows to construct more efficient SFE protocols in such cases. We additionally show how to integrate our solution with the SFE protocol of [5], thus reducing the overhead even further.

C. Baum—Supported by The Danish National Research Foundation and The National Science Foundation of China (under the grant 61061130540) for the Sino-Danish Center for the Theory of Interactive Computation, within which part of this work was performed; by the CFEM research center (supported by the Danish Strategic Research Council) within which part of this work was performed; and by the Advanced ERC grant MPCPRO.

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Notes

  1. 1.

    We let \(\mathcal {T}\) accept only descriptions of \(f\) where the graph representing the circuit \(\mathcal {C}_f\) is directed and acyclic.

  2. 2.

    Approaches based on SNARKs have smaller proof size but require much more work on the prover’s side, which is why we do not mention them.

  3. 3.

    These are building blocks are used in many SFE protocols. We hence assume that they are available and cheap.

  4. 4.

    To the best of our knowledge, a similar idea was first introduced in [17].

  5. 5.

    We used the same technique, but for a different reason, in \(\varPi _\textsc {SIREval}\). It was first introduced in the context of SFE with garbled circuits in [6, 18].

  6. 6.

    This means that we have to change the function \(g_b'(\cdot ,\cdot )\) slightly, due to a technique that avoids selective failure-attacks in FJN14. This change does not increase the size of the privacy-free circuit that is sent, since only XOR gates are added.

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Acknowledgements

We want to thank Ivan Damgård and Tore Frederiksen for helpful discussions.

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Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Carsten Baum

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  1. Carsten Baum
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Correspondence to Carsten Baum .

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Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Baum, C. (2016). On Garbling Schemes with and Without Privacy. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_25

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_25

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  • Publisher Name: Springer, Cham

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