With the increasing interest in Secure Multi-Party Computation protocols (MPC), there have been several works such as the SPDZ1protocol that tackled this problem under a malicious security with dishonest majority attack model. However, most of these MPC efforts assume that the nodes running the computations are also supplying the inputs, which is not a realistic assumption for many real-life applications. In this paper, we extend the SPDZ protocol to enable clients outsource data and computation to the clouds while ensuring the correctness of the results, in addition to integrity and confidentiality of the input and output. We guarantee that the computation among nodes is done correctly by verifying their output’s Message Authentication Codes (MACs) at the end. Specifically, we delegate this task to an honest server. Our approach strives to minimize the burden on clients while enabling cheating detection even when assuming a malicious attack model with dishonest majority.
With the increasing interest in Secure Multi-Party Computation protocols (MPC), there have been several works such as the SPDZ1protocol that tackled this problem under a malicious security with dishonest majority attack model. However, most of these MPC efforts assume that the nodes running the computations are also supplying the inputs, which is not a realistic assumption for many real-life applications. In this paper, we extend the SPDZ protocol to enable clients outsource data and computation to the clouds while ensuring the correctness of the results, in addition to integrity and confidentiality of the input and output. We guarantee that the computation among nodes is done correctly by verifying their output’s Message Authentication Codes (MACs) at the end. Specifically, we delegate this task to an honest server. Our approach strives to minimize the burden on clients while enabling cheating detection even when assuming a malicious attack model with dishonest majority.
Abstract. Secure multiparty computation (MPC) as a service is becoming a tangible reality. In such a service, a population of clients wish to utilize a set of servers to delegate privately and reliably a given computation on their inputs. MPC protocols have a number of desired properties including tolerating active misbehavior by some of the servers and guaranteed output delivery. A fundamental result is that in order to achieve the above, an honest majority among servers is necessary. There are settings, however, where this condition might be overly restrictive, making it important to investigate models where this impossibility result can be circumvented, allowing secure computation to be performed even when the number of malicious participants outweighs the number of honest participants. To this end, we introduce the two-tier model for MPC, where a set of m parties that are guaranteed to be honest (the first tier) remains “hidden ” within a set of n − m servers which are of dubious trustworthiness (the second tier), and where the objective is to perform MPC withstanding a number of active misbehaviors that is larger than m/2. Indeed, assuming αn of the second-tier servers are dishonest (where α ∈ (0, 1)), we present an MPC protocol that can withstand up to (1 − )(1 − α)n/2 additional faults, for any > 0 and m = ω(logn). Somewhat surprisingly, this allows the total number of faulty parties to exceed n/2 across both tiers. We demonstrate that the two-tier model naturally arises in various settings, as in the case, for example, of a resource-constrained service provider wishing to utilize a pre-existing set of servers. 1
In the last few years the efficiency of secure multi-party computation (MPC) increased in several orders of magnitudes. However, this alone might not be enough if we want MPC protocols to be used in practice. A crucial property that is needed in many applications is that everyone can check that a given (secure) computation was performed correctly – even in the extreme case where all the parties involved in the computation are corrupted, and even if the party who wants to verify the result was not participating. This is especially relevant in the clients-servers setting, where many clients provide input to a secure computation performed by a few servers. An obvious example of this is electronic voting, but also in many types of auctions one may want independent verification of the result. Traditionally, this is achieved by using non-interactive zero-knowledge proofs during the computation.A recent trend in MPC protocols is to have a more expensive preprocessing phase followed by a very efficient online phase, e.g., the recent so-called SPDZ protocol by Damgård et al. Applications such as voting and some auctions are perfect use-case for these protocols, as the parties usually know well in advance when the computation will take place, and using those protocols allows us to use only cheap information-theoretic primitives in the actual computation. Unfortunately no protocol of the SPDZ type supports an audit phase.In this paper, we show how to achieve efficient MPC with a public audit. We formalize the concept of publicly auditable secure computation and provide an enhanced version of the SPDZ protocol where, even if all the servers are corrupted, anyone with access to the transcript of the protocol can check that the output is indeed correct. Most importantly, we do so without significantly compromising the performance of SPDZ i.e. our online phase has complexity approximately twice that of SPDZ.
