  To any nilpotent group of class n, one can associate a non-interactive key
exchange protocol between n+1 users. The multilinear commutator maps associated
to nilpotent groups play a key role in this protocol. In the present paper, we
analyze the security of this key exchange when applied to finite p-groups, both
in the generic case and for explicit families of groups. We show, moreover, how
infinite pro-p groups can be employed as platforms for any number of users.
