Round optimal distributed key generation of threshold cryptosystem based on discrete logarithm problem

Abstract

We propose a distributed key generation protocol for discrete logarithm problem based threshold cryptosystems by introducing an efficient (publicly) verifiable encryption scheme from any homomorphic encryption with a non-interactive proof of fairness. Previous constructions of the same kind are either only based on a narrow definition of homomorphism or only a unique encryption scheme is considered. Our construction generalizes the scope of such design to a broader range of encryption schemes with efficient constructions of proofs of fairness. Since the protocol is round optimal (one-round) in the distributed fashion, adaptive adversary is not different from a static adversary, thus a simplified protocol design is possible. Our scheme is extremely capable for an environment with already built public key infrastructure. The verifiable encryption with fairness developed here can be used as building blocks of a variety of cryptographical applications like publicly verifiable secret sharing (PVSS), e-voting and auction schemes. © Springer-Verlag Berlin Heidelberg 2003.