Encrypting Pictures Using Chaotic Cellular Automata

It’s been more than ten years now since the idea emerged of using chaos to encrypt messages.

The approach is straightforward. Start with a message, superimpose it on a chaotic signal and send. If the chaos is carefully chosen, this signal can seem random and so look like background noise. To reveal the original message, the receiver must be in possession of the same chaotic signal and simply needs to subtract this from the encrypted message. Voila!

Today, Marina Jeaneth Machicao and a few pals at the University of San Paul in Brazil reveal a straightforward way of extending this method to images.

Their idea is to use a cellular automaton to generate a pseudorandom signal. A cellular automaton is a grid-like array in which each cell can be either black or white at any instant. In the next time step, however, each square changes according to a predetermined rule and the colour of the squares around it.

The trick, of course, is to find a rule that generates a pseudorandom output so that the resulting grid looks like noise.

These guys examine a number of automata to see which generates the most random output. They measure the quality of randomness after 20 million iterations using standard statistical tests known as ENT and DIEHARD. They settle on one called Fredkin B1357/S02468, which gives consistently random results.

One crucial point is that the output of this automata is precisely determined by its starting state. Use a different pattern of cells and you end up with an entirely different output.

That’s important because they say this starting state can act as a password. That means the automata can be freely distributed so that anyone can use it but only a person with the password can decrypt any given message.

So here’s how it works. Start by entering the password to produce a starting pattern of cells in the cellular automaton. Then run through 20 million iterations to generate a pseudorandom output. Superimpose this on the picture you want to encrypt and then send it.

A receiver with the correct password can view the image by carrying out the procedure in reverse.

That’s an interesting approach but it raises a number of important questions. The most obvious of these is how secure such a system would be.

The problem is this. Although the output looks random, it is generated by an entirely deterministic process. That’s a potential weakness that an eavesdropper would hope to exploit. Indeed cryptographers have found all kinds of loopholes in similar kinds of pseudorandom generators.

However, others have shown the cellular automata can generate outputs that are essentially indistinguishable from natural randomness. Indeed, Stephen Wolfram, one of the pioneers in this area, thinks the universe gets its randomness from cellular automaton-like processes. The random number generator in Wolfram’s Mathematica software uses exactly this approach.

It may be that Machicao and co will be able to prove some kind of computational security—that an encrypted message would take a significant amount of computing power to crack. So these kinds of messages would be useful for short term secrecy.

But if not, then it would be a brave cryptographer who entrusted secrets to this method.

Ref: arxiv.org/abs/1112.6326: Chaotic Encryption Method Based on Life-Like Cellular Automata