International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Homomorphic Secret Sharing for Low Degree Polynomials

Russell W. F. Lai
Giulio Malavolta
Dominique Schröder
DOI: 10.1007/978-3-030-03332-3_11
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Presentation: Slides
Conference: ASIACRYPT 2018
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.
  title={Homomorphic Secret Sharing for Low Degree Polynomials},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  author={Russell W. F. Lai and Giulio Malavolta and Dominique Schröder},