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Adaptive Security, Erasures, and Network Assumptions in Communication-Local MPC

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Theory of Cryptography (TCC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15367))

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Abstract

The problem of reliable/secure all-to-all communication over low-degree networks has been essential for communication-local (CL) n-party MPC (i.e., MPC protocols where every party directly communicates only with a few, typically polylogarithmic in n, parties) and more recently for communication over ad hoc networks, which are used in blockchain protocols. However, a limited number of adaptively secure solutions exist, and they all make relatively strong assumptions on the ability of parties to act in some specific manner before the adversary can corrupt them. Two such assumptions were made in the work of Chandran et al. [ITCS ’15]—parties can (a) multisend messages to several receivers simultaneously; and (b) securely erase the message and the identities of the receivers, before the adversary gets a chance to corrupt the sender (even if a receiver is corrupted).

A natural question to ask is: Are these assumptions necessary for adaptively secure CL MPC? In this paper, we characterize the feasibility landscape for all-to-all reliable message transmission (RMT) under these two assumptions, and use this characterization to obtain (asymptotically) tight feasibility results for CL MPC.

  • First, we prove a strong impossibility result for a broad class of RMT protocols, termed here store-and-forward protocols, which includes all known communication protocols for CL MPC from standard cryptographic assumptions. Concretely, we show that no such protocol with a certain expansion rate can tolerate a constant fraction of parties being corrupted.

  • Next, under the assumption of only a PKI, we show that assuming secure erasures, we can obtain an RMT protocol between all pairs of parties with polylogarithmic locality (even without assuming multisend) for the honest majority setting. We complement this result by showing a negative result for the setting of dishonest majority.

  • Finally, and somewhat surprisingly, under stronger assumptions (i.e., trapdoor permutations with a reverse domain sampler, and compact and malicious circuit-private FHE), we construct a polylogarithmic-locality all-to-one RMT protocol, which is adaptively secure and tolerates any constant fraction of corruptions, without assuming either secure erasures or multisend. This last result uses a novel combination of adaptively secure (e.g., non-committing) encryption and (static) FHE to bypass the impossibility of compact adaptively secure FHE by Katz et al. [PKC’13], which we believe may be of independent interest. Intriguingly, even such assumptions do not allow reducing all-to-all RMT to all-to-one RMT (a reduction which is trivial in the non-CL setting). Still, we can implement what we call sublinear output-set RMT (SOS-RMT for short). We show how SOS-RMT can be used for SOS-MPC under the known bounds for feasibility of MPC in the standard (i.e., non-CL) setting assuming, in addition to SOS-RMT, an anonymous PKI.

R. Ostrovsky—This research was supported in part by NSF grants CNS-2246355, CCF-2220450, US-Israel BSF grant 2022370, and by Sunday Group.

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Notes

  1. 1.

    As a side note, an interesting side effect of the recent popularity of blockchain protocols is that, as they also rely on gossiping for communication, results on the feasibility of sublinear-communication protocols provide insights on basic feasibility questions in the blockchain context as well (see related work for further details).

  2. 2.

    As shown in  [33, 36], this property is impossible to obtain from simple point-to-point communication in the standard adaptive and rushing adversary setting [10].

  3. 3.

    Here “low” specifically means asymptotically smaller than the adversary’s corruption budget.

  4. 4.

    Here, we use “full” MPC to refer to the standard MPC formulation where no party is left out; this is in contrast to “almost-everywhere” MPC [27], where some of the parties are not given any correctness and privacy guarantees.

  5. 5.

    Since we will be running at most polylogarithmic-round protocols, we can assume wlog that the hidden graph is a multi-graph consisting of polylogarithmic, independent copies of polylogarithmic-degree hidden graph setup.

  6. 6.

    Recall that the hidden graph is directed.

  7. 7.

    WLOG, we assume that valid RMT messages are from a fixed-size domain.

  8. 8.

    Recall that this can be replaced by an SKI or a NIKE scheme assuming the PKI supports it.

  9. 9.

    Note that Theorem 3 implies that if we assume erasures as an atomic operation and no atomic multisend, then no MPC as in the above theorem exists if \(t>(\frac{1}{2}+\epsilon '') n\) for some constant \(\epsilon ''\). However, this is anyway implied by the tightness of the condition \(t<n/2\) for adaptive security even in the complete (i.e., non-CL) point-to-point channels setting, and is therefore omitted.

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Authors and Affiliations

  1. Microsoft Research, Bengaluru, India

    Nishanth Chandran

  2. Texas A&M University, Texas, USA

    Juan Garay

  3. University of California, Los Angeles, USA

    Ankit Kumar Misra & Rafail Ostrovsky

  4. Purdue University, West Lafayette, USA

    Vassilis Zikas

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  1. Nishanth Chandran
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  5. Vassilis Zikas
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Correspondence to Ankit Kumar Misra .

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  1. NTT Research, Sunnyvale, CA, USA

    Elette Boyle

  2. University of Virginia, Charlottesville, VA, USA

    Mohammad Mahmoody

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Chandran, N., Garay, J., Misra, A.K., Ostrovsky, R., Zikas, V. (2025). Adaptive Security, Erasures, and Network Assumptions in Communication-Local MPC. In: Boyle, E., Mahmoody, M. (eds) Theory of Cryptography. TCC 2024. Lecture Notes in Computer Science, vol 15367. Springer, Cham. https://doi.org/10.1007/978-3-031-78023-3_10

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