  We present three voting protocols with unconditional privacy and
information-theoretic correctness, without assuming any bound on the number of
corrupt voters or voting authorities. All protocols have polynomial complexity
and require private channels and a simultaneous broadcast channel. Our first
protocol is a basic voting scheme which allows voters to interact in order to
compute the tally. Privacy of the ballot is unconditional, but any voter can
cause the protocol to fail, in which case information about the tally may
nevertheless transpire. Our second protocol introduces voting authorities which
allow the implementation of the first protocol, while reducing the interaction
and limiting it to be only between voters and authorities and among the
authorities themselves. The simultaneous broadcast is also limited to the
authorities. As long as a single authority is honest, the privacy is
unconditional, however, a single corrupt authority or a single corrupt voter
can cause the protocol to fail. Our final protocol provides a safeguard against
corrupt voters by enabling a verification technique to allow the authorities to
revoke incorrect votes. We also discuss the implementation of a simultaneous
broadcast channel with the use of temporary computational assumptions, yielding
versions of our protocols achieving everlasting security.
