Wednesday, February 08, 2006

Foolproof Cryptography based on Navier-Stokes?

Here's the outline of an encryption algorithm that has no hope of being cracked.

Suppose you got a tank of water and some dye. When the water's all steady and stagnant, introduce your message in the water - scribble it in english using GRE words using a dye in the water. And then, shake the tank. Remember how you shake the tank, of course. Shake it like crazy. Make it turbulent. Let the dye mix up.

And at a precise instant, note the concentration of the dye at every point in space, the pressure at every point in space, the velocity at every point in space - and send that information as your "encoded" message.

In the "cipher", describe the geometry too ... essentially, describle all the final conditions and the problem. Cracking the code would essentially mean solving (DNSing) the time - reversed N/S ( the same as the original equation, with a negative viscosity instead!That makes it unphysical, for this spontaneously destroys entropy in an adiabatic system).

Basically the only people who will be able to "decipher" this information will be people who have access to an excellent DNS code and a Deep Thought (of the H2G2 fame) calibre computer. Such encryption shall lead to a DNS race between governments of the world - in the spirit of the current Nuclear Arms race. Larger chunks of national budgets will be awarded to DNS.

In the unlikely evemt that these efforts should culminate in a "crack", fret not. Use GRE words in the original message; it shall stay un-understood, though deciphered!

2 comments:

Akhilesh said...

A rather intriguing line of reasoning has been thrown by Dr. G, my Turbulence instructor this semester, and an internationally acclaimed expert on the subject.

He claims that viscosity creates an "amenesia" within turbulence. A reverese DNS would just "blow" up, and not reach any result.

So, I wonder, and I do so out loud, is that information (the thingy written by the dye) lost forever? Or is there a way to solve the reverse navier stokes, in principle?

Akhilesh said...

And now I know.

Diffusion loses information - in the sense that the information "magnitude" dies with time.

And finally, it will be lost unto noise.

Note that a purely hypothetical situation with infinite signal clarity would still preserve the information.

But in the real world, nope. Can't do reverse N/S. Can't even do reverse Fick or Reverse Heat.

The second law wins again.