Distributed key generation is a main component of threshold cryptosystems. It allows \(n\) participants to take part and generate a pair of public key and secret key required for the threshold cryptosystem without having to rely on a trusted party (dealer). Each participant in additional receive a partial secret key and a partial public key. While the public key and partial public keys is seen by everyone, the private key is maintained as a (virtual) secret of a \(t,n\) secret sharing scheme, where each share is the partial secret key of a participant [GJKR99]. No adversary with limited computational power can learn any information of the secret key unless it control the required amount of participants.