# Multi-party Computation with Hybrid Security

## Matthias Fitzi and Thomas Holenstein and J{ü}rg Wullschleger

```
```It is well-known that n players connected only by pairwise secure channels can
achieve multi-party computation secure against an active adversary if and only
if t < n/2 of the players are corrupted with respect to computational security,
or t < n/3 of the players are corrupted with respect to unconditional security.

In this paper we examine to what extent it is possible to achieve conditional
(such as computational) security based on a given intractability assumption
with respect to some number T of corrupted players while simultaneously
achieving unconditional security with respect to a smaller threshold t <= T.
In such a model, given that the intractability assumption cannot be broken by
the adversary, the protocol is secure against T corrupted players. But even
if it is able to break it, the adversary is still required to corrupt more
than t players in order to make the protocol fail.

For an even more general model involving three different thresholds tp, ts, and
T, we give tight bounds for the achievability of multi-party computation.
As one particular implication of this general result, we show that multi-party
computation computationally secure against T < n/2 actively corrupted players
(which is optimal) can additionally guarantee unconditional security against
t <= n/4 actively corrupted players ``for free''.