A key establishment protocol is a protocol whereby a shared secret becomes available to two or more parties, for subsequent cryptographic applications. The paper describes an algebraic key establishment protocol for secret key establishment between two individuals communicating over a public channel. This protocol is based on feasibly computable monoids and the foundation of the method lies in the difficulty of solving equations over algebraic structures. As an example, a group-theoretic implementation of the protocol is given. Here an adversary observing all communications over the public channel can break the scheme and determine the secret key provided that a system of conjugacy equations over the associated group is feasibly solvable.