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

TL;DR

This paper explores the theoretical possibility of secure classical information transmission without key exchange by mathematically modeling the Kish-Sethuraman cipher using four-dimensional Clifford algebra, aiming for practical physical realization.

Contribution

It provides a mathematical representation of the KS cipher using Clifford algebra, advancing the understanding of secure classical communication without key exchange.

Findings

Mathematical description of the KS cipher achieved

Potential for physical realization with increased security

Reduction in complexity of secure communication protocols

Abstract

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 and indeed we find a solution within a four dimensional Clifford algebra. 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.