## Cryptology ePrint Archive: Report 2018/1065

Homomorphic Secret Sharing for Low Degree Polynomials

Russell W. F. Lai and 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.

Category / Keywords: secret sharing

Original Publication (in the same form): IACR-ASIACRYPT-2018

Date: received 2 Nov 2018

Contact author: russell lai at cs fau de

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2018/1065

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