Public Key Cryptography: A Dynamical Systems Perspective

The well-known Diffie-Hellman Key Exchange Protocol and the RSA cryptosystem are investigated from a different viewpoint than usual. Using the recently defined concept of a discretely chaotic dynamical system, we show that the security of theses cryptosystems, when interpreted as dynamical systems, relies on the discrete chaoticity of their orbits. Algebraic requirements on the parameters are translated into statements about the period lengths of the orbits.