Editing Secure communications without key exchange (section)

==Project description==
All existing cryptographic schemes involve, one way or another, the sharing or exchange of a cryptographic key. An open question is: can secure transmission be achieved without any form of key exchange? No one has ever achieved this, so this is an exciting project.

An analogy is to suppose Bob wishes to transmit a written message to Alice; Bob hides the message in a box that he securely padlocks before sending it to Alice. After receiving the box, Alice adds a second padlock and sends the box back to Bob. Then Bob unlocks his padlock, leaving the box still secured by Alice's lock, and sends it back to Alice who can then remove her lock, open the box and read the message. 

Notice that neither Alice nor Bob shared their keys.  They both kept them secret.  This is the aim. This is called the KS-cipher or Kish-Sethuraman cipher. But nobody has ever figured out a way to do this mathematically. Once a mathematical description can be made, we can then translate that into real electrical signals.

Notice in the mechanical example, the position of the two padlocks commutes.  Mathematically, we know that a simple 2D rotations and XOR operations also commute and so could be candidates.  However, you can trivially show that an eavesdropper can crack these schemes, and so they do not work.

So what we want you to do is to extend the idea of data being encoded in a 3D space (instead of 2D) and then be rotated randomly to hide the data. Does that work?  Then try 4D and so on.  It's possible 6D might work but we are not sure yet.

As part of the project we'd like you create animations to help understand rotations in higher dimensions, such as shown here:
http://eusebeia.dyndns.org/4d/vis/10-rot-1

An extension of this project that you should work with in parallel is to use internet round-trip times as a source of randomness for an alternative implementation. Bob and Alice repeatedly send packets back and forth. There will be random timing variations. But there will be a degree of correlation between Alice and Bob, that is not shared by Eve. The idea is to investigate an error correction protocol that can improve the fidelity of the key received by Bob, but where any scheme adopted by Eve simply increases her error. Bob and Alice have the advantage of multiple resends until the key is finally distilled. Although this process is slow, we are not concerned by speed for key distribution. The important thing is to establish proof-of-concept at any speed.  We shall call this the RTKS-cipher, or the random time Kish-Sethuraman cipher.