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Efficient Pseudorandom Correlation Generators: Silent OT Extension and More

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Book cover Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11694))

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Abstract

Secure multiparty computation (MPC) often relies on correlated randomness for better efficiency and simplicity. This is particularly useful for MPC with no honest majority, where input-independent correlated randomness enables a lightweight “non-cryptographic” online phase once the inputs are known. However, since the amount of randomness typically scales with the circuit size of the function being computed, securely generating correlated randomness forms an efficiency bottleneck, involving a large amount of communication and storage.

A natural tool for addressing the above limitations is a pseudorandom correlation generator (PCG). A PCG allows two or more parties to securely generate long sources of useful correlated randomness via a local expansion of correlated short seeds and no interaction. PCGs enable MPC with silent preprocessing, where a small amount of interaction used for securely sampling the seeds is followed by silent local generation of correlated pseudorandomness.

A concretely efficient PCG for Vector-OLE correlations was recently obtained by Boyle et al. (CCS 2018) based on variants of the learning parity with noise (LPN) assumption over large fields. In this work, we initiate a systematic study of PCGs and present concretely efficient constructions for several types of useful MPC correlations. We obtain the following main contributions:

  • PCG foundations. We give a general security definition for PCGs. Our definition suffices for any MPC protocol satisfying a stronger security requirement that is met by existing protocols. We prove that a stronger security requirement is indeed necessary, and justify our PCG definition by ruling out a stronger and more natural definition.

  • Silent OT extension. We present the first concretely efficient PCG for oblivious transfer correlations. Its security is based on a variant of the binary LPN assumption and any correlation-robust hash function. We expect it to provide a faster alternative to the IKNP OT extension protocol (Crypto 2003) when communication is the bottleneck. We present several applications, including protocols for non-interactive zero-knowledge with bounded-reusable preprocessing from binary LPN, and concretely efficient related-key oblivious pseudorandom functions.

  • PCGs for simple 2-party correlations. We obtain PCGs for several other types of useful 2-party correlations, including (authenticated) one-time truth-tables and Beaver triples. While the latter PCGs are slower than our PCG for OT, they are still practically feasible. These PCGs are based on a host of assumptions and techniques, including specialized homomorphic secret sharing schemes and pseudorandom generators tailored to their structure.

  • Multiparty correlations. We obtain PCGs for multiparty correlations that can be used to make the (input-dependent) online communication of MPC protocols scale linearly with the number of parties, instead of quadratically.

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Notes

  1. 1.

    This can be formalized by requiring that the joint states of the parties in the end of the offline phase can be swapped by computationally indistinguishable states, given which the online protocol is secure against computationally unbounded parties.

  2. 2.

    In Sect. 1.1 below we describe an alternative LPN-based approach to constructing PCG for OT that dispenses with assumption (2), but requires at least quadratic computation in the output length n.

  3. 3.

    We caution that we have not implemented our constructions. Our estimates are based on counting basic operations and estimating their cost; the actual running times may vary due to other costs we neglected such as cache misses. We leave the task of optimizing and implementing our constructions to future work.

  4. 4.

    FSS is actually equivalent to HSS for a related class of functions, but we differentiate between the two for convenience, depending on the applications.

  5. 5.

    We view elements of \({\mathbb {F}}_{p}\) embedded into \({\mathbb {F}}_{q}\) throughout, so that the multiplication \({\varvec{u}} \cdot x\) happens over \({\mathbb {F}}_{q}\).

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Acknowledgements

We would like to thank Peter Rindal and Melissa Rossi for helpful discussions and pointers, and the anonymous Crypto 2019 reviewers for their comments.

E. Boyle, N. Gilboa, and Y. Ishai supported by ERC Project NTSC (742754). E. Boyle additionally supported by ISF grant 1861/16 and AFOSR Award FA9550-17-1-0069. G. Couteau supported by ERC Project PREP-CRYPTO (724307). N. Gilboa additionally supported by ISF grant 1638/15 and a grant by the BGU Cyber Center. Y. Ishai additionally supported by ISF grant 1709/14, NSF-BSF grant 2015782, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. L. Kohl supported by ERC Project PREP-CRYPTO (724307), by DFG grant HO 4534/2-2 and by a DAAD scholarship. This work was done in part while visiting the FACT Center at IDC Herzliya, Israel. P. Scholl supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 731583 (SODA), and the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC).

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Authors and Affiliations

  1. IDC Herzliya, Herzliya, Israel

    Elette Boyle

  2. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Geoffroy Couteau & Lisa Kohl

  3. Ben-Gurion University of the Negev, Beersheba, Israel

    Niv Gilboa

  4. Technion, Haifa, Israel

    Yuval Ishai

  5. Aarhus University, Aarhus, Denmark

    Peter Scholl

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  1. Elette Boyle
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    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P. (2019). Efficient Pseudorandom Correlation Generators: Silent OT Extension and More. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11694. Springer, Cham. https://doi.org/10.1007/978-3-030-26954-8_16

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