## Efficient Multi-Party Computation with Dispute Control

### Zuzana Beerliova-Trubiniova and Martin Hirt

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 (active or passive) adversary. In the information-theoretic model MPC is possible if and only if $t<n/2$ (where active security with $t\ge n/3$ requires a trusted key setup).

Known passive MPC protocols require a communication of $\O(n^2)$ field elements per multiplication. Recently, the same communication complexity was achieved for active security with $t<n/3$. It remained an open question whether $\O(n^2)$ complexity is achievable for $n/3\le t<n/2$.

We answer this question in the affirmative by presenting an active MPC protocol that provides optimal ($t<n/2$) security and communicates only $\O(n^2)$ field elements per multiplication. Additionally the protocol broadcasts $\O(n^3)$ field elements *overall*, for the whole computation.

The communication complexity of the new protocol is to be compared with the most efficient previously known protocol for the same model, which requires *broadcasting* $\Omega(n^5)$ field elements per multiplication. This substantial reduction in communication is mainly achieved by applying a new technique called *dispute control*: During the course of the protocol, the players keep track of disputes that arise among them, and the ongoing computation is adjusted such that known disputes cannot arise again. Dispute control is inspired by the player-elimination framework. However, player elimination is not suited for models with $t\ge n/3$.

## BibTeX Citation

@inproceedings{BeeHir06, author = {Zuzana {Beerliova-Trubiniova} and Martin Hirt}, title = {Efficient Multi-Party Computation with Dispute Control}, editor = {Shai Halevi and Tal Rabin}, booktitle = {Theory of Cryptography Conference --- TCC 2006}, pages = {305--328}, series = {Lecture Notes in Computer Science}, volume = {3876}, year = {2006}, month = {3}, publisher = {Springer-Verlag}, }