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Improvements for Gate-Hiding Garbled Circuits

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Progress in Cryptology – INDOCRYPT 2017 (INDOCRYPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10698))

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Abstract

Garbled circuits have been highly optimized for practice over the last several years. Today’s most efficient constructions treat different types of gates (e.g., AND vs. XOR) differently; as such, they leak the type of each gate. In many applications of garbled circuits, the circuit itself is public, so such leakage is tolerable. In other settings, however, it is desirable to hide the type of each gate.

In this paper we consider optimizing garbled circuits for the gate-hiding case. We observe that the best state-of-the-art constructions support only a limited class of gate functions, which turns out to undermine their improvements in several settings. These state-of-the-art constructions also require a non-minimal hardness assumption.

We introduce two new gate-hiding constructions of garbled circuits. Both constructions achieve the same communication complexity as the best state-of-the-art schemes, but support a more useful class of boolean gates and use only the minimal assumption of a secure PRF.

Partially supported by NSF awards 1149647 & 1617197.

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Notes

  1. 1.

    The “extra” 4 bits come from using the point-permute optimization. In practice one would typically use the underlying cryptographic primitive (e.g., AES) in a way that gives security \(\lambda =127\), and then the garbled gates become a clean multiple of 128 bits in length. All of the constructions in this work use the point-permute optimization, which we discuss in greater detail in Sect. 2.4.

  2. 2.

    KKS also show how to reduce the size of garbled gates at the input layer of a circuit. In this work we focus on internal gates of a circuit, and assume that the input gates represent only a small fraction of the circuit.

  3. 3.

    In this paper we restrict our attention to constructions based on symmetric-key primitives only. There exist garbled circuit constructions based on very expensive primitives (functional encryption, FHE) where the cost of every garbled gate is constant.

  4. 4.

    Absorbing the NOT gate into its “upstream” gate may not always work, since the upstream gate may have multiple fan-out.

  5. 5.

    This fact is explicitly mentioned in [7].

  6. 6.

    If all the coefficients were to be made public, then we are back in the original situation of [7], and leaking the parity of the gate seems inevitable for this choice of evaluation equation.

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Authors and Affiliations

  1. Oregon State University, Corvallis, USA

    Mike Rosulek

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  1. Mike Rosulek
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Correspondence to Mike Rosulek .

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Editors and Affiliations

  1. Indian Institute of Science (IISc), Bengaluru, India

    Arpita Patra

  2. Department of Computer Science, University of Bristol, Bristol, United Kingdom

    Nigel P. Smart

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Rosulek, M. (2017). Improvements for Gate-Hiding Garbled Circuits. In: Patra, A., Smart, N. (eds) Progress in Cryptology – INDOCRYPT 2017. INDOCRYPT 2017. Lecture Notes in Computer Science(), vol 10698. Springer, Cham. https://doi.org/10.1007/978-3-319-71667-1_17

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