# Information Security and Cryptography Research Group

## Collusion-Preserving Computation

### Joël Alwen, Jonathan Katz, Ueli Maurer, and Vassilis Zikas

Advances in Cryptology — CRYPTO 2012, Lecture Notes in Computer Science, Springer-Verlag, vol. 7417, pp. 124-143, Aug 2012.

In collusion-free protocols, subliminal communication is impossible and parties are thus unable to communicate “any information beyond what the protocol allows”. Collusion-free protocols are interesting for several reasons, but have specifically attracted attention because they can be used to reduce trust in game-theoretic mechanisms. Collusion-free protocols are impossible to achieve (in general) when all parties are connected by point-to-point channels, but exist under certain physical assumptions (Lepinksi et al., STOC 2005) or in specific network topologies (Alwen et al., Crypto 2008).

We provide a “clean-slate” definition of the stronger notion of collusion preservation. Our goals in revisiting the definition are:

– To give a definition with respect to arbitrary communication resources (that includes as special cases the communication models from prior work). We can then, in particular, better understand what types of resources enable collusion-preserving protocols.

– To construct protocols that allow no additional subliminal communication in the case when parties can communicate (a bounded amount of information) via other means. (This property is not implied by collusion-freeness.)

– To provide a definition supporting composition, so that protocols can be designed in a modular fashion using sub-protocols run among subsets of the parties.

In addition to proposing the definition, we explore implications of our model and show a general feasibility result for collusion-preserving computation of arbitrary functionalities.

## BibTeX Citation

@inproceedings{AKMZ12,
author       = {Joël Alwen and Jonathan Katz and Ueli Maurer and Vassilis Zikas},
title        = {Collusion-Preserving Computation},
editor       = {Reihaneh Safavi-Naini and Ran Canetti},
booktitle    = {Advances in Cryptology --- CRYPTO 2012},
pages        = {124-143},
series       = {Lecture Notes in Computer Science},
volume       = {7417},
year         = {2012},
month        = {8},
publisher    = {Springer-Verlag},
}