I am looking for a scheme for dynamic threshold public-key encryption, which includes dynamic distributed key generation.
Namely, the number of parties that participate in DKG is bounded, but unknown. The list of public keys of each party is known, but we don’t know who will participate and who won't. So the number can be in the range $1,\dots,N$ (where $N$ is the total number of parties).
We want the protocol to be three rounds, one message per round:
Round 1. $m$ of $n$ parties participate in DKG, where $n$ is the known maximum number of participants, and $m$ is the actual number of participants, unknown at the time a party sends a message. The public and (shared) secret keys are the result of all the submitted messages.
Round 2. All $n$ voters (not only those that participated in the first round) can submit the encrypted message.
Round 3. Some subset of parties that participated in round 1, (say 0.6 of $m$), can decrypt the homomorphic sum of the encrypted messages.
We don’t know how many people show up in round 1, thus we want it to be dynamic. Then we don’t know how many people show up in round 3; but, we assume that at least some subset (say 0.6 of $m$) will. That’s why we need the threshold property of the decryption scheme.
