[Resource Topic] 2018/1065: Homomorphic Secret Sharing for Low Degree Polynomials

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Homomorphic Secret Sharing for Low Degree Polynomials

Authors: Russell W. F. Lai, Giulio Malavolta, Dominique Schröder


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.

ePrint: https://eprint.iacr.org/2018/1065

Slides: https://asiacrypt.iacr.org/2018/files/SLIDES/THURSDAY/P512/Malavolta.pdf

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