Sharing secrets is as old as humanity, and evidence of coded messages has been traced back to ancient civilizations. Cryptography is a technique intended to code a message into an incomprehensible string of characters that can only be decoded by the intended recipient. And, just as the lock on your front door can only be opened by those with the key, well-encrypted messages can only be unscrambled by those in possession of a key. Decryption keys generally take the form of a huge number, or a long text string, which can be used to decode messages through the use of various algorithms.
If two people, call them Alice and Bob, want to communicate securely, Alice can whisper a key into Bob’s ear. Then, once they have departed, they can communicate at ease—even over insecure channels like phone lines or the internet. Before Alice sends a message, she uses their shared key to scramble the message using some agreed process. At the other end, Bob uses the same key to unscramble the message. Anyone who intercepted the encrypted message en route would see only garbled text since they do not know the key.
But suppose that Alice and Bob live far apart. Alice could no longer whisper the key into Bob’s ear. Instead, they would need to find a way to transmit the key from one to the other. Once transmitted, they would each have the secret key and they could go about encrypting and decrypting their messages as before. The challenge lies in sharing the key, and data security experts call this the secure key distribution (SKD) problem.
This is where quantum physics comes to the rescue. By applying the principle of quantum entanglement, Alice can transmit a secret key to Bob in such a way that it cannot be intercepted without their knowledge. Entanglement is a purely quantum property that emerges in systems of two (or more) quantum entities. Quantum cryptography is thus accomplished through a physical process, not just a mathematical one, so it is far more robust than classical cryptography.
QUANTUM LEAP
RSA, one of today’s most widely used public-key cryptography systems, creates a public key that is the product of two large prime numbers. To crack such a code, you would need to rapidly identify the prime factors of the key. This is beyond the limits of today’s computers, but would be a snap for a quantum computer. This quantum-induced vulnerability in classical cryptography emphasizes the need for new systems, possibly based on quantum cryptography.
By shining a high frequency laser through a special type of crystal, Alice can create a real-world entangled state that is of great utility to quantum cryptography. Occasionally, while passing through the crystal, the high-energy photon will split into two lower-energy photons.
Given that the two “daughter” photons trace their origin to the same photon, they will be joined at the hip in several ways. First of all, conservation of energy tells us that the energy of the two daughter photons must equal that of that of the original photon. In addition, the polarization states of the two photons will be linked.
DEFINITION
Polarization is a property of light that depends on the direction in which its electric field is oscillating. For example, a photon traveling straight at you could have an electric field oscillating vertically or horizontally.
Polarization is a property that derives from the oscillating electric field that corresponds to each photon. The important point for this discussion is that each photon emerging from Alice’s special crystal can take on one of two possible, perpendicular states (which we’ll call “V” for vertical and “H” for horizontal). To measure the polarization of a photon produced by her crystal, Alice would hold up a filter aligned either vertically or horizontally. A vertical filter only allows V-state photons to pass through and be detected. H-state photons will be blocked by a vertical filter and nothing will be transmitted. Likewise, a horizontal filter only allows H-state photons to pass through and be detected.
Stated differently, a V-state photon is transmitted 100 percent of the time by a vertical filter and 0 percent of the time by a horizontal filter. If you set the filter to some arbitrary angle between vertical and horizontal, there is some intermediate probability that the photon will be transmitted. For example, at 45 degrees above horizontal, the transmission probability is 50 percent.
More important, due to quantum entanglement the two photons in each pair must be in opposite polarization states. Prior to any measurements, both photons will exist in superpositions of states V and H. When Alice measures one photon, she will find it in either state V or state H. She won’t be able to predict which of these states she’ll find it in, but the act of measurement will collapse the entangled wave function into a single quantum state. Whenever she finds the first photon in state V she will know that the second photon in the pair (sent to Bob) must be in state H, and vice-versa.
Alice and Bob can use these pairs of entangled photons to generate and share their secret key with security. It works like this. Alice generates the entangled photon pairs one by one. For each photon she sets her filter, at random, at one of two angles (say, horizontal and 30 degrees above horizontal), and then writes down whether the photon is transmitted or not. Meanwhile, the second photon makes its way to Bob. When it arrives, he sets his filter, at random, at one of two angles. It is essential that one of his angles matches one of Alice’s and that the other is different. Let’s say he sets his filter either at 30 degrees or 60 degrees. For each photon they select their filter settings randomly and independently, never knowing which filter setting the other had chosen.
Once they have both measured a bunch of photons, Alice gives Bob a call and they go over each measurement one by one. Since this conversation is held in any open channel, which may or may not be secure, the only information they reveal is which filter setting they used for each photon. When they used different types of filters, they discard the result (for the moment, at least). When they used the same filter setting—30 degrees in our example—they keep the result.
The reason for their doing so is that quantum entanglement implies that the two photons behave identically when interacting with filters at the same setting. In these cases, they write down a 0 for each time the photon was transmitted and a 1 for each time it wasn’t. Alice and Bob then possess two exact copies of a random string of 1’s and 0’s (called a random binary string), which can then be converted into a number or a word using any standard binary algorithm. The more measurements they take, the longer their binary code can be and the more complex their key.
So, we see that Alice and Bob can share a key using this procedure. But is it really secret? If someone, who we will call Eve, were to eavesdrop on their phone conversation, she would only hear information about the filter settings used. She would not know what the measurement results were, however, so would have no information about the actual binary string that resulted from the nondiscarded measurements.
Ah, you say, but what if Eve could have somehow gotten between Alice and Bob so that she too could have measured the photon before it got to Bob? Her measurements would destroy the photons. So, to cover her tracks she would have to generate new ones and transmit them to Bob. Eve’s new photons would not be entangled with the photons that Alice detected, however, since they were prepared separately. Therefore, if Alice and Bob can confirm that the photons they measure are truly entangled, they can be certain that their key exchange has not been compromised.
To conduct the “entanglement test,” Alice and Bob examine the results of the measurements when they applied different filter settings. For each of these, they discuss the results of their measurements and compare this to Bell’s Inequality. If their measurements violate Bell’s Inequality, they know that the photons were truly entangled and that their secret key is indeed secret.
QUANTUM LEAP
Besides the quantum entanglement method described here, a second method of quantum cryptography can also be deployed. It is called “prepare and measure,” and it is grounded in the Heisenberg uncertainty principle. In this case, Alice generates random photons, in arbitrary polarization states, and transmits them to Bob. They then use the same procedure to deduce their secret key. The presence of Eve is detected using the notion that any measurement Eve makes on an intercepted photon will necessarily alter its quantum state, which Bob will be able to detect.
Security isn’t enough for this technology to be useful. It also needs to be widely practical, especially regarding the transfer of photons over long distances via fiber optic cables. Experimenters have proven that entangled states can be generated and transmitted over distances covering hundreds of kilometers. New tests are even being conceived that will test the ability of transmitting entangled states down to Earth from orbiting satellites.
Quantum cryptography, although still in its infancy, has already been applied by commercial firms that now offer “turnkey” SKD systems. There are skeptics of the real-world feasibility of this technology, but if we think of how laser technology has evolved from a purely fundamental research tool to one used widely in our everyday life, we can be hopeful about the future of this quantum application.
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