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Title:
Scooby: Improved Multi-Party Homomorphic Secret Sharing Based on FHE
Authors: Ilaria Chillotti, Emmanuela Orsini, Peter Scholl, Nigel Paul Smart, and Barry Van Leeuwen
Abstract:We present new constructions of multi-party homomorphic secret sharing (HSS) based on a new primitive that we call homomorphic encryption with decryption to shares (HEDS). Our first construction, which we call Scooby, is based on many popular fully homomorphic encryption (FHE) schemes with a linear decryption property. Scooby achieves an n-party HSS for general circuits with complexity O(|F| + \log n), as opposed to O(n^2 \cdot |F|) for the prior best construction based on multi-key FHE. Scooby can be based on (ring)-LWE with a super-polynomial modulus-to-noise ratio. In our second construction, Scrappy, assuming any generic FHE plus HSS for NC1-circuits, we obtain a HEDS scheme which does not require a super-polynomial modulus. While these schemes all require FHE, in another instantiation, Shaggy, we show how in some cases it is possible to obtain multi-party HSS without FHE, for a small number of parties and constant-degree polynomials. Finally, we show that our Scooby scheme can be adapted to use multi-key fully homomorphic encryption, giving more efficient spooky encryption and setup-free HSS. This latter scheme, Casper, if concretely instantiated with a B/FV-style multi-key FHE scheme, for functions F which do not require bootstrapping, gives an HSS complexity of O(n \cdot |F| + n^2 \cdot \log n).
ePrint: https://eprint.iacr.org/2022/862
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