Optimally efficient multi-valued byzantine agreement

Abstract. We present a new technique for robust secret reconstruction with O(n) communication complexity. By applying this technique, we achieve O(n) communication complexity per multiplication for a wide class of robust practical Multi-Party Computation (MPC) protocols. In particular our technique applies to robust threshold computationally secure protocols in the case of t < n/2 in the pre-processing model. Previously in the pre-processing model, O(n) communication complexity per multiplication was only known in the case of computationally secure non-robust protocols in the dishonest majority setting (i.e. with t < n) and in the case of perfectly-secure robust protocols with t < n/3. A similar protocol was sketched by Damgård and Nielsen, but no details were given to enable an estimate of the communication complexity. Surprisingly our robust reconstruction protocol applies for both the synchronous and asynchronous settings.

Section: B1 Primitivesmentioning

confidence: 99%

Section: Threshold Somewhat Homomorphic Encryption (She)mentioning

confidence: 99%

Section: B2 the Ideal One-time Setup Functionalitymentioning

confidence: 99%

Section: Generating Shared Multiplicationmentioning

confidence: 99%

See 2 more Smart Citations

Linear Overhead Optimally-Resilient Robust MPC Using Preprocessing

Choudhury

Orsini

Patra

et al. 2016

“…As our focus in this work is on reducing the overall number of broadcast rounds, rather than broadcast (or otherwise) communication complexity, we forgo explicit treatment of the latter. We do however note that protocols described herein can be compiled via generic techniques into significantly more communication-efficient versions; see work of Fitzi and Hirt [FH06], as well as recent work by BenSasson et al [BFO12].…”

Section: Introductionmentioning

confidence: 99%

Broadcast (and Round) Efficient Verifiable Secret Sharing

Garay

Givens

Ostrovsky

et al. 2014

Verifiable secret sharing (VSS) is a fundamental cryptographic primitive, lying at the core of secure multi-party computation (MPC) and, as the distributed analogue of a commitment functionality, used in numerous applications. In this paper we focus on unconditionally secure VSS protocols with honest majority.In this setting it is typically assumed that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a "broadcast" channel. Because broadcast cannot be simulated on a point-to-point network when a third or more of the parties are corrupt, it is impossible to construct VSS (and more generally, MPC) protocols in this setting without using a broadcast channel (or some equivalent addition to the model).A great deal of research has focused on increasing the efficiency of VSS, primarily in terms of round complexity. In this work we consider a refinement of the round complexity of VSS, by adding a measure we term broadcast complexity. We view the broadcast channel as an expensive resource and seek to minimize the number of rounds in which it is invoked as well.We construct a (linear) VSS protocol which uses the broadcast channel only twice in the sharing phase, while running in an overall constant number of rounds.

Robust Multiparty Computation with Linear Communication Complexity

Hirt

Nielsen

2006

Self Cite

Abstract. We present a robust multiparty computation protocol. The protocol is for the cryptographic model with open channels and a polytime adversary, and allows n parties to actively securely evaluate any poly-sized circuit with resilience t < n/2. The total communication complexity in bits over the point-to-point channels is O(Snκ + n BC), where S is the size of the circuit being securely evaluated, κ is the security parameter and BC is the communication complexity of one broadcast of a κ-bit value. This means the average number of bits sent and received by a single party is O(Sκ + BC), which is almost independent of the number of participating parties. This is the first robust multiparty computation protocol with this property.