The world of cryptography has undergone a quiet revolution in recent years. That’s largely because of the advent of techniques that exploit the laws of quantum mechanics to send messages with perfect privacy. So-called quantum cryptography ensures that an eavesdropper cannot decode a message under guarantee by the laws of physics.
But sometimes perfect privacy isn’t enough. Sometimes the knowledge that a message has been sent is all that an adversary needs. So the question arises of how to hide a message so that an eavesdropper cannot tell whether it has been sent or not.
The discipline, known as steganography or covert communication, is as old as its cryptographic cousin but has received much less attention in recent years. But that changes today thanks to the work of Boulat Bash at the University of Massachusetts in Amherst and a few pals who have worked out how to camouflage messages in a way that is guaranteed mathematically.
And they’ve put their ideas into practice with a proof-of-principle demonstration. “We have built the ﬁrst operational system that provides mathematically proven covert communication over a physical channel,” they say.
The technique is relatively straightforward, relying on a method of communication known as pulse position modulation. This divides each second (or other unit of time) into a number of time bands which each correspond to a symbol. Alice sends a message to Bob by transmitting pulses during bands that correspond to the required symbol, which Bob then looks up in the order he receives them.
There’s an important caveat, of course. This system requires the sender and receiver to agree on the band structure and the symbols they refer to. And this must be done in advance in secret.
This allows Alice and Bob to send encrypted messages (the length of which depend on the length of the information shared in advance).
The question is how to hide this information. And the answer is in plain view. Bash and co assume that the message is sent using photons and that the environment supplies a certain amount of noise against which their signal is camouflaged. For example, they assume that photon detectors are not perfect and so always produce a certain number of dark counts in which they register a photon without receiving one.
Bash and co’s focus is on calculating the number of signaling photons that can be sent in this noisy environment while guaranteeing that an eavesdropper cannot distinguish them from the background. This is possible because the watcher (Willie, as Bash and co call him) does not know when the signaling pulses are sent and always detects additional noisy photons that further confuse matters.
The breakthrough is in showing that the message can always be camouflaged with an arbitrary probability of detection, provided noise is within certain limits. Bash and co show this is true even when Willie collects all the photons that Bob does not receive.
In other words, Alice and Bob can choose the secrecy of their message in advance. And although they can’t choose perfect secrecy, they can get as close as they like to it. So Alice and Bob might choose a lower bit rate for messages for which they want a lower chance of detection.
To prove the viability of their scheme, Bash and co have built and tested a prototype that sends messages via an optical fiber. Alice transmits the pulses and a beam splitter at the other end ensures that Willie collects all the photons that do no travel to Bob.
And the experiment works well. “We demonstrated that provably covert optical communication is practically achievable,” say Bash and co.
That should have some interesting applications. But just who might be interested in such covert communications, Bash and co do not say. Suggestions please in the comments section.
Ref: arxiv.org/abs/1404.7347: Covert Optical Communication