Asynchronous Multiparty Computation: Theory and Implementation

Abstract

Abstract. We propose an asynchronous protocol for general multiparty computation. The protocol has perfect security and communication complexity O(n 2 |C|k), where n is the number of parties, |C| is the size of the arithmetic circuit being computed, and k is the size of elements in the underlying field. The protocol guarantees termination if the adversary allows a preprocessing phase to terminate, in which no information is released. The communication complexity of this protocol is the same as that of a passively secure solution up to a constant factor. It is secure against an adaptive and active adversary corrupting less than n/3 players. We also present a software framework for implementation of asynchronous protocols called VIFF (Virtual Ideal Functionality Framework), which allows automatic parallelization of primitive operations such as secure multiplications, without having to resort to complicated multithreading. Benchmarking of a VIFF implementation of our protocol confirms that it is applicable to practical non-trivial secure computations.

Linear Overhead Optimally-Resilient Robust MPC Using Preprocessing

“…This may not be acceptable for most practical applications of MPC. To get rid of the latter difficulty, [19] introduced the following variant of the traditional asynchronous communication setting, which we refer as partial asynchronous setting:…”

“…In [19] it was shown how to securely realize a variant of F PREP , augmented with abort (we call this functionality F PREP-ABORT ), in the partial asynchronous setting with t < n/3. The functionality F PREP-ABORT is similar to F PREP except that the functionality distributes the generated values to the honest parties depending upon the choice of the adversary: if adversary sends an OK signal then F PREP-ABORT distributes the information to the honest parties in the same way as done in F PREP , otherwise it sends ⊥ to the honest parties.…”

“…To securely realize F PREP-ABORT in the partial asynchronous setting with t < n/3, [19] used the following approach: assume there exists a secure realization of F PREP , say Π PREP , in a synchronous setting with broadcast (in [19], two instantiations of Π PREP are presented). Protocol Π PREP is then executed in the partial asynchronous setting in a "special" way to ensure that no additional information is revealed prematurely (more on this in the sequel).…”

“…Finally the parties run an ABA protocol to agree on whether the preprocessing succeeded and accordingly they either abort or successfully terminate the protocol. From the above discussion, it is clear that we can securely realize F PREP-ABORT with t < n/2 in the partial asynchronous setting following the blueprint of [19], provided that we have the following two components: (a) A secure realization of F PREP with t < n/2 in the synchronous communication setting with broadcast; (b) An ABA protocol with t < n/2. The former is presented in the previous section.…”

“…Now we discuss how to run the protocol Π PREP in the partial asynchronous setting following the method of [19]. The basic idea is to execute Π PREP over an asynchronous network where a (honest) party P i starts computation for round i + 1 only when it receives all the communication that it is supposed to receive in the ith round (for instance, if the ith step specifies that it should receive some information from all the parties, then it waits to receive some information from all the parties and not just from n − t parties).…”