Paper 2018/1065 Original: eprint.iacr.org/2018/1065 ↗
Homomorphic Secret Sharing for Low Degree Polynomials
Abstract
Homomorphic secret sharing (HSS) allows $n$ clients to secret-share data to $m$ servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced computation over private data. In this work, we present the first plain-model homomorphic secret sharing scheme that supports the evaluation of polynomials with degree higher than 2. Our construction relies on any degree-$k$ (multi-key) homomorphic encryption scheme and can evaluate degree-$\left( (k+1)m -1 \right)$ polynomials, for any polynomial number of inputs $n$ and any sub-logarithmic (in the security parameter) number of servers $m$. At the heart of our work is a series of combinatorial arguments on how a polynomial can be split into several low-degree polynomials over the shares of the inputs, which we believe is of independent interest.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2018-11-09: last updated
- 2018-11-09: published
- Short URL
- https://ia.cr/2018/1065
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/1065,
author = {Russell W. F. Lai and Giulio Malavolta and Dominique Schröder},
title = {Homomorphic Secret Sharing for Low Degree Polynomials},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/1065},
year = {2018},
url = {https://eprint.iacr.org/2018/1065}
}