Private Key Exchange Using Quantum Physics

by Jared DeWitt

This article explains how the BB84 protocol functions.  The short answer is quantum indeterminacy, yet the specifics are fascinating and easier to understand than might at first appear.

The BB84 was developed by Charles H. Bennett and Gilles Brassard together in 1984 so, while this protocol is not new by any means, its use is very new.  For example, in 2007 this protocol was used to transmit ballot results for the Swiss elections, making news all over the world.

Alice and Bob can help explain how this works.

Alice is trying to share a private key with Bob.  They're in separate physical locations, but they have a fiber line connecting them.  In addition, an eavesdropper (Eve) has tapped their fiber line, hoping to intercept their private key exchange (what a cunning little devil she is!).

Alice sends a randomly generated key to Bob, which she transmits bit by bit.

Our "bits" in this protocol are actually photons going down the fiber line, one at a time.  The BB84 protocol uses four states of photon polarization comprised into two basis, rectilinear and diagonal.  In a rectilinear basis the photon can have horizontal or vertical polarization, and in a diagonal basis it can have left or right polarization, for a total of four possible orientations.

So Alice doesn't just send any old photon down the line, but instead slaps one of those four polarization states on each one, keeping track of everything she sends.  So how does that make a 1 or 0 for our binary bits?

To put it simply, horizontal and left are going to equal binary 0, and vertical and right are going to equal binary 1.

Let's check in on Bob, who just got his first photon from Alice.

In order to determine whether this photon is a 1 or a 0, he has to measure its polarization.

The problem is that Bob can't just look at it and know what its polarization is.  If the photon's polarization is rectilinear, for example, then he has to measure it as rectilinear.

If he doesn't, then the photon will change its polarization randomly to one in the basis he measures the photon in.  To help you understand this, think of trying to see what color a bouncy ball is.

The bouncy ball can only be one of four colors (red, blue, yellow, or green).  You have one set of glasses that can only see red and blue, and another set of glasses that can only see yellow and green.

You have to choose which glasses to view the ball with.  If you use your red/blue glasses and the ball is actually green, the ball will magically change colors to either red or blue and stay that way (elementary particles are tricky little bastards).  So what does Bob do?

He has no idea how to measure it, so he guesses and keeps track of what basis he used to measure the photon with.  He gets his answer and waits for the next photon.  This process is done until he's received the entire key from Alice, the length of which they had previously determined.

Now both Alice and Bob have the key, but because Bob had to guess between the two bases in which to measure, their keys are going to vary.

Since Bob had a 50% chance of guessing the correct basis used by Alice on a given photon, about half of his bits aren't going to match up.  This is corrected when Bob and Alice use a public medium (telephone, email, IM, etc.) to let each other know what basis they used for each bit, which allows Bob to throw out the bits that were measured incorrectly.  Now they should each have a key which can be used to encrypt their conversation.

So what's Eve up to?

Normally, if Eve tapped their fiber line and they used standard protocols to transmit their private key, there is a chance that Eve would also have their key and could listen to their conversation.  But in this scenario, Eve would have to guess the basis in which Alice transmitted the photon, just as Bob did.

She would then have to retransmit the photon with the correct polarization down the line to Bob.  But only 50% of Eve's sent photons would be correct.

Since Eve has tampered with the data sent to Bob, he would now have a different key than Alice.  The result would be garbled data when their encrypted conversation starts.  Bob and Alice would then know that the line had been compromised and would discontinue its use.

This example used photon polarization but could easily be adaptable to use electrons and their spin.  I know this doesn't share the same spirit of the rest of the articles in this publication, but hopefully you're starting to think about the future of security.

In just a few years, it's going to be a strange new world.