verify that indeed the parties do follow the protocol. In other words, it is public knowledge whether a party performed correctly or tried to cheat.
Kiayias and Yung [1] presented a self-tallying dispute-free voting scheme with perfect ballot secrecy with security based on the Decisional Diffie-Hellman (DDH) assumption. Later Damgård and Jurik [2] suggested a somewhat similar scheme based on the Decisional Composite Residuosity (DCR) assumption [3]. Both schemes work in the random oracle model and assume an authenticated broadcast channel; in the present paper, we use this model too.
Kiayias and Yung [1, 4, 5] rely on a method they call zero-sharing for achieving maximal privacy. Not only do they build a voting protocol from this, but they also suggest protocols for anonymous vetoing and simultaneous disclosure of secrets.
Our contributions. Our first contribution is a new voting scheme that has the same security properties as [1, 2] but is simpler and more efficient. We base our scheme on the DDH assumption, i.e., ElGamal encryption, but the same ideas can be used in combination with the DCR assumption. The reason for this choice is that it is easy to generate in a distributed manner suitable groups where the DDH assumption is well founded. Distributed generation of a suitable group for the DCR assumption is more complicated [6].
Our second contribution is to construct an anonymous broadcast channel with perfect message secrecy, i.e., no matter which parties are dishonest, they are not able to tell among the honest senders who sent a particular message. This scheme is related to voting in the sense that using this anonymous channel to cast votes gives us a self-tallying voting scheme with perfect ballot secrecy, but it may of course also have many other applications.
1.1 Model
Throughout the paper, we assume all parties have access to an authenticated broadcast channel with memory. We imagine this in the form of a message board that all parties can access. Each party has a special designated area where he, and nobody else, can write. No party can delete any messages from the message board. One way of implementing such a message board would be to have a central server on the Internet handling the messages. We discuss this further in Section 4.
When considering security of the protocols we imagine that there is an active polynomial time adversary $\mathcal{A}$ trying to break them. $\mathcal{A}$ is static, i.e., from the beginning of the protocol it has control over a fixed set of parties.
The parties in the protocol work semi-synchronously; the protocol proceeds in phases and in each phase parties may act in random order. We let the adversary decide when to change to the next phase. Since the protocols we design are intended for use with a small number of participants, we find this to be a reasonable assumption. Should several parties by accident happen to execute their action at the same time anyway, then it is quite easy to recover.