Key agreements based on function composition

Abstract

Two protocols are presented that accomplish the same goal as the original Diffie-Hellman protocol, namely, to establish a common secret key using only public messages. They are based on n-fold composition of some suitable elementary function. The first protocol is shown to fail always when the elementary function is chosen to be linear. This does not preclude its use for a suitable nonlinear elementary function. The second protocol is shown to be equivalent to the Diffie-Hellman protocol when the elementary function is chosen to be linear. Some examples are given to illustrate the use of both protocols. It is still an open problem whether the presented approach allows for an improvement in terms of speed and/or security over the original DH-protocol.