A group theoretic approach to public-key cryptography

A public key cryptosystem is an algorithmic method for securely sending private information over an insecure channel in which the communicating parties have no common key. At the heart of a public-key cryptosystem is a two-party secure computation referred to as a protocol. The first generation of public-key cryptosystems employ protocols whose security is based on the difficulty of solving algorithmic problems associated with finite abelian groups. We discuss a new method for constructing public-key cryptosystems that employ protocols whose security is based on the difficulty of solving systems of equations over non-abelian groups. We illustrate our method using braid groups and their representations. A further application of our approach yields a new class of Diffie-Hellman type protocols.