Abstract
All shared secret or shared control schemes devised thus far are autocratic in
the sense that they depend in their realization on the exsistance of a single
party-which may be either an individual or a device-that is unconditionally
trusted by all the participants in the scheme [5,6]. The function of this trusted
party is to first choose the secret (piece of information) and then to construct
and distribute in secret to each of the participants the private pieces of
information which are their shares in the shared secret or control scheme. The
private pieces of information are constructed in such a way that any authorized
concurrence (subset) of the participants will jointly have sufficient information
about the secret to reconstruct it while no unauthorized collection of them will
be able to do so. For many applications, though, there is no one who is trusted
by anyone else. In the absence of a trusted party or authority, no one can be
trusted to know the secret and hence-until now-it has appeared to be impossible
to construct and distribute the private pieces of information needed to realize
a shared control scheme. It is worth noting that in commercial and/or international
applications, this situation is more nearly the norm than then exception.