Quantum Encryption: Fighting Quantum with Quantum
In my previous article, I talked about Shor’s Algorithm- a quantum algorithm that can be applied to break current RSA encryption. Luckily for us, current quantum computers have been using Shor’s to factor numbers such as 21, not 512 bit RSA keys. However, this has just been due to the limitations of quantum hardware. As technological advancements occur, we need a way of combatting quantum decryption to properly secure our data.
One way we can do this is by fighting quantum with quantum, using Quantum Key Distribution (QKD).
BB84 Protocol
According to the BB84 protocol, QKD would work as follows:
Let’s say you have two people that are sending data to each other — Alice and Bob. Alice randomly generates the digital key to “unlock” the data, which is a series of 0s and 1s.
For simplicity’s sake — let’s make Alice’s randomly generated key 011010.
Each element of the key is going to be encoded by the polarization of a given photon, and it can either be done on a rectilinear basis or a diagonal basis.
Using a rectilinear basis, a 0 would be encoded by polarizing a photon 0 degrees and a 1 would be encoded by polarizing a photon 90 degrees. The same is for the diagonal basis except it polarizes the photon at 45 and 135 degrees, as shown by the figure below:
When sending out her key, Alice would choose the basis she encodes her protons with at random for each photon.
Using R to represent a Rectilinear Basis and D to represent a Diagonal Basis, let’s say that Alice sends her photons using RRRDRD.
Once Alice has sent her photons, Bob now has to receive and measure them. However, Alice won’t tell Bob the measurement basis by which she chose to encode the electrons. Instead, Bob will choose at random which measurement basis he would use for each photon. Note that choosing a measurement basis that is not the one that Alice chose gives Bob a 50/50 chance of choosing between 0 and 1. Choosing the correct measurement basis means that he gets a 100% chance of measuring what Alice initially meant to send.
For example, Bob chooses to measure the photons using the measurement basis of DRRDDR. Notice how the first, fifth, and sixth photons were measured using the incorrect measurement basis — so they would collapse randomly to measure either 0 or 1.
Now that both have their keys and measurement bases stored, they can announce (publicly, it doesn’t matter) what was the measurement basis that each used. If both used the same measurement basis for a given photon, then the value of that photon is kept as a part of the key. Digits, where different measurement bases are used, are discarded.
What Makes It Unbreakable?
The reason that someone can't eavesdrop on this communication of photons is because of the laws of quantum mechanics. An outsider measuring the photon can make it collapse from its polarized state and lose the original information it was carrying. It is also impossible to make an exact copy of that photon without making it collapse.
Alice and Bob can agree on a small subset of their keys to compare and see whether or not they match. If they don’t, that means that someone interfered with the photons being sent and the key is discarded.
The chances of the eavesdropper going undetected exponentially decrease as the number of digits in the key increases, or more specifically the number of digits that Alice and Bob cross-check. The hacker would have to be extremely lucky so that every photon in that subset that Alice and Bob cross-reference with each other has either been measured with the correct measurement basis or randomly collapsed down to the correct polarization state.
Alternate Solutions
The feasibility of this in the near future is pretty muddy. For something like this to work, we would need a functional quantum internet — which is not necessarily going to come anytime soon. Sending photons across the country while retaining its polarized state is a pretty difficult task.
However, we still have the problem of quantum computers being able to break RSA encryption. What steps can we take to make sure that our data is safe until then?
Currently, the National Institute of Standards and Technology has been directing a process to find one or more quantum-resistant public-key cryptographic algorithms in preparation for when quantum computers can crack RSA encryption. There are mainly three groups of proposed cryptographic algorithms — lattice, code-based, and multivariate.
You can see their 3rd round of finalists here:
https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions
Overall, Quantum Key Distribution is an amazing way of securing your data that relies on the unpredictability of the laws of quantum mechanics. However, it has its own physical limitations now, which is why currently there is a call for encryption algorithms that can combat the rise of quantum computers.
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