International Association
for Cryptologic Research

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 then show how to use our threshold scheme to achieve general secure multiparty computation (MPC) with only transparent set-up, i.e., with no secret trapdoors involved.

To achieve this, we also design a new zero-knowledge protocol for proving multiplicative relations between encrypted values. As a result, the zero-knowledge proofs needed to get active security add only a constant factor overhead. Finally, we explain how to 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.