  The purpose of the paper is to give new key agreement protocols (a
multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a
generalization of the Diffie-Hellman protocol from abelian to solvable groups)
and a new homomorphic public-key cryptosystem. They rely on difficulty of the
conjugacy and membership problems for subgroups of a given group. To support
these and other known cryptographic schemes we present a general technique to
produce a family of instances being matrix groups (over finite commutative
rings) which play a role for these schemes similar to the groups $Z\_n^*$ in
the existing cryptographic constructions like RSA or discrete logarithm.
