### A Zero-One Law for Secure Multi-Party Computation with Ternary Outputs (full version)

Gunnar Kreitz

##### Abstract

There are protocols to privately evaluate any function in the honest-but-curious setting assuming that the honest nodes are in majority. For some specific functions, protocols are known which remain secure even without an honest majority. The seminal work by Chor and Kushilevitz [CK91] gave a complete characterization of Boolean functions, showing that each Boolean function either requires an honest majority, or is such that it can be privately evaluated regardless of the number of colluding nodes. The problem of discovering the threshold for secure evaluation of more general functions remains an open problem. Towards a resolution, we provide a complete characterization of the security threshold for functions with three different outputs. Surprisingly, the zero-one law for Boolean functions extends to Z_3, meaning that each function with range Z_3 either requires honest majority or tolerates up to $n$ colluding nodes.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. This is the full version of a paper accepted for publication at TCC 2011
Contact author(s)
gkreitz @ kth se
History
Short URL
https://ia.cr/2011/002

CC BY

BibTeX

@misc{cryptoeprint:2011/002,
author = {Gunnar Kreitz},
title = {A Zero-One Law for Secure Multi-Party Computation with Ternary Outputs (full version)},
howpublished = {Cryptology ePrint Archive, Paper 2011/002},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/002}},
url = {https://eprint.iacr.org/2011/002}
}

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