In recent years, lattice-based secure multi-party computation (MPC) has seen a rise in popularity and is used more and more in large scale applications like privacy-preserving cloud computing, electronic voting, or auctions. Many of these applications come with the following high security requirements: a computation result should be publicly verifiable, with everyone being able to identify a malicious party and hold it accountable, and a malicious party should not be able to corrupt the computation, force a protocol restart, or block honest parties or an honest third-party (client) that provided private inputs from receiving a correct result. The protocol should guarantee verifiability and accountability even if all protocol parties are malicious. While some protocols address one or two of these often essential security features, we present the first publicly verifiable and accountable, and (up to a threshold) robust SPDZ-like MPC protocol without restart. We propose protocols for accountable and robust online, offline, and setup computations. We adapt and partly extend the lattice-based commitment scheme by Baum et al. (SCN 2018) as well as other primitives like ZKPs. For the underlying commitment scheme and the underlying BGV encryption scheme we determine ideal parameters. We give a performance evaluation of our protocols and compare them to state-of-the-art protocols both with and without our target security features: public accountability, public verifiability and robustness.
We initiate the study of secure multi-party computation (MPC) in a server-aided setting, where the parties have access to a single server that (1) does not have any input to the computation; (2) does not receive any output from the computation; but (3) has a vast (but bounded) amount of computational resources. In this setting, we are concerned with designing protocols that minimize the computation of the parties at the expense of the server. We develop new definitions of security for this server-aided setting that generalize the standard simulation-based definitions for MPC and allow us to formally capture the existence of dishonest but non-colluding participants. This requires us to introduce a formal characterization of non-colluding adversaries that may be of independent interest. We then design general and special-purpose server-aided MPC protocols that are more efficient (in terms of computation and communication) for the parties than the alternative of running a standard MPC protocol (i.e., without the server). Our main general-purpose protocol provides security when there is at least one honest party with input. We also construct a new and efficient server-aided protocol for private set intersection and give a general transformation from any secure delegated computation scheme to a server-aided two-party protocol. ∗Microsoft Research. senyk@microsoft.com. †University of Calgary. pmohassel@cspc.ucalgary.ca. Work done while visiting Microsoft Research. ‡Columbia University. mariana@cs.columbia.edu. Work done as an intern at Microsoft Research.
SPDZ refers to a family of protocols for Secure Multi-Party Computation (MPC) that lie at the foundation of very popular software frameworks for MPC, such as SCALE-MAMBA and MP-SPDZ. SPDZ provides good efficiency while guaranteeing security even when all but one of the participants are corrupted. This seemingly optimal property comes at a price: the protocol only offers security with abort, meaning that even a single cheating participant can force the protocol to abort, leaving honest participants with no clue on what the correct output is, or who cheated. This is especially problematic since cheating participants are able to obtain the correct output of the computation, effectively `stealing' it. We propose a *hybrid secure* adaptation to SPDZ, which retains the existing security guarantees, but in case the number of cheating players is less than half of the total, we achieve *fairness*, meaning that either all players obtain the correct output of the computation, or no player does. The `less than half' threshold of corrupted players has been proven to be a tight bound to achieve fairness. Aside from the description of the protocol and its security proof, we also present a proof-of-concept implementation, and evaluate its practical performance, thereby demonstrating that our solution has negligible overhead compared to standard SPDZ in most application scenarios.
Dishonest majority considered in the SPDZ(the nickname of the protocol of Damgard et al. from Crypto 2012) protocols implies the impossibility of fairness(which means that corrupted parties can prevent the honest parties from learning output). The corrupted parties can learn the outputs of the honest parties and abort the protocol. Settling for the second best, there are many works focusing on the detection of the cheaters. We construct a SPDZ-like protocol which achieves fairness when at mostn/2parties behave maliciously and supports identifiable abort for dishonest majority. We suggest a sharing stage after the parties finish their computation. The parties share the returns of the computation in this stage. The correctness of the sharing is guaranteed by verifiable secret sharing and homomorphic signature. The honest parties can reconstruct the outputs of the cheaters in the setting of an honest majority. We can't prevent the corrupted parties from learning the outputs and aborting the protocol for dishonest majority. Therefore, the sharing stage does not harm to the honest parties. Instead, we provide the honest parties with the identities of all cheaters in this case.