Secure Distributed Key Generation for Discrete-Log Based Cryptosystems

Abstract

Distributed key generation is a main component of threshold cryptosystems and distributed cryptographic computing in general. Solutions to the distributed generation of private keys for discrete-log based cryptosystems have been known for several years and used in a variety of protocols and in many research papers. However, these solutions fail to provide the full security required and claimed by these works. We show how an active attacker controlling a small number of parties can bias the values of the generated keys, thus violating basic correctness and secrecy requirements of a key generation protocol. In particular, our attacks point out to the places where the proofs of security fail.Based on these findings we designed a distributed key generation protocol which we present here together with a rigorous proof of security. Our solution, that achieves optimal resiliency, can be used as a drop-in replacement for key generation modules as well as other components of threshold or proactive discrete-log based cryptosystems.KeywordsThreshold CryptographyDistributed Key GenerationVSSDiscrete Logarithm