Paper 2026/608

Can Adaptive Communication Graphs Lower the Bottleneck Complexity of (Secure) Multiparty Computation?

Abstract

The bottleneck complexity of a (secure) multiparty computation protocol is one measure of its communication-efficiency. It captures how well the communication load is balanced, and is defined as the maximum communication complexity required by any one party within the protocol execution. Prior works on this topic restricted attention to protocols with fixed communication graphs, i.e. whether or not a given party communicates to another only depends on the round number. We demonstrate the power of adaptively choosing communication graphs by developing various bottleneck-efficient protocols, both with and without security. Done naÏvely, protocols with adaptive communication graphs can exploit unnatural tricks, such as "communicating with silence." To ensure our protocols are meaningful, we additionally stipulate that they should run correctly even in asynchronous networks (where we make no assumption on the adversarial message-delays other than being finite). [Bottleneck complexity of arbitrary functions.] With fixed communication graphs, Boyle, Jain, Prabhakaran, and Yu (ICALP'18) established the existence of a function $f\colon\{0,1\}^n\to\{0,1\}$ requiring $\Omega(n)$-bit bottleneck complexity, which is matched by the trivial protocol of having all parties send their inputs to one party. By adaptively choosing communication graphs, we show that any function $f\colon\{0,1\}^n\to\{0,1\}$ can be computed (securely) with bottleneck $O(n/\log n)$ (which we prove is essentially optimal), even in \emph{asynchronous} networks. [Bottleneck complexity of symmetric functions.] Prior works have demonstrated that special classes of symmetric functions, such as additive [Eriguchi, Asiacrypt'23] or abelian [Keller, Orlandi, Paskin-Cherniavsky, Ravi, ITC'23] functions can be computed bottleneck-efficiently with fixed communication graphs. We both expand the class of symmetric functions achievable with low bottleneck complexity, as well as show how input-adaptive communication graphs can be leveraged to further reduce the bottleneck complexity of some of our protocols.