Paper 2024/032

Verifiable FHE via Lattice-based SNARKs

Shahla Atapoor, COSIC, KU Leuven
Karim Baghery, COSIC, KU Leuven
Hilder V. L. Pereira, Universidade Estadual de Campinas
Jannik Spiessens, COSIC, KU Leuven
Abstract

Fully Homomorphic Encryption (FHE) is a prevalent cryptographic primitive that allows for computation on encrypted data. In various cryptographic protocols, this enables outsourcing computation to a third party while retaining the privacy of the inputs to the computation. However, these schemes make an honest-but-curious assumption about the adversary. Previous work has tried to remove this assumption by combining FHE with Verifiable Computation (VC). Recent work has increased the flexibility of this approach by introducing integrity checks for homomorphic computations over rings. However, efficient FHE for circuits of large multiplicative depth also requires non-ring computations called maintenance operations, i.e. modswitching and keyswitching, which cannot be efficiently verified by existing constructions. We propose the first efficiently verifiable FHE scheme that allows for arbitrary depth homomorphic circuits by utilizing the double-CRT representation in which FHE schemes are typically computed, and using lattice-based SNARKs to prove components of this computation separately, including the maintenance operations. Therefore, our construction can theoretically handle bootstrapping operations. We also present the first implementation of a verifiable computation on encrypted data for a computation that contains multiple ciphertext-ciphertext multiplications. Concretely, we verify the homomorphic computation of an approximate neural network containing three layers and more than 100 ciphertexts in less than 1 second while maintaining reasonable prover costs.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
A minor revision of an IACR publication in CIC 2024
DOI
10.62056/a6ksdkp10
Keywords
Fully-Homomorphic EncryptionVerifiable FHELattice-based SNARKsComputation on Encrypted Data
Contact author(s)
shahla atapoor @ esat kuleuven be
baghery karim @ gmail com
hilder @ unicamp br
jannik spiessens @ esat kuleuven be
History
2024-04-30: revised
2024-01-08: received
See all versions
Short URL
https://ia.cr/2024/032
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/032,
      author = {Shahla Atapoor and Karim Baghery and Hilder V. L. Pereira and Jannik Spiessens},
      title = {Verifiable {FHE} via Lattice-based {SNARKs}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/032},
      year = {2024},
      doi = {10.62056/a6ksdkp10},
      url = {https://eprint.iacr.org/2024/032}
}
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