Topology-Hiding Computation Beyond Semi-Honest Adversaries
Rio LaVigne, Chen-Da Liu Zhang, Ueli Maurer, Tal Moran, Marta Mularczyk, and Daniel Tschudi
Topology-hiding communication protocols allow a set of parties, connected by an incomplete network with unknown communication graph, where each party only knows its neighbors, to construct a complete communication network such that the network topology remains hidden even from a powerful adversary who can corrupt parties. This communication network can then be used to perform arbitrary tasks, for example secure multi-party computation, in a topology-hiding manner.
Previously proposed protocols could only tolerate passive corruption. This paper proposes protocols that can also tolerate fail-corruption (i.e., the adversary can crash any party at any point in time) and so-called semi-malicious corruption (i.e., the adversary can control a corrupted party's randomness), without leaking more than an arbitrarily small fraction of a bit of information about the topology. A small-leakage protocol was recently proposed by Ball et al. [Eurocrypt'18], but only under the unrealistic set-up assumption that each party has a trusted hardware module containing secret correlated pre-set keys, and with the further two restrictions that only passively corrupted parties can be crashed by the adversary, and semi-malicious corruption is not tolerated. Since leaking a small amount of information is unavoidable, as is the need to abort the protocol in case of failures, our protocols seem to achieve the best possible goal in a model with fail-corruption.
Further contributions of the paper are applications of the protocol to obtain secure MPC protocols, which requires a way to bound the aggregated leakage when multiple small-leakage protocols are executed in parallel or sequentially. Moreover, while previous protocols are based on the DDH assumption, a new so-called PKCR public-key encryption scheme based on the LWE assumption is proposed, allowing to base topology-hiding computation on LWE. Furthermore, a protocol using fully-homomorphic encryption achieving very low round complexity is proposed.
BibTeX Citation
@inproceedings{LLMMMT18,
author = {Rio LaVigne and Chen-Da Liu Zhang and Ueli Maurer and Tal Moran and Marta Mularczyk and Daniel Tschudi},
title = {Topology-Hiding Computation Beyond Semi-Honest Adversaries},
booktitle = {Theory of Cryptography --- TCC},
pages = 3--35,
series = {LNCS},
volume = 11240,
year = 2018,
month = 11,
organization = {Springer},
publisher = {Springer International Publishing},
}