How can we use foxes and rabbits help transmit secret messages? No animal cruelty is necessary - a new technique encodes messages using a predator-prey model normally used to predict the changes in animal populations. This advance in steganography could revolutionize the art of secrecy.
Cryptography is the art of disguising messages so they're incomprehensible to anyone but the recipient, while steganography is the art of disguising messages' very existence. One famous example of steganographic communication comes from Greek historian Herodotus, who told the story of a slave whose head was shaved bald and then tattooed with a message. When the slave's hair grew back, nobody suspected the tattoo's existence, allowing him to travel freely to the recipient, shave his head, and reveal the message.
In our information age, steganographers more often conceal information within a digital file. The file may look like an innocent photo, except that the ones and zeroes in the code of certain pixels have been modified. One technique involves taking a digital image and imperceptibly brightening certain pixels - perhaps every tenth, or hundredth, or ninety-third - to hide another image. Similarly, you could have a text message where letters correspond to the amount of the color shift. Although this technique effectively hides secrets from the naked eye, computer programs can pick out the message from the mess by detecting the changed pixel distribution.
But now there's a new steganographic method that can fool computers as well as people. It's described in Physical Review E, and uses predator-prey models to further disguise a hidden message.
In general, a predator-prey model uses mathematical equations to predict how a population of, say, rabbits and foxes will wax and wane over time. We would expect that as the rabbit population increases, they create more prey for the foxes, whose population will increase in response. But as more and more foxes eat the rabbits, the rabbit population declines, decreasing the foxes' food supply and forcing their population to decline as well. Based on common-sense rules like these, predator-prey models use different equations to predict the exact details of this cycle, taking into account the environment, the availability of resources, and the initial populations of each species.
Applying one particular predator-prey model to a set of initial conditions creates a self-organizing system, which mimics the way a real population of foxes and rabbits (or lions and antelope, or anteaters and ants, etc.) would migrate to different regions in order to optimize survival. But it turns out that we can take the algorithm that the model is based on and apply to the pixels of an image. This sets up an evolving pattern, shifting the original image until it becomes incomprehensible.
A Lithuanian research group started crafting a hidden message by generating a random static-filled image containing no information. Next, they brightened certain pixels of the fuzzy blank slate to embed their image. As in traditional digital steganography, this technique left the message mostly, but not entirely, masked by noise in the original image. To conceal the hidden image even more thoroughly, researchers next applied the predator-prey equations to the image over and over again. Because the chosen equations "diffuse" the initial conditions, each application of the equations spread the brightened pixels outwards a little bit more. Because the pixels do not move in a linear way, it is impossible to reverse this diffusion process in order to pull the pixels back into their original formation. Diffusing the pixels of the image hides the message from even a computer program designed to crack this type of code.
Here, the original image that we want to hide is a dot-skeleton map of the globe, but after steganographic transformation, it is lost in a mass of static.
In order to recover the hidden image, the recipients must know two things: the original fuzzy blank image in which the message was embedded, and the predator-prey equations. They apply the predator-prey equations to the blank image, creating diffused patterns similar to the coded one but containing no information. Finally, they subtract their image from the secret message image, to leave a legible, albeit blurred, version of the original.
Although the seemingly random static pattern that hides this communication may look suspicious when attached to an e-mail, even precisely calibrated computer programs would fail to extract any information from it. It may not be as innocent looking as an empty-handed messenger, but it does eliminate that annoying wait for the hair to grow back.