### Secure Multiparty Computation from Threshold Encryption based on Class Groups

##### Abstract

We construct the first actively-secure threshold version of the cryptosystem based on class groups from the so-called CL framework (Castagnos and Laguillaumie, 2015). We show how to use our threshold scheme to achieve general universally composable (UC) secure multiparty computation (MPC) with only transparent set-up, i.e., with no secret trapdoors involved. On the way to our goal, we design new zero-knowledge (ZK) protocols with constant communication complexity for proving multiplicative relations between encrypted values. This allows us to use the ZK proofs to achieve MPC with active security with only a constant factor overhead. Finally, we adapt our protocol for the so called "You-Only-Speak-Once" (YOSO) setting, which is a very promising recent approach for performing MPC over a blockchain. This is possible because our key generation protocol is simpler and requires significantly less interaction compared to previous approaches: in particular, our new key generation protocol allows the adversary to bias the public key, but we show that this has no impact on the security of the resulting cryptosystem.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint.
Keywords
mpczero-knowledgethreshold encryptionclass groups
Contact author(s)
braun @ cs au dk
ivan @ cs au dk
orlandi @ cs au dk
History
2023-02-23: revised
See all versions
Short URL
https://ia.cr/2022/1437

CC BY

BibTeX

@misc{cryptoeprint:2022/1437,
author = {Lennart Braun and Ivan Damgård and Claudio Orlandi},
title = {Secure Multiparty Computation from Threshold Encryption based on Class Groups},
howpublished = {Cryptology ePrint Archive, Paper 2022/1437},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1437}},
url = {https://eprint.iacr.org/2022/1437}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.