An Improved Threshold Homomorphic Cryptosystem Based on Class Groups

Lennart Braun; Guilhem Castagnos; Ivan Damgård; Fabien Laguillaumie; Kelsey Melissaris; Claudio Orlandi; Ida Tucker

Paper 2024/717

An Improved Threshold Homomorphic Cryptosystem Based on Class Groups

Lennart Braun

, Aarhus University

Guilhem Castagnos, University of Bordeaux

Ivan Damgård

, Aarhus University

Fabien Laguillaumie

, University of Montpellier

Kelsey Melissaris

, Aarhus University

Claudio Orlandi

, Aarhus University

Ida Tucker

, PQShield

Abstract

We present distributed key generation and decryption protocols for an additively homomorphic cryptosystem based on class groups, improving on a similar system proposed by Braun, Damgård, and Orlandi at CRYPTO '23. Our key generation is similarly constant round but achieves lower communication complexity than the previous work. This improvement is in part the result of relaxing the reconstruction property required of the underlying integer verifiable secret sharing scheme. This eliminates the reliance on potentially costly proofs of knowledge in unknown order groups. We present a new method to batch zero-knowledge proofs in unknown order groups which strengthens these improvements. We also present a protocol which is proven secure against adaptive adversaries in the single inconsistent player (SIP) model. Our protocols are secure in the universal composability (UC) framework and provide guaranteed output delivery. We demonstrate the relative efficiency of our techniques by presenting the running times and communication costs associated with our implementation of the statically secure protocol and provide a direct comparison with alternate state of the art constructions.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. SCN 2024
DOI: 10.1007/978-3-031-71073-5_2
Keywords: threshold encryption class groups
Contact author(s): braun @ cs au dk
guilhem castagnos @ math u-bordeaux fr
ivan @ cs au dk
fabien laguillaumie @ lirmm fr
kelsey @ cs au dk
orlandi @ cs au dk
ida tucker91 @ pqshield com
History: 2024-10-28: last of 2 revisions; 2024-05-09: received; See all versions
Short URL: https://ia.cr/2024/717
License: CC BY

BibTeX

@misc{cryptoeprint:2024/717,
      author = {Lennart Braun and Guilhem Castagnos and Ivan Damgård and Fabien Laguillaumie and Kelsey Melissaris and Claudio Orlandi and Ida Tucker},
      title = {An Improved Threshold Homomorphic Cryptosystem Based on Class Groups},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/717},
      year = {2024},
      doi = {10.1007/978-3-031-71073-5_2},
      url = {https://eprint.iacr.org/2024/717}
}