Paper 2022/780

An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption

Christian Mouchet, École Polytechnique Fédérale de Lausanne
Elliott Bertrand, Effixis SA.
Jean-Pierre Hubaux, École Polytechnique Fédérale de Lausanne

We propose and implement a multiparty homomorphic encryption (MHE) scheme with a $t$-out-of-$N$-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 (RLWE) 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 $N$-out-of-$N$-threshold access structure of the original scheme into a $t$-out-of-$N$-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.

Available format(s)
Cryptographic protocols
Publication info
Published by the IACR in JOC 2023
Multiparty homomorphic EncryptionThreshold access-structure
Contact author(s)
christian mouchet @ epfl ch
2023-03-22: revised
2022-06-17: received
See all versions
Short URL
Creative Commons Attribution


      author = {Christian Mouchet and Elliott Bertrand and Jean-Pierre Hubaux},
      title = {An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2022/780},
      year = {2022},
      doi = {10.1007/s00145-023-09452-8},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.