Simple and Efficient Perfectly-Secure Asynchronous MPC

Abstract

Abstract. Secure multi-party computation (MPC) allows a set of n players to securely compute an agreed function of their inputs, even when up to t players are under the control of an adversary. Known asynchronous MPC protocols require communication of at least Ω(n 3 ) (with cryptographic security), respectively Ω(n 4 ) (with information-theoretic security, but with error probability and non-optimal resilience) field elements per multiplication.We present an asynchronous MPC protocol communicating O(n 3 ) field elements per multiplication. Our protocol provides perfect security against an active, adaptive adversary corrupting t < n/4 players, which is optimal. This communication complexity is to be compared with the most efficient previously known protocol for the same model, which requires Ω(n 5 ) field elements of communication (i.e., Ω(n 3 ) broadcasts). Our protocol is as efficient as the most efficient perfectly secure protocol for the synchronous model and the most efficient asynchronous protocol with cryptographic security.Furthermore, we enhance our MPC protocol for a hybrid model. In the fully asynchronous model, up to t honest players might not be able to provide their input in the computation. In the hybrid model, all players are able to provide their input, given that the very first round of communication is synchronous. We provide an MPC protocol with communicating O(n 3 ) field elements per multiplication, where all players can provide their input if the first communication round turns out to be synchronous, and all but at most t players can provide their input if the communication is fully asynchronous. The protocol does not need to know whether or not the first communication round is synchronous, thus combining the advantages of the synchronous world and the asynchronous world. The proposed MPC protocol is the first protocol with this property.

Communication Efficient Perfectly Secure VSS and MPC in Asynchronous Networks with Optimal Resilience

“…Type Resilience CC in bits [8,15] Perfect t < n/4 (optimal) O(n 6 log |F|) [44] Perfect t < n/4 (optimal) Ω(n 5 log |F|) [5] Perfect t < n/4 (optimal) O(n 3 log |F|) [10] Statistical t < n/3 (optimal) Ω(n 11 (log |F|) 4 ) [38] Statistical t < n/3 (optimal) O(n 5 log |F|) [40] Statistical t < n/4 (non-optimal) O(n 4 log |F|) [31] Statistical t < n/4 (non-optimal) O(n 2 log |F|) This article Statistical t < n/4 (non-optimal) O(n 2 log |F|) This article Perfect t < n/4 (optimal) O(n 2 log |F|)…”

“…Our perfect AMPC protocol has optimal resilience. From Table 1, the best known perfect AMPC with optimal resilience [5] communicates O(n 3 log |F|) bits per multiplication.…”

“…Hence, we call any perfectly secure AVSS protocol designed with exactly n = 4t + 1 parties as an optimally resilient, perfectly secure AVSS protocol. Such AVSS protocols are proposed in [8,15,5].…”

“…This approach is used in al most all the MPC schemes (both synchronous as well as asynchronous) proposed in the recent years ( [4,23,6]). An alternative of the above mentioned approach proposed in [5] and used by us in this paper is to evaluate the multiplication gates using pre-computed (t, 2t)-sharing of random values. A (t, 2t)-sharing [5] of a value r ∈ F consists of a t-sharing and a 2t-sharing of r using independent polynomials of degree at most t and 2t respectively.…”

“…Thus any perfectly secure AMPC protocol designed with exactly n = 4t+1 parties is said to be an optimally resilient perfectly secure AMPC protocol. Optimally resilient, perfectly secure AMPC protocols are reported in [8,44,5]. Among these, the AMPC protocol of [5] provides the best communication complexity, which is O(n 3 log(|F|)) bits per multiplication gate, where the computation is done over a finite field F, such that |F| > n.…”