As more of a study in multidimensional reflections I devised and built the software for an encryption system that obfuscates a message through essentially multidimensional billiards.
The process works like this:
I define two boundaries, a large outer hypercube within which is a smaller hypercube. Bounded within the large hypercube and containing the smaller hypercube is what I like to visualize as a multifaceted multidimensional crystal made up of randomly tilted hyperplanes tangent to the vertices of the interior hypercube.
The method of encryption is that you select a point on the outer hypercube that corresponds to the plaintext value you are encrypting. You then select a point within the interior hypercube, this is the encryption key. You then follow the path of the vector extended from the plaintext to the key and continue to reflect it off of the crystal walls until you reach a predefined reflection count after which you let the reflection escape the crystal and strike the outer bounding hypercube. The point and vector that strikes on the outer hypercube is the cyphertext.
If you have the same crystal you can reverse this process by firing the cyphertext back through the crystal to return to the plaintext.
So in summary, the plaintext is mapped to a point on the “surface” of a hyperdimensional container and a laser is shot from that point into a random location within a bounded multidimensional crystal and after reflecting within the crystal a number of times the light emerges striking the hyperdimensional container once again, illuminating the cyphertext out. I can’t speak to the efficacy of this method, but it was entertaining to build and there is something sexy about the idea of firing lasers into multidimensional crystals. I considered a number of variations on this theme but this is the essence of what I studied and built.
