In recent years, actively secure SPDZ-like protocols for dishonest majority, like SPDZ2k, Overdrive2k, and MHz2k, over base rings Z2k have become more and more efficient. In this paper, we present a new actively secure MPC protocol Multipars that outperforms these state-of-the-art protocols over Z2k by more than a factor of 2 in the two-party setup in terms of communication. Multipars is the first actively secure N-party protocol over Z2k that is based on linear homomorphic encryption (LHE) in the offline phase (instead of oblivious transfer or somewhat homomorphic encryption in previous works). The strong performance of Multipars relies on a new adaptive packing for BGV ciphertexts that allows us to reduce the parameter size of the encryption scheme and the overall communication cost. Additionally, we use modulus switching for further size reduction, a new type of enhanced CPA security over Z2k, a truncation protocol for Beaver triples, and a new LHE-based offline protocol without sacrificing over Z2k. We have implemented Multipars and therewith provide the fastest preprocessing phase over Z2k. Our evaluation shows that Multipars offers at least a factor of 8 lower communication costs and up to a factor of 15 faster runtime in the WAN setting compared to the currently best available actively secure MPC implementation over Z2k.
Abstract. Recently, there has been huge progress in the field of con-cretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two-party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully-secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present an MPC protocol that is fully-secure in the presence of malicious adversaries and for any number of corrupted par-ties. Our construction is based on the constant-round BMR protocol of Beaver et al., and is the first version of that protocol that is concretely efficient for the dishonest majority case. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase we present both a generic construction (using any underlying MPC protocol), and a highly efficient instantiation based on the SPDZ proto-col. Our estimates show the protocol to be considerably more efficient than previous fully-secure multi-party protocols. 1
Some of the most efficient protocols for Multi-Party Computation (MPC) follow a two-phase approach where correlated randomness, in particular Beaver triples, is generated in the offline phase and then used to speed up the online phase. Recently, more complex correlations have been introduced to optimize certain operations even further, such as matrix triples for matrix multiplications. In this paper, our goal is to improve the efficiency of the triple generation in general and in particular for classical field values as well as matrix operations. To this end, we modify the Overdrive LowGear protocol to remove the costly sacrificing step and therewith reduce the round complexity and the bandwidth. We extend the state-of-the-art MP-SPDZ implementation with our new protocols and show that the new offline phase outperforms state-of-the-art protocols for the generation of Beaver triples and matrix triples. For example, we save in bandwidth compared to Overdrive LowGear.
Secure multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also
38.4% fewer. As a result, total online execution time is
56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.
Secure multiparty computation (MPC) over Z2kis more efficient than computations over fields, and studying MPC protocols under malicious security has practical application value. Malicious security with a dishonest majority over rings remains challenging. The most popular approach is SPDZ2k, however, this is a specific protocol that does not support the transformation of any existing semi-honest MPC protocols into malicious security protocols. The zero knowledge proof (ZKP)-based compiler satisfies this requirement. Existing state-of-the-art protocols have logarithmic online communication overhead in terms of the circuit size |C|, and their direct application to rings is nontrivial as they were originally designed for finite fields. In this work, we investigate the communication overhead to develop malicious security protocols. We bridge the gap between malicious security with abort and semi-honest security, by constructing a “GMW-style” verification protocol to achieve malicious security in a dishonest majority setting. This approach incurs a constant online communication overhead by enhancing the machinery of zero-knowledge fully linear interactive oracle proof (zk-FLIOP). Additionally, we extend the zk-FLIOP to work over any ring by invoking reverse multiplication friendly embeddings (RMFEs). Our results show that the online communication complexity of the verification process depends on only the security parameter, the number of parties, and the ring size. Furthermore, for small-scale circuits over Z2, we designed a distributed lookup table argument where both the total communication complexity and the computational cost are independent of the circuit size but of the input wires.
Abstract We construct the first actively-secure Multi-Party Computation (MPC) protocols with an arbitrary number of parties in the dishonest majority setting, for an arbitrary field
F F with constant communication overhead over the “passive-GMW” protocol (Goldreich, Micali and Wigderson, STOC ‘87). Our protocols rely on passive implementations of Oblivious Transfer (OT) in the Boolean setting and Oblivious Linear function Evaluation (OLE) in the arithmetic setting. Previously, such protocols were only known over sufficiently large fields (Genkin et al. STOC ‘14) or a constant number of parties (Ishai et al. CRYPTO ‘08). Conceptually, our protocols are obtained via a new compiler from a passively-secure protocol for a distributed multiplication functionality
FMULT F MULT , to an actively-secure protocol for general functionalities. Roughly,
FMULT F MULT is parameterized by a linear-secret sharing scheme
S S , where it takes
S S -shares of two secrets and returns
S S -shares of their product. We show that our compilation is concretely efficient for sufficiently large fields, resulting in an overhead of 2 when securely computing natural circuits. Our compiler has two additional benefits: (1) It can rely on any passive implementation of
FMULT F MULT , which, besides the standard implementation based on OT (for Boolean) and OLE (for arithmetic), allows us to rely on implementations based on threshold cryptosystems (Cramer et al. Eurocrypt ‘01), and (2) it can rely on weaker-than-passive (i.e., imperfect/leaky) implementations, which in some parameter regimes yield actively-secure protocols with overhead less than 2. Instantiating this compiler with an “honest-majority” implementation of
FMULT F MULT , we obtain the first honest-majority protocol (with up to one-third corruptions) for Boolean circuits with constant communication overhead over the best passive protocol (Damgård and Nielsen, CRYPTO ‘07).
Abstract. We introduce a new approach to multiparty computation (MPC) basing it on homomorphic threshold crypto-systems. We show that given keys for any sufficiently efficient system of this type, general MPC protocols for n parties can be devised which are secure against an active adversary that corrupts any minority of the parties. The total number of bits broadcast is O(nk|C|), where k is the security parameter and |C | is the size of a (Boolean) circuit computing the function to be securely evaluated. An earlier proposal by Franklin and Haber with the same complexity was only secure for passive adversaries, while all earlier protocols with active security had complexity at least quadratic in n. We give two examples of threshold cryptosystems that can support our construction and lead to the claimed complexities. 1