The use of quantum mechanics to encrypt messages may foil eavesdroppers and code-breakers for good
“AT THE speed of light, Hephaestus’s sacred fire/ Blazed from beacon tower to beacon tower.” Thus, according to Aeschylus, spake Clytemnestra, an ancient queen of Mycenae, explaining how she received tidings that her husband Agamemnon was on his way home from the Trojan war. Perhaps Agamemnon would have done better to have turned up unannounced. The news left the queen and her lover just enough time to plot the cuckold’s assassination.
When Agamemnon sent the message, though, he probably worried less about betrayal than interception. Using signal fires or flashes of sunlight reflected from a mirror was (and is) a cheap and simple way to broadcast information. But although such signals were used until the early 20th century to co-ordinate military manoeuvres, they are vulnerable to espionage: a clever onlooker can easily observe the flashes of light and crack the message, even if it is encoded.
It may seem surprising, therefore, that some physicists at Los Alamos National Laboratories in New Mexico believe that they can transmit messages through the open air in complete secrecy, by exploiting the quantum-mechanical properties of light. In June 2001, at the International Conference on Quantum Information, in Rochester, New York, they explained how to build a system that will broadcast uncrackable messages via satellite.
All keyed up
Modern cryptography, such as that employed in a widely used program, Pretty Good Privacy (PGP), relies on the mathematical manipulation of data. To encrypt, or “lock”, a message, the program performs a series of mathematical steps on it, using a number more than a hundred digits long. Only that number’s correct mate, or “key”, is able to undo these steps and unpack the message.
The size of these numbers, and the mathematical formula that links them, make it, in effect, impossible to work out the key by computational brute force. One of today’s keys could not be calculated even if all of today’s computers worked for the lifespan of the universe on the task. Surely that is safety enough?
Perhaps not (that is why the software is called “pretty good” and not “perfect”). Future advances in computing may be enough to overwhelm the defences of PGP and its kind. More prosaically, a thief who stole a key could impersonate its careless owner—and nobody would ever know the difference.
Richard Hughes, the leader of the team at Los Alamos, thinks that using photons (the particles, or “quanta”, of the quantum theory of light) to manufacture and distribute keys would correct these weaknesses. Individual photons possess properties that are governed by one of the basic laws of quantum mechanics, the uncertainty principle. A photon’s polarisation, for example, can be measured against any of three yardsticks: the horizontal axis, the diagonal axis, and the circular axis. However, the more that is known about one of these, the less can be known about the others. In other words, if an exact measurement is taken of a photon’s horizontal polarisation, nothing at all can be known about its polarisation on the diagonal or circular axes. Take the same measurement twice, and the answer will remain the same; but take one and then another, and the first answer becomes worthless.
A light in the distance
This feature of photons means that they can be used to construct single-use, self-destructing keys, rather like the envelopes in spy movies that conveniently explode when they get into the wrong hands. To agree upon a key, the sender and the recipient (by convention called Alice and Bob) must arrange to open a channel for sending the photons. Alice makes a string of photons, measures the polarisation of each as she pleases, and then sends them off to Bob. Bob measures the polarisation of each of the photons as it arrives, in any way he chooses.
From this point on, Bob and Alice can communicate without cloak or dagger. Bob rings up Alice and tells her what sort of measurements he performed, though not his results. Some of his measurements are likely to have overlapped with Alice’s. She tells him which measurements to keep, and which to discard. They now both know which bits they share information about, and so are able to agree on the spot upon a private key that consists of this common string of bits.
Eve, an eavesdropper listening to their conversation, requires Alice’s original string of photons in order to make head or tail of this exchange. This is where the natural safeguards of quantum physics make their advantages felt. If Alice had sent a beam of photons to Bob, Eve could have intercepted the beam and split it into two, taking a portion and sending the rest on to Bob, who may not notice the loss. But individual photons cannot be split: any photons that Eve intercepts, Bob will surely miss.
Should Eve adopt the so-called “bucket-brigade” strategy—to intercept and resend photons as quickly as she can—she will still give her presence away. The uncertainty principle dictates that Eve cannot copy Alice’s photons exactly. The error she introduces by making faulty copies will be enough to trigger Bob’s suspicions. Alice and Bob can then compress their common key in a way that will frustrate Eve’s efforts.
In theory, the system also protects against future snooping. Because the mould that made this unique quantum key—the string of photons—is lost forever, it would remain invulnerable even if the daughters or grand-daughters of Eve were to possess unlimited computing power. And since the quantum key is not only made and used, but also discarded, on the spot, nobody can spirit it away and use it to impersonate Alice or Bob later on.
Other teams have already sent quantum keys over long stretches of optical fibre. But Dr Hughes’s group has a loftier goal. Next month, it will test a system for distributing quantum keys under the cloudless skies of New Mexico. With a very faint laser, an outpost will emit a string of photons. Ten kilometres away, a telescope will try to discern these brief scintillations against the immense background noise of desert daylight. Early trials have suggested that the system will be able to send single photons reliably, day or night, and will not blink out of service when weather conditions do not suit it.
Since transmitting photons through the dense air at ground level is harder than transmitting straight up through the atmosphere to an orbiting satellite, Dr Hughes’s experiment opens up the possibility that earth-to-satellite quantum-cryptography channels could be built. Once that happens, anybody within range of the satellite would have a completely secure way to get a quantum key. It seems that the ultimate in cryptographic technology may share much in common with the primitive. Telescopes hunting for distant glimmers of light will make a comeback. The flashes will just be a bit flashier.