Pasta: A Case for Hybrid Homomorphic Encryption

Christoph Dobraunig; Lorenzo Grassi; Lukas Helminger; Christian Rechberger; Markus Schofnegger; Roman Walch

Paper 2021/731

Pasta: A Case for Hybrid Homomorphic Encryption

Christoph Dobraunig, Lamarr Security Research, Graz, Austria

Lorenzo Grassi, Digital Security Group, Radboud University, Nijmegen

Lukas Helminger, Graz University of Technology / Know-Center GmbH, Graz, Austria

Christian Rechberger, Graz University of Technology, Graz, Austria

Markus Schofnegger, Graz University of Technology, Graz, Austria

Roman Walch, Graz University of Technology / Know-Center GmbH, Graz, Austria

Abstract

The idea of hybrid homomorphic encryption (HHE) is to drastically reduce bandwidth requirements when using homomorphic encryption (HE) at the cost of more expensive computations in the encrypted domain. To this end, various dedicated schemes for symmetric encryption have already been proposed. However, it is still unclear if those ideas are already practically useful, because (1) no cost-benefit analysis was done for use cases and (2) very few implementations are publicly available. We address this situation in several ways. We build an open-source benchmarking framework involving several use cases covering three popular libraries. Using this framework, we explore properties of the respective HHE proposals. It turns out that even medium-sized use cases are infeasible, especially when involving integer arithmetic. Next, we propose Pasta, a cipher thoroughly optimized for integer HHE use cases. Pasta is designed to minimize the multiplicative depth, while also leveraging the structure of two state-of-the-art integer HE schemes (BFV and BGV) to minimize the homomorphic evaluation latency. Using our new benchmarking environment, we extensively evaluate Pasta in SEAL and HElib and compare its properties to 8 existing ciphers in two use cases. Our evaluations show that Pasta outperforms its competitors for HHE both in terms of homomorphic evaluation time and noise consumption, showing its efficiency for applications in real-world HE use cases. Concretely, Pasta outperforms Agrasta by a factor of up to 82, Masta by a factor of up to 6 and Hera up to a factor of 11 when applied to the two use cases.

Note: The accompanying open-source benchmarking framework can be found at https://github.com/IAIK/hybrid-HE-framework.git

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in TCHES 2023
Keywords: homomorphic encryption hybrid homomorphic encryption Pasta SEAL HElib TFHE
Contact author(s): roman walch @ iaik tugraz at
History: 2023-04-06: revised; 2021-06-03: received; See all versions
Short URL: https://ia.cr/2021/731
License: CC BY

BibTeX

@misc{cryptoeprint:2021/731,
      author = {Christoph Dobraunig and Lorenzo Grassi and Lukas Helminger and Christian Rechberger and Markus Schofnegger and Roman Walch},
      title = {Pasta: A Case for Hybrid Homomorphic Encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/731},
      year = {2021},
      url = {https://eprint.iacr.org/2021/731}
}