# Passive Corruption in Statistical Multi-Party Computation

## Martin Hirt and Christoph Lucas and Ueli Maurer and Dominik Raub

The goal of Multi-Party Computation (MPC) is to perform an arbitrary computation in a distributed, private, and fault-tolerant way. For this purpose, a fixed set of n parties runs a protocol that tolerates an adversary corrupting a subset of the parties, preserving certain security guarantees like correctness, secrecy, robustness, and fairness. Corruptions can be either passive or active: A passively corrupted party follows the protocol correctly, but the adversary learns the entire internal state of this party. An actively corrupted party is completely controlled by the adversary, and may deviate arbitrarily from the protocol. A mixed adversary may at the same time corrupt some parties actively and some additional parties passively.

In this work, we consider the statistical setting with mixed adversaries and study the exact consequences of active and passive corruptions on secrecy, correctness, robustness, and fairness separately (i.e., hybrid security).
Clearly, the number of passive corruptions affects the thresholds for secrecy, while the number of active corruptions affects all thresholds. It turns out that in the statistical setting, the number of passive corruptions in particular also affects the threshold for correctness, i.e., in all protocols there are (tolerated) adversaries for which a single additional passive corruption is sufficient to break correctness. This is in contrast to both the perfect and the computational setting, where such an influence cannot be observed. Apparently, this effect arises from the use of information-theoretic signatures, which are part of most (if not all) statistical protocols.