  Several of the basic cryptographic constructs have associated algebraic
structures. Formal models proposed by Dolev and Yao to study the
(unconditional) security of public key protocols form a group. The security of
some types of protocols can be neatly formulated in this algebraic setting. We
investigate classes of two-party protocols. We then consider extension of the
formal algebraic framework to private-key protocols. We also discuss concrete
realization of the formal models. In this case, we propose a definition in
terms of pseudo-free groups.
