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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 435–464Cite as

Post-Quantum Multi-Party Computation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12696))

Abstract

We initiate the study of multi-party computation for classical functionalities in the plain model, with security against malicious quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of constant-round post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and quantum polynomial hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest:

  • A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of (a circular variant of) the LWE problem. This immediately yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys.

  • A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.

To prove the security of our protocol, we develop a new straight-line non-black-box simulation technique against parallel sessions that does not clone the adversary’s state. This technique may also be relevant to the classical setting.

A. Agarwal and D. Khurana—This material is based on work supported in part by DARPA under Contract No. HR001120C0024. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

V. Goyal—Supported in part by the DARPA SIEVE program, NSF award 1916939, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Notes

  1. 1.

    We actually require this commitment to also satisfy a property called non-malleability, which we discuss later in this section.

  2. 2.

    In the body of the paper we actually resort to a slightly stronger tool, namely a secure function evaluation protocol with statistical circuit privacy.

  3. 3.

    As a historical remark, while the name is inspired by Einstein’s quote “spooky action at a distance” referring to entangled quantum states, the concept of spooky encryption (as defined in [21]) is entirely classical.

  4. 4.

    We also remark here that [34] presented a multi-key scheme based on this paradigm, but with the same drawbacks. Note that compactness and classical encryption are crucial in our setting, as per the discussion in the previous section.

  5. 5.

    Actually this expansion should be done slightly more carefully, see Sect. 4.4 in the full version for details.

  6. 6.

    In particular this state may not always be efficiently sampleable, in which case it would be difficult to build an efficient reduction.

  7. 7.

    Above we described a construction of one-to-one non-malleable commitment, though a hybrid argument [48] shows that one-to-one implies many-to-one.

  8. 8.

    We use the syntax that for key k, a ciphertext of message m is computed as \(\mathsf {ct}\leftarrow \mathsf {Enc}(k,m)\) and decrypted as .

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Authors and Affiliations

  1. University of Illinois Urbana-Champaign, Urbana, USA

    Amit Agarwal & Dakshita Khurana

  2. UC Berkeley, Berkeley, USA

    James Bartusek

  3. NTT Research and CMU, Pittsburgh, USA

    Vipul Goyal

  4. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta

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  2. UCLouvain, Louvain-la-Neuve, Belgium

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Agarwal, A., Bartusek, J., Goyal, V., Khurana, D., Malavolta, G. (2021). Post-Quantum Multi-Party Computation. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_16

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