### Homomorphic Secret Sharing for Low Degree Polynomials

Russell W. F. Lai, Giulio Malavolta, and Dominique Schröder

##### 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.

Available format(s)
Publication info
Keywords
secret sharing
Contact author(s)
russell lai @ cs fau de
History
Short URL
https://ia.cr/2018/1065

CC BY

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},
note = {\url{https://eprint.iacr.org/2018/1065}},
url = {https://eprint.iacr.org/2018/1065}
}

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