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Statistical Security in Two-Party Computation Revisited

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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 present a new framework for building round-optimal one-sided statistically secure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer \(\textsf {eOT}\) with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables the first instantiations of round-optimal one-sided statistically secure 2PC protocols from the CDH assumption and certain families of isogeny-based assumptions.

As part of our compiler, we introduce the following new one-sided statistically secure primitives in the pre-processing model that might also be of independent interest:

  1. 1.

    Three round statistically sender private random-OT where only the last OT message depends on the receiver’s choice bit and the sender receives random outputs generated by the protocol.

  2. 2.

    Four round delayed-input statistically sender private conditional disclosure of secrets where the first two rounds of the protocol are independent of the inputs of the parties.

The above primitives are directly constructed from \(\textsf {eOT}\) and hence we obtain their instantiations from the same set of assumptions as our 2PC.

S. Badrinarayanan—Work done while the author was affiliated with Visa Research USA.

S. Patranabis—Most of the work was done while the author was affiliated with Visa Research USA.

P. Sarkar—Supported by NSF Awards 1931714, 1414119, and the DARPA SIEVE program.

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Notes

  1. 1.

    Throughout this paper, when we refer to the LPN assumption, we refer to the “extremely low-noise” variant of LPN with noise parameters in the \(O\left( \left( \log n\right) ^2/n\right) \) regime, as used in many recent works, including [BF22].

  2. 2.

    We consider that our \(\textsf {eOT}\) protocol provides statistical receiver privacy, as opposed to the elementary OT protocol defined in [DGH+20] which only provides computational receiver privacy.

  3. 3.

    For the five round protocol, receiver is the party that obtains output first (at the end of round four) and sender is the party that obtains output at the end of round five.

  4. 4.

    Reciprocal CSIDH is quantum equivalent to computational CSIDH, which is weaker than decisional CSIDH. However, reciprocal CSIDH and decisional CSIDH assumptions are incomparable in the classical setting.

  5. 5.

    It is different from the notion of semi-malicious security [MW16] where the adversary in addition to generating the the protocol messages in the support of the distribution of all honestly generated transcripts, also outputs the input and randomness that was used, on a special tape.

  6. 6.

    Reciprocal CSIDH assumption is quantum equivalent to computational CSIDH and it is incomparable to decisional CSIDH.

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Authors and Affiliations

  1. Snap, Seattle, USA

    Saikrishna Badrinarayanan

  2. IBM Research India, Bangalore, India

    Sikhar Patranabis

  3. Department of Computer Science, Boston University, Boston, USA

    Pratik Sarkar

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  1. Saikrishna Badrinarayanan
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  2. Sikhar Patranabis
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  3. Pratik Sarkar
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Correspondence to Pratik Sarkar .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

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

    Vinod Vaikuntanathan

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Badrinarayanan, S., Patranabis, S., Sarkar, P. (2022). Statistical Security in Two-Party Computation Revisited. 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_7

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