Cryptology ePrint Archive: Report 2004/318

Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

Martin Hirt and Jesper Buus Nielsen

Abstract: We give improved upper bounds on the communication complexity of optimally-resilient secure multiparty computation in the cryptographic model. We consider evaluating an $n$-party randomized function and show that if $f$ can be computed by a circuit of size $c$, then $\O(c n^2 \kappa)$ is an upper bound for active security with optimal resilience $t < n/2$ and security parameter $\kappa$. This improves on the communication complexity of previous protocols by a factor of at least $n$. This improvement comes from the fact that in the new protocol, only $\O(n)$ messages (of size $\O(\kappa)$ each) are broadcast during the \emph{whole} protocol execution, in contrast to previous protocols which require at least $\O(n)$ broadcasts \emph{per gate}.

Furthermore, we improve the upper bound on the communication complexity of passive secure multiparty computation with resilience $t<n$ from $\O(c n^2 \kappa)$ to $\O(c n \kappa)$. This improvement is mainly due to a simple observation.

Category / Keywords: cryptographic protocols /

Publication Info: Asiacrypt 2005

Date: received 23 Nov 2004, last revised 10 May 2006

Contact author: hirt at inf ethz ch

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