Quantum Key Distribution (QKD)

1. Quantum Key Distribution (QKD) John A Clark Dept. of Computer Science University of York, UK jac@cs.york.ac.uk

2. 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…?

3. 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 Alice Bob Eve

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

5. 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

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

7. Measured as a 0 (absorbed) with prob=sin2 q. Measured as a 1 (permitted) with prob=cos2 q. Measuring a Photon Suppose photon has polarisation at angle q to a horizontal filter. q

8. Intensity 1.0 Intensity 0.5 Intensity 0 Intensity 0.125 Blocking is Freedom

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

10. Rectilinear Basis • Suppose now that Alice sends a 0 in this scheme and that Bob uses a photon detector with the same basis. Alice Sends0 Bob Receives0 Alice Sends1 Bob Receives1

11. Diagonal Basis • Can also arrange this with a diagonal basis Alice Sends0 Bob Receives0 Alice Sends1 Bob Receives1

12. Basis Mismatch • What if Alice and Bob choose different bases? Alice Sends0 Bob Receives0 Bob Receives1 Each result with probability 1/2

13. 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, 135o =>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.

14. 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.

15. 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 Sends0 Eve Measures0 To Bob Alice Sends1 Eve Measures1 To Bob

16. 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) 0 and 1 equally likely results Alice Sends0 Eve Measures0 To Bob Eve Measures1 0 and 1 equally likely results To Bob

17. 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.

18. 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.

19. When We are in Harmony • Throw away results when bases disagree and keep results when bases agree Keep Value Discard Value Discard Value Keep Value Alice Bob

20. 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.

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

22. 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.

23. 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.

24. 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.

25. 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.

26. 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).

27. 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.

28. 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.

29. 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.