A one-restricted key agreement scheme is a method by which initially a trus
ted authority distributes private individual pieces of information to a set
of users. Later, each member of any group of users of a given size, referr
ed to as a conference, can compute a common key by exchanging messages over
a broadcast channel all users have access to. Such schemes can be used to
establish only one common key. In this paper we analyse tau-restricted key
agreement schemes. Such schemes allow the computation of up to tau common k
eys for tau distinct conferences. For certain values of the parameters the
scheme that we propose distributes less information than the trivial one ob
tained by considering tau copies of a one-restricted scheme.