Abstract
Secure multi-party computation (MPC) allows a set \(\mathcal{P}\) of n players to evaluate a function f in presence of an adversary who corrupts a subset of the players. In this paper we consider active, general adversaries, characterized by a so-called adversary structure \(\mathcal{Z}\) which enumerates all possible subsets of corrupted players. In particular for small sets of players general adversaries better capture real-world requirements than classical threshold adversaries.
Protocols for general adversaries are “efficient” in the sense that they require \(|\mathcal{Z}|^{\mathcal{O}(1)}\) bits of communication. However, as \(|\mathcal{Z}|\) is usually very large (even exponential in n), the exact exponent is very relevant. In the setting with perfect security, the most efficient protocol known to date communicates \(\mathcal{O}(|\mathcal{Z}|^3\)) bits; we present a protocol for this setting which communicates \(\mathcal{O}(|\mathcal{Z}|^2\)) bits. In the setting with statistical security, \(\mathcal{O}(|\mathcal{Z}|^3\)) bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication \(\mathcal{O}(|\mathcal{Z}|^2\)) bits is known); we present a protocol for this setting (without limitations) which communicates \(\mathcal{O}(|\mathcal{Z}|^1\)) bits.
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Hirt, M., Tschudi, D. (2013). Efficient General-Adversary Multi-Party Computation. In: Sako, K., Sarkar, P. (eds) Advances in Cryptology - ASIACRYPT 2013. ASIACRYPT 2013. Lecture Notes in Computer Science, vol 8270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42045-0_10
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