Vocabulary

What do the following terms and word combinations mean?

Eavesdrop, quantum coin flipping, quantum bit commitment, measure (v), be a bit off, rectilinear basis, random result, prearranged code.

Texts

Pre-reading task

What do you know about quantum cryptography?

Comment on the efficiency of the quantum cryptography methods.

Text 1. Quantum cryptography.

Quantum cryptography is another kind of cryptography in this world. With it, you can create a communications channel where it is impossible to eavesdrop without disturbing the transmission. The laws of physics secure this quantum channel: even if the eavesdropper can do whatever he wants, even if the eavesdropper has unlimited computing power. Charles Bennett, Gilles Brassard, Claude Crepeau and others have expanded on this idea, describing quantum key distribution, quantum coin flipping, quantum bit commitment.

According to quantum mechanics, particles don't actually exist in any single place. They exist in several places at once, with probabilities of being in different places if someone looks. However, it isn't until a scientist comes along and measures the particle that it "collapses" into a single location. But you can't measure every aspect (for example, position and speed) of a particle at the same time. If you measure one of those two quantities, the very act of measuring it destroys any possibility of measuring the other quantity. The quantum world has a fundamental uncertainty and there's no way to avoid it.

That uncertainty can be used to generate a secret key. As they travel, photons vibrate in some direction; up and down, left to right or more likely at some angle. Normal sunlight is unpolarized; the photons vibrate every which way. When a large group of photons vibrate in the same direction they are polarized. Polarization filters allow only photons that are polarized in a certain direction through; the rest are blocked. For example, a horizontal polarization filter only allows horizontally polarized photons through. Turn that filter 90 degrees, and only vertically polarized photons can come through.

Let's say you have a pulse of horizontally polarized photons. If they try to pass through a horizontally polarized filter, they all get through. Slowly turn that filter 90 degrees; the number of photons getting through gets smaller and smaller, until none get through. You'd think that turning the filter just a little will block all the photons, since the photons are horizontally polarized. But in quantum mechanics, each particle has a probability of suddenly switching its polarization to match the filter. If the angle is a little bit off, it has a high probability. If the angle is 90 degrees off, it has zero probability. And if the angle is 45 degrees off, it has a 50 percent probability of passing through the filter.

Answer the questions

What laws of physics is quantum cryptography based on? Why can't you measure every aspect of a particle at the some time? How do polarization filters work?

Text 2. Read the text and describe the process of secret key generation.

Polarization can be measured in any basis: two directions at right angles. An example basis is rectilinear: horizontal and vertical. Another is diagonal: left-diagonal and right-diagonal. If a photon pulse is polarized in a given basis and you measure it in the same basis, you learn the polarization. If you measure it in the wrong basis, you get a random result. We're going to use this property to generate a secret key:

For example: Alice and Bob are users, and Eve is an eavesdropper.

1) Alice sends Bob a string of photon pulses. Each of the pulses is randomly polarized in one of four directions: horizontal, vertical, left-diagonal, and right-diagonal.

2) Bob has a polarization detector. He can set his detector to measure rectilinear polarization or he can set his detector to measure diagonal polarization. He can't do both; quantum mechanics won't let him. Measuring one destroys any possibility of measuring the other.

Now, when Bob sets his detector correctly, he will record the correct polarization. If he sets his detector to measure rectilinear polarization and the pulse is polarized rectilinearly, he will learn which way Alice polarized the photon. If he sets his detector to measure diagonal polarization and the pulse is polarized rectilinearly, he will get a random measurement. He won't know the difference.

3) Bob tells Alice, over an insecure channel, what settings he used.

4) Alice tells Bob which settings were correct.

5) Alice and Bob keep only those polarizations that were correctly measured.

Using a prearranged code, Alice and Bob each translate those polarization measurements into bits. For example, horizontal and left-diagonal might equal one, and vertical and right-diagonal might equal zero.

So, Alice and Bob have generated bits as many as they like. On the average, Bob will guess the correct setting 50 percent of the time, so Alice has to send 2n photon pulses to generate n bits. They can use these bits as a secret key for a symmetric algorithm or they can guarantee perfect secrecy and generate enough bits for a one-time pad.

The really cool thing is that Eve cannot eavesdrop. Just like Bob, she has to guess which type of polarization to measure; and like Bob, half of her guesses will be wrong. Since wrong guesses change the polarization of the photons, she can't help introducing errors in the pulses as she eavesdrops. If she does, Alice and Bob will end up with different bit strings.

6) So, Alice and Bob compare a few bits in their strings. If there are discrepancies, they know they are being bugged. If there are none, they discard the bits they used for comparison and use the rest.

Improvement to this protocol allows Alice and Bob to use their bits even in the presence of Eve. They could compare only the parity of subsets of the bits. Then, if no differences are found, they only have to discard one bit of the subset. This detects eavesdropping with only a 50 percent probability, but if they do this with n different subsets Eve's probability of eavesdropping without detection is only 1 in 2".

There's no such thing as passive eavesdropping in the quantum world. If Eve tries to recover all the bits, she will necessarily break the communications.