Quantum Key Distribution (QKD) John A Clark Dept. of Computer Science University of York, UK

Communication The only really secure cryptosystem is the one-time pad (provided you use it only once, which hasn’t always been the case). Essentially both participants possess the same random bit stream b1 b2 b3 b4….. The sender has a message m1 m2 m3 m4 …. Encodes message as c1 c2 c3 c4 Receiver applies b1 b2 b3 b4 to obtain message But how can we distribute this keystream b1 b2 b3 b4…?

When Alice met Bob Communicants will (following tradition) be Alice and Bob, trying to communicate their love… Eve isn’t happy about this. She wants to listen in and interfere AliceBob Eve

Basic Scheme Basic scheme based on polarisation of photons y x z Photons are transverse magnetic waves – magnetic and electric fields are perpendicular to the direction of propagation. Also they are perpendicular to each other.

Photons We will assume that we are dealing with linearly polarised light but other schemes are possible (e.g. with circularly polarised light). We need to create photons that with an electric field oscillating in the desired magnetic plane. One way to do this is by passing light through an appropriate polariser More sophisticated way is to use a Pockels Cell. Only vertically polarised photons emerge

Detecting Photons Possible to detect absorption by using a Calcite crystal Photon Detector

Measuring a Photon  Suppose photon has polarisation at angle  to a horizontal filter. Measured as a 0 (absorbed) with prob=sin 2 . Measured as a 1 (permitted) with prob=cos 2 .

Blocking is Freedom Intensity 1.0 Intensity 0.5 Intensity 0 Intensity 0.125

Basic Scheme Basic scheme assumes that the polarisation of photons can be arranged. For example Vertical Polarisation denotes 0 Horizontal Polarisation denotes 1

Rectilinear Basis Suppose now that Alice sends a 0 in this scheme and that Bob uses a photon detector with the same basis. Alice Sends 0 Alice Sends 1 Bob Receives 0 Bob Receives 1

Diagonal Basis Can also arrange this with a diagonal basis Alice Sends 0 Alice Sends 1 Bob Receives 0 Bob Receives 1

Basis Mismatch What if Alice and Bob choose different bases? Alice Sends 0 Bob Receives 0 Bob Receives 1 Each result with probability 1/2

Use of Basis Summary A sender can encode a 0 or a 1 by choosing the polarisation of the photon with respect to a basis Vertical => 0 Horizontal => 1; or 45 degrees => 0, 135 o =>1 The receiver Bob can observe (measure) the polarisation with respect to either basis. If same basis then bits are correctly received If different basis then only 50% of bits are correctly received. This notion underpins one of the basic quantum cryptography key distribution schemes.

What’s Eve up To? Now Eve gets in on the act and chooses to measure the photon against some basis and then retransmit to Bob.

Eve’s Dropping In Suppose Eve listens in using the same basis as Alice, measures the photon and retransmits a photon as measured (she goes undetected) Alice Sends 0 Alice Sends 1 To Bob Eve Measures 0 Eve Measures 1

Eve’s Dropping In Suppose Eve listens in using a different basis to Alice Similarly if Alice sends a 1 (or if Alice uses diagonal basis and Eve uses rectilinear one) Alice Sends 0 To Bob Eve Measures 0 Eve Measures 1 0 and 1 equally likely results

Summary of Eve’s Droppings If Eve gets the basis wrong, then even if Bob gets the same basis as Alice his measurements will only be 50 percent correct. If Alice and Bob become aware of such a mismatch they will deduce that Eve is at work. A scheme can be created to exploit this.

Alice and Bob To send and receive a photon Alice and Bob choose a basis randomly. Alice sends a 0 or 1 using her basis and Bob uses his basis to measure it. Alice records the basis she used and the value sent. Bob records the basis he used and the value he measured.

When We are in Harmony Throw away results when bases disagree and keep results when bases agree Keep Value Discard Value Keep Value Discard Value AliceBob

We Agree Alice and Bob exchange a sequence of bit values encoded in photon polarisation with bases chosen at random. Bob announces via an unjammable channel which bases he used in each case. Alice tells Bob whether choices of basis were correct. They throw away any bit values where the basis choice disagreed and keep those bit values were the basis choice agreed.

Has Eve Listened In? Now we need to determine whether Eve has been listening in. How might this be done?

Has Eve Listened In? Can pick some bits at random and tell each other what values were sent and received. Sufficiently many mismatches then high chance of Eve at work.

Has Eve Listened In? Can pick some random subset and determine the parity of the bit values sent and received. If parities disagree then Eve may have been at work or else there has been an error. Even if agree, parity information has been publicly broadcast – so we discard the final contributing bit. Can repeat this process numerous times to gain increased confidence.

Creating Photons In practice creating a single photon may not be that easy. Can be done with dim light pulses. But if two photons get created one can be captured and measured whilst the other goes through to Alice. They would both have the same polarisation so the security here would be broken.

Keeping it All in Line The kit used to carry out key distribution way may be rather sensitive to disturbance. May need continuous adjustment to maintain right physical set up etc.

Entangled States We have described the best known of protocols for key distribution. Various others are possible. For example, based on entanglement with elements of an entangled pair sent to each of Bob and Alice. Scheme due to Artur Ekert (Oxford).

General Usage Significant interest in QKD. We don’t need to use it for everything. Can use it to distribute key distribution keys. Keys we can use to carry out conventional key distribution protocols securely. Note: no prior contact is necessary.

Aside QKD here relies on being able to detect Eve’s interfering. Possible to go to other extreme and assume that data will be intercepted: More conventional schemes proposed where trillions of bits per second would be transmitted and only sender and receiver know the (very small) time window for the key. Idea is to swamp an interceptor with so much data that they cannot possibly cope.

Summary Have outlined basics of a photon-based scheme that allows a key to be created and shared between two communicants in a manner that allows eavesdropping to be detected. Makes use of one of the fundamental features of quantum mechanics Looking (measuring) disturbs things QKD works! Experiments over 10’s of kilometres using fibre optics. Work also in free space. Aim for QKD with low orbiting satellites.