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

The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. 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. We select Clifford's geometric algebra for this task as it is a natural formalism to handle rotations in spaces of various dimension. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a physical realization having benefits in increased security with reduced complexity.