Paper 2016/643
On the Computational Overhead of MPC with Dishonest Majority
Jesper Buus Nielsen and Samuel Ranellucci
Abstract
We consider the situation where a large number $n$ of players want to securely compute a large function $f$ with security against an adaptive, malicious adversary which might corrupt $t < cn$ of the parties for some given $c \in [0,1)$. In other words, only some arbitrarily small constant fraction of the parties are assumed to be honest. For any fixed $c$, we consider the asymptotic complexity as $n$ and the size of $f$ grows. We are in particular interested in the computational overhead, defined as the total computational complexity of all parties divided by the size of $f$. We show that it is possible to achieve polylogarithmic computational overhead for all $c < 1$. Prior to our result it was only known how to get polylogarithmic overhead for $c < \frac{1}{2}$. We therefore significantly extend the area where we can do secure multiparty computation with polylogarithmic overhead. Since we allow that more than half the parties are corrupted, we can only get security with abort, i.e., the adversary might make the protocol abort before all parties learn their outputs. We can, however, for all $c$ make a protocol for which there exists $d > 0$ such that if at most $d n$ parties are actually corrupted in a given execution, then the protocol will not abort. Our result is solely of theoretical interest.
Metadata
 Available format(s)
 Category
 Cryptographic protocols
 Publication info
 Preprint. MINOR revision.
 Keywords
 secure computationMPCthreshold cryptography
 Contact author(s)
 samuel_ran @ hotmail com
 History
 20170428: last of 2 revisions
 20160621: received
 See all versions
 Short URL
 https://ia.cr/2016/643
 License

CC BY
BibTeX
@misc{cryptoeprint:2016/643, author = {Jesper Buus Nielsen and Samuel Ranellucci}, title = {On the Computational Overhead of {MPC} with Dishonest Majority}, howpublished = {Cryptology {ePrint} Archive, Paper 2016/643}, year = {2016}, url = {https://eprint.iacr.org/2016/643} }