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An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption
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| Abstract: | We propose and implement a multiparty homomorphic encryption (MHE) scheme with a $$t$$ t -out-of- $$N$$ N -threshold access-structure that is efficient and does not require a trusted dealer in the common random string model. We construct this scheme from the ring-learning-with-error assumptions and as an extension of the MHE scheme of Mouchet et al. (PETS 21). By means of a specially adapted share re-sharing procedure, this extension can be used to relax the $$N$$ N -out-of- $$N$$ N -threshold access-structure of the original scheme into a $$t$$ t -out-of- $$N$$ N -threshold one. This procedure introduces only a single round of communication during the setup phase, after which any set of at least t parties can compute a t -out-of- t additive sharing of the secret-key with no interaction; this new sharing can be used directly in the scheme of Mouchet et al. We show that, by performing Shamir re-sharing over the MHE ciphertext-space ring with a carefully chosen exceptional set, this reconstruction procedure can be made secure and has negligible overhead. Moreover, it only requires the parties to store a constant-size state after its setup phase. Hence, in addition to fault tolerance, lowering the corruption threshold also yields considerable efficiency benefits, by enabling the distribution of batched secret-key operations among the online parties. We implemented and open-sourced our scheme in the Lattigo library. |
BibTeX
@article{jofc-2023-33068,
title={An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption},
journal={Journal of Cryptology},
publisher={Springer},
volume={36},
doi={10.1007/s00145-023-09452-8},
author={Christian Mouchet and Elliott Bertrand and Jean-Pierre Hubaux},
year=2023
}