Distributed Key Generation for SM2 and Its Application to Threshold Encryption

Distributed key generation (DKG) is a crucial tool to achieve decentralized cryptographic functions such as distributed signatures and generating random beacon. Although numerous DKG protocols have been proposed, most of them only support the key generation of group elements rather than field elements, which is incompatible with the Chinese cryptography standard SM2 algorithms. In this paper, we first propose a distributed key generation protocol for SM2 algorithms. This protocol allows for the key generation of field element shares and eliminates the costly complaint rounds that greatly dominate communication cost in DKG. Further, as a somewhat direct application, we apply the keys generated from the DKG protocol for SM2 to design a threshold SM2 encryption scheme. Unlike previous threshold SM2 encryption schemes, our scheme does not require any trusted authority to share the key in advance and is proved secure under the malicious adversary model.