Quantum Cryptography

1. Quantum Cryptography By TaipanTamsare

2. Outline • Motivation • Quantum Physics • Polarization • Quantum Cryptography • Eavesdropping and Detection • Current State Affairs • Summary

3. Motivation • Why Quantum Cryptography? • Nearly Impossible to steal • Detect if someone is listening • “Secure”

4. Quantum Physics • Light waves are propagated as discrete particles known as photons. • Polarization of the light is carried by the direction of the angular momentum, or spin of the photons.

5. b ψ  a  Polarized photons • Polarization can be modeled as a linear combination of basis vectors vertical () and horizontal () • A quantum state of a photon is described as a vector • quantum cryptography often uses photons in 1 of 4 polarizations (in degrees): 0, 45, 90, 135

6. Vertically polarized light Unpolarized light Filter tilted at angle q Vertical aligned filter Polarization by a Filter

7. Polarization by a Filter

8. Quantum Cryptography • Two physically separated parties can create and share random secret keys. • Allows them to verify that the key has not been intercepted. • Quantum Key Distribution(QKD)

9. Quantum Key Distribution

11. BB84 QKD protocol • Alice • Encodes her information randomly in one of the two bases… • For example,

12. BB84 Alice prepares 16 bits 0101100010101100 in the following bases, BAABAABAAAABBBBA Thus the following states are sent to Bob: +10-10+0101+--+0

13. BB84 Bob receives the stream of qubits and measures each one in a random basis: ABAABAAABABBBBAB

14. BB84 So Bob gets 1-00-0+0+0-+--1+

15. BB84 • Then Alice and Bob compare their measurement bases, not the results, via a public channel.

16. BB84 • So Bob and Alice are left with 7 useable bits out of 16 _ _ 0 _ _ 0 _ 0 _ 0_ 0 1 1 _ _ These bits will be the shared key they use for encryption.

17. Eavesdropping • Now enter Eve… She wants to spy on Alice and Bob. • So she intercepts the bit stream from Alice, measures it, and prepares a new bit stream to Bob based on her measurements…

18. Eavesdropping

19. Eavesdropping • Eve has to re-send all the photons to Bob • Will introduce an error, since Eve don't know the correct basis used by Alice • Bob will detect an increased error rate

20. Eavesdropping • Thus, of the bits Bob measures in the correct bases, there is 50% that eve had changed the basis of the bit. And thus it is equally likely that Bob measure 0 or 1 and thus an error is detected 25% of the time.

21. Detecting Eavesdropping • When Alice and Bob need to test for eavesdropping • By randomly selecting a number of bits from the key and compute its error rate • Error rate < Emax assume no eavesdropping • Error rate > Emax assume eavesdropping(or the channel is unexpectedly noisy)Alice and Bob should then discard the whole key and start over

22. Current State of Affairs • Commercial quantum key distribution products exist

23. Current State of Affairs • Current fiber-based distance record: 200 km

24. Summary • The ability to detect eavesdropping ensures secure exchange of the key • The use of one-time-pads ensures security • Equipment can only be used over short distances • Equipment is complex and expensive

25. References • Zelam Ngo, David McGrogan • Biometrics and Cryptography UTC/CSE • VasilPenchev, Assoc. Prof., PhD