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How to Obfuscate MPC Inputs

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

We introduce the idea of input obfuscation for secure two-party computation (io2PC). Suppose Alice holds a private value x and wants to allow clients to learn \(f(x,y_i)\), for their choice of \(y_i\), via a secure computation protocol. The goal of io2PC is for Alice to encode x so that an adversary who compromises her storage gets only oracle access to the function \(f(x,\cdot )\). At the same time, there must be a 2PC protocol for computing f(x, y) that takes only this encoding (and not the plaintext x) as input.

We show how to achieve io2PC for functions that have virtual black-box (VBB) obfuscation in either the random oracle model or generic group model. For functions that can be VBB-obfuscated in the random oracle model, we provide an io2PC protocol by replacing the random oracle with an oblivious PRF. For functions that can be VBB-obfuscated in the generic group model, we show how Alice can instantiate a “personalized” generic group. A personalized generic group is one where only Alice can perform the algebraic operations of the group, but where she can let others perform operations in that group via an oblivious interactive protocol.

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Notes

  1. 1.

    Essentially, our protocol for \(\textsf{IOEval} \) simply allows the client to make some fixed number of OPRF queries. Instead of using those OPRF queries for k sequential evaluations of the function, the client can schedule the OPRF queries in parallel—e.g., the first query in all k evaluations, then the second query in all k evaluations, etc.

  2. 2.

    Following e.g., [19], we assume that \(\mathcal {A}\) always sends a \(\textsf{Compromise}\) message to \(\textsf{S} \) and \(\mathcal {F}_{\textrm{VOPRF}}\) simultaneously. These two actions correspond to a single action in the real protocol, i.e. compromising the server.

  3. 3.

    This is indeed possible in our protocol but would be mitigated if the common-group oracle had a group-multiplication feature exactly as powerful as \(\textsf {OfflineMult}\) of \(\mathcal {F}_{\textsf {pgg}}\).

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Authors and Affiliations

  1. Oregon State University, Corvallis, OR, 97331, USA

    Ian McQuoid, Mike Rosulek & Jiayu Xu

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  1. Ian McQuoid
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Correspondence to Ian McQuoid .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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McQuoid, I., Rosulek, M., Xu, J. (2022). How to Obfuscate MPC Inputs. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_6

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  • DOI: https://doi.org/10.1007/978-3-031-22365-5_6

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