Efficient and succinct zero-knowledge arguments in the CL framework

Multiparty computation (MPC) aims at allowing a set of participants to perform computation together on private inputs. In order to protect the privacy of the users and guarantee the correctness of the computation, MPC relies on several cryptographic tools, among which asymmetric encryption and zero-knowledge proofs. In this talk, we focus on using the CL encryption scheme, a linearly homomorphic encryption scheme based on class groups of imaginary quadratic fields, for MPC. In this context, it is crucial to design short and computationally efficient zero-knowledge protocols, which is particularly challenging, due to the unknown order of the underlying groups for CL. To overcome this difficulty, we define a new notion of soundness, called partial extractability, that allows us to improve the efficiency of CL related zero-knowledge proofs.

(Joint work with Guilhem Castagnos and Fabien Laguillaumie.)