Chapter 10: Quantum Cryptography

Classical Cryptography

Before we can understand quantum cryptography, we need to first understand classical cryptography. To do this, we can consider RSA encryption. The name for this encryption method comes from the scholars credited with inventing it: Ron Rivest, Adi Shamir, and Leonard Adleman. RSA works by using public and private keys to encrypt and decrypt information. Imagine someone—let’s call them Bob—wants to send information to their friend—let’s call them Alice. Alice’s public key can be seen by anyone and used to encrypt information. In fact, Bob will use her public key to encrypt his secret message. However, only Alice has access to her private key, which she will use to decrypt Bob’s message.

But, how can two different keys be used to scramble and unscramble the same data? The answer is prime numbers. Simply put, Alice’s public key is the product of two large prime numbers. Her private key relies on knowing what those two prime numbers are. The reason people can know the product of these prime numbers (i.e. the public key) without knowing the numbers themselves (i.e. the private key) is because of how difficult it is to factor large numbers. This process is known as prime factorization. When dealing with large numbers, prime factorization is hard and time-consuming for even the most advanced computers we have today.

For example, it’s easy to confirm that 7,121 and 11,827 multiply to give 84,220,067—you can quickly plug this into a calculator. But, it requires much more effort to start with 84,220,067 and factor it into prime numbers. 

However, as quantum computing becomes more robust, RSA encryption is becoming less and less secure. Once we have an algorithm or a computer that can quickly factor large numbers into primes, anyone can figure out what Alice’s private key is and use it to decrypt messages she’s received. As a result, people have turned to quantum cryptography in an attempt to develop the next generation of secure communication methods.

Quantum Cryptography

Quantum cryptography involves encryption techniques that take advantage of quantum mechanics principles. Let’s take a look at quantum key distribution (QKD), a widely-studied quantum encryption method. Unlike classical RSA encryption, QKD is not used to share any messages. As its name suggests, QKD is used to share a private key that will be used to both encrypt and decrypt messages. Additionally, QKD is special because it alerts parties to the presence of an eavesdropper.

QKD often involves sending photons through an optical fiber, which you can think of as a very small tube that light can travel through. A photon is a kind of qubit. As a reminder, a bit is a classical unit of information and can take on a value of 0 or 1. A qubit is a quantum unit of information and can take on a value of 0, 1, or a superposition of the two.

Photons are special because they can carry information through their polarization. If we think of light as a wave and a photon as a packet of light, then we can think of a photon’s polarization as the direction in which the light wave is bouncing back and forth. For example, if the light wave oscillates up and down, we consider the photon vertically polarized. If the light wave oscillates left to right, we consider the photon horizontally polarized. 

Using this information, we can now break down how Alice and Bob share a secret key with each other via QKD. Let’s say that Alice sends Bob a photon using a machine that is aligned vertically. The resulting vertically-polarized photon corresponds to a 0 bit. If Bob’s detector is also aligned vertically, he will also measure a 0 bit. But, if for some reason his detector is aligned with some other direction (e.g. diagonally) he only will measure the same bit as Alice half of the time. 

After Alice has sent Bob several photons, they can sit down and discuss. Specifically, Alice will share how her machine was aligned for each photon and Bob will share how his detector was aligned for each measurement. They will only keep the bits where the machine and detector were aligned in the same direction, and these bits will form their private key!

Before Alice and Bob can start encrypting and decrypting messages with this key, they need to make sure no one was eavesdropping on them. To do this, they sacrifice a few of the bits they measured when the machine and detector were aligned in the same direction. Since Alice’s bit must match Bob’s bit in these cases, any bit discrepancies are due to an eavesdropper—let’s call her Eve. Remember that quantum mechanics says that measuring a qubit’s quantum state destroys it. So, if Eve measures one of Alice’s photons with her own detector, she will irreversibly change its polarization. As a result, Bob’s bit measurement will be affected by Eve’s eavesdropping, allowing him and Alice to deduce that an unwanted party is listening in.

Food for Thought

QKD is promising in theory, but can you think of any challenges that arise when actually trying to execute this form of secure communication? Hint: can we actually reliably detect a single photon at a time?