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Quantum cryptography

We have seen that quantum computers have the power to break RSA. But using quantum mechanics we also gain cryptographic power in another way.
Abstract purple image depicting the interior of a computer
© University of York

We have seen that quantum computers have the power to break RSA, hence in a world with quantum computers our use of this cryptographic method is certainly taken away. However, by using quantum mechanics we also gain cryptographic power in another way.

The field of quantum information theory has the goal of discovering what the laws of quantum mechanics buy us in terms of information processing ability. Not only do we get more computing power using quantum computers, but we also get more cryptographic power using quantum cryptography.

Usual cryptographic schemes like the ones you have studied earlier rely on the hardness of particular problems for their security. RSA relies on the hardness of factoring, for instance, which breaks down in the presence of quantum computers. Quantum cryptography, on the other hand, offers provable security guarantees without assuming hardness of some task. Instead, security is proven even against an adversary with unlimited computing power.

A detailed discussion of quantum mechanics would take us beyond this course. However, we can provide you with a flavour of a quantum protocol using an analogy based on the idea of a special Q-box, which mimics some quantum features but which is easier to understand. The basic idea that we want to convey here is that using this Q-box it is possible to detect the presence of an eavesdropper, something that is not possible when sending signals using usual classical means. (In the classical setting, if someone intercepts and reads an email before sending it on unaltered then neither the sender nor the receiver is able to tell.)

The Q-box analogy

Imagine a box with four possible internal states: Top-Left (TL), Top-Right (TR), Bottom-Left (BL) and Bottom-Right (BR).

Setting the state

The state of the box can be set by a user in one of four ways (which do not match the internal states):

  • the user can choose Top: in this case, the internal state is randomly set to either TL or TR;
  • the user can choose Bottom: in this case, the internal state is randomly set to either BL or BR;
  • the user can choose Left: in this case, the internal state is randomly set to either TL or BL;
  • the user can choose Right: in this case, the internal state is randomly set to either TR or BR.

Q-box

Importantly, the detailed assignment (i.e. which of the four internal states is present) cannot be known by the user. Thinking of the four internal states as the four quadrants of the box in the picture above, all that the user can choose is within which half of the box the true internal state lies: if the user chooses Top then they don’t know whether the internal state is actually TL or TR.

Readout

There are two possible ways to readout from the box:

  • we can readout whether the internal state is a Top (T) state or a Bottom (B) state (“T/L measurement”)
  • we can readout whether the internal state is a Left state or a Right state (“L/R measurement”)

Importantly: it is impossible to read out both pieces of information, and taking a measurement destroys the state. So if we choose to make a T/B measurement, and get the readout Top, we can never know whether the internal state was actually TL or TR.

In the next article, we’ll see how Alice and Bob can securely use the Q-box to share random strings with one another.

© University of York
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The Mathematics of Cryptography: From Ancient Rome to a Quantum Future

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