  Rabi and Sherman [RS97] presented novel digital signature and unauthenticated
secret-key agreement protocols, developed by themselves and by Rivest and
Sherman. These protocols use ``strong,'' total, commutative (in the case of
multi-party secret-key agreement), associative one-way functions as their key
building blocks. Though Rabi and Sherman did prove that associative one-way
functions exist if $\p \neq \np$, they left as an open question whether any
natural complexity-theoretic assumption is sufficient to ensure the existence
of ``strong,'' total, commutative, associative one-way functions. In this
paper, we prove that if $\p \neq \np$ then ``strong,'' total, commutative,
associative one-way functions exist.
