The double-padlock problem: is secure classical information transmission possible without key exchange?

The idealized Kish-Sethuraman (KS) cipher is known to offer perfect information theoretical security with classical physical means. However, realization of the protocol is hitherto an open problem, as the required mathematical operators have not been identified in the previous literature. A mechanical analogy of this protocol can be seen as sending a message in a box using two padlocks; one locked by the Sender and the other locked by the Receiver, so that theoretically the message remains secure at all times. We seek a mathematical representation of this process, considering that it would be very unusual if there was a physical process with no mathematical description and indeed we find a solution within a three and four dimensional Clifford algebra. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a classical physical realization having benefits in increased security with reduced complexity.