A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity

Abstract

We present a new secure multiparty computation protocol in the preprocessing model that allows for the evaluation of a number of instances of a boolean circuit in parallel, with a small online communication complexity per instance of 10 bits per party and multiplication gate. Our protocol is secure against an active dishonest majority, and can also be transformed, via existing techniques, into a protocol for the evaluation of a single "well-formed" boolean circuit with the same complexity per multiplication gate at the cost of some overhead that depends on the topology of the circuit. Our protocol uses an approach introduced recently in the setting of honest majority and information-theoretical security which, using an algebraic notion called reverse multiplication friendly embeddings, essentially transforms a batch of evaluations of an arithmetic circuit over a small field into one evaluation of another arithmetic circuit over a larger field. To obtain security against a dishonest majority we combine this approach with the well-known SPDZ protocol that operates over a large field. Structurally our protocol is most similar to MiniMAC, a protocol which bases its security on the use of error-correcting codes, but our protocol has a communication complexity which is half of that of MiniMAC when the best available binary codes are used. With respect to certain variant of MiniMAC that utilizes codes over larger fields, our communication complexity is slightly worse; however, that variant of MiniMAC needs a much larger preprocessing than ours. We also show that our protocol also has smaller amortized communication complexity than Committed MPC, a protocol for general fields based on homomorphic commitments, if we use the best available constructions for those commitments. Finally, we construct a preprocessing phase from oblivious transfer based on ideas from MASCOT and Committed MPC.

Concretely efficient secure multi-party computation protocols: survey and more

“…For the case of binary field (i.e., F = F 2 ), we mainly consider two types of MPC protocols in the malicious setting: TinyOT-style [104, 106-110, 164, 165] and MiniMAC-style [164,[166][167][168][169]. In particular, the sub-protocols for generating authenticated triples underlying in the TinyOT-style protocols can be used to design constant-round MPC protocols with malicious security [106][107][108][109][110].…”

“…In MiniMAC, an IT-MAC on message x ∈ F k is defined as C(x) * ∆ where ∆ ∈ F k , C is a linear error-correcting code with a large minimum distance and * is the componentwise product. MiniMAC-style MPC protocols [164,[166][167][168][169] also work for layered Boolean circuits where the gates of a Boolean circuit are partitioned into ordered layers and a layer only consists of gates of the same type. The recent MiniMAC-style protocol [166] adopts an algebraic tool called reverse multiplication friendly embedding (RMFE) [170] that is originally proposed for honest-majority MPC, and obtains a lower communication cost.…”

“…MiniMAC-style MPC protocols [164,[166][167][168][169] also work for layered Boolean circuits where the gates of a Boolean circuit are partitioned into ordered layers and a layer only consists of gates of the same type. The recent MiniMAC-style protocol [166] adopts an algebraic tool called reverse multiplication friendly embedding (RMFE) [170] that is originally proposed for honest-majority MPC, and obtains a lower communication cost. Besides, for small fields, TinyTable-style protocols [112,171,172] are proposed and very suitable for secure AES or 3DES evaluation using the one-time truth table approach.…”