  Each member of an $n$-person team has a secret, say a password. The $k$ out
of $n$ gruppen secret sharing requires that any group of $k$ members should be
able to recover the secrets of the other $n-k$ members, while any group of
$k-1$ or less members should have no information on the secret of other team
member even if other secrets leak out. We prove that when all secrets are
chosen independently and have size $s$, then each team member must have a share
of size at least $(n-k)s$, and we present a scheme which achieves this bound
when $s$ is large enough. This result shows a significant saving over $n$
independent applications of Shamir's $k$ out of $n-1$ threshold schemes which
assigns shares of size $(n-1)s$ to each team member independently of $k$.
  We also show how to set up such a scheme without any trusted dealer, and how
the secrets can be recovered, possibly multiple times, without leaking
information. We also discuss how our scheme fits to the much-investigated
multiple secret sharing methods.
