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1. The More The Merrier: Reducing the Cost of Large Scale MPC

   Gordon, S. Dov; Starin, Daniel; Yerukhimovich, Arkady (January 2021, Eurocrypt)

   Canteaut, Anne; Standaert, Francois-Xavier (Ed.)

   Secure multi-party computation (MPC) allows multiple par-ties to perform secure joint computations on their private inputs. To-day, applications for MPC are growing with thousands of parties wish-ing to build federated machine learning models or trusted setups for blockchains. To address such scenarios we propose a suite of novel MPC protocols that maximize throughput when run with large numbers of parties. In particular, our protocols have both communication and computation complexity that decrease with the number of parties. Our protocols build on prior protocols based on packed secret-sharing, introducing new techniques to build more efficient computation for general circuits. Specifically, we introduce a new approach for handling linear attacks that arise in protocols using packed secret-sharing and we propose a method for unpacking shared multiplication triples without increasingthe asymptotic costs. Compared with prior work, we avoid the log|C|overhead required when generically compiling circuits of size |C| for use in a SIMD computation, and we improve over folklore “committee-based” solutions by a factor of O(s), the statistical security parameter. In practice, our protocol is up to 10X faster than any known construction, under a reasonable set of parameters. 

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2. The More The Merrier: Reducing the Cost of Large Scale MPC

   Gordon, S. Dov; Starin, Daniel; Yerukhimovich, Arkady (January 2021, Eurocrypt)

   Canteaut, Anne; Standaert, Francois-Xavier (Ed.)

   Secure multi-party computation (MPC) allows multiple par-ties to perform secure joint computations on their private inputs. To-day, applications for MPC are growing with thousands of parties wish-ing to build federated machine learning models or trusted setups for blockchains. To address such scenarios we propose a suite of novel MPC protocols that maximize throughput when run with large numbers of parties. In particular, our protocols have both communication and computation complexity that decrease with the number of parties. Our protocols build on prior protocols based on packed secret-sharing, introducing new techniques to build more efficient computation for general circuits. Specifically, we introduce a new approach for handling linear attacks that arise in protocols using packed secret-sharing and we propose a method for unpacking shared multiplication triples without increasingthe asymptotic costs. Compared with prior work, we avoid the log|C|overhead required when generically compiling circuits of size |C| for use in a SIMD computation, and we improve over folklore “committee-based” solutions by a factor of O(s), the statistical security parameter. In practice, our protocol is up to 10X faster than any known construction, under a reasonable set of parameters. 

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

   Chandran, Nishanth; Garay, Juan; Misra, Ankit_Kumar; Ostrovsky, Rafail; Zikas, Vassilis (December 2024, TCC 2024 Conference proceeeding)

   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 polylogarithmiclocality 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 SOSRMT 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. 

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

   Chandran, Nishanth; Garay, Juan; Misra, Ankit_Kumar; Ostrovsky, Rafail; Zikas, Vassilis (December 2024, Springer Nature Link)

   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. 

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5. CostCO: An automatic cost modeling framework for secure multi-party computation

   https://doi.org/10.1109/EuroSP53844.2022.00017  

   Fang, Vivian; Brown, Lloyd; Lin, William; Zheng, Wenting; Panda, Aurojit; Popa, Raluca Ada (June 2022, 2022 IEEE 7th European Symposium on Security and Privacy (EuroS&P))

   The last decade has seen an explosion in the number of new secure multi-party computation (MPC) protocols that enable collaborative computation on sensitive data. No single MPC protocol is optimal for all types of computation. As a result, researchers have created hybrid-protocol compilers that translate a program into a hybrid protocol that mixes different MPC protocols. Hybrid-protocol compilers crucially rely on accurate cost models, which are handwritten by the compilers' developers, to choose the correct schedule of protocols. In this paper, we propose CostCO, the first automatic MPC cost modeling framework. CostCO develops a novel API to interface with a variety of MPC protocols, and leverages domain-specific properties of MPC in order to enable efficient and automatic cost-model generation for a wide range of MPC protocols. CostCO employs a two-phase experiment design to efficiently synthesize cost models of the MPC protocol's runtime as well as its memory and network usage. We verify CostCO's modeling accuracy for several full circuits, characterize the engineering effort required to port existing MPC protocols, and demonstrate how hybrid-protocol compilers can leverage CostCO's cost models. 

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