The BB84 scheme

This one is a trip down memory lane for me. My undergraduate project was in Materials Science, but specifically, I was making a Single Photon Source (SPS) for Quantum Key Distribution (QKD). As the materials person, all I need to know is that making a single photon is what’s required. However, I wanted to learn the underlying principles. So.

BB84 is a scheme for Quantum Key Distribution - that is, deciding on a key in a tamper-evident manner using the behaviour of entities as described by quantum mechanics. The system works as such:

Alice chooses an array of bits, $x \in {0,1}^i$, and a \emph{basis} of the same length, both at random, and sends $x$ as single photons encoded in $b$ to Bob:

Bob chooses a basis at random, and receives Alice’s signal. Alice and Bob then \emph{publicly} discuss which bits were both transmitted and measured in the same basis, and compare a subset of these bits.

By superposition rules, any interceptor must receive the messages without knowing the basis: on retransmitting, there is a $1/4$ chance they will encode wrongly. Alice and Bob will discover this on comparing bits, and conclude they are being eavesdropped.

BB84 has been doubted as a solution for the menace of Quantum cryptanalysis - since you’re using symmetric encryption. Unfortunately, I have to come to the conclusion - it doesn’t do much a PKI does not, and without any quantum, and post-quantum cryptography is looking good. I won’t lie, Learning With Errors makes this look easy, but it’s not something you’re going to have to worry about beyond switching ciphers in 5-10 years time (if, frankly, ever). You probably won’t even do that - TLS 3.0 or whatever will do it for you.