Introduction to Quantum Cryptography

1. Introduction to Quantum Cryptography Nick Papanikolaou nikos@dcs.warwick.ac.uk

2. The Art of Concealment • To exchange sensitive information, encryption is used • Encryption schemes in use today are under serious threat by quantum computers • The study of Quantum Computing and Quantum Information has yielded: • ways of breaking codes • ways of making better codes

3. This Talk • About Cryptography • Making Quantum Codes • Breaking Classical Codes Announcement: Nick’s office hours (Rm 327): Tuesdays 3-4pm Thursdays 2-3pm

4. Cryptography • Cryptography is the science of encoding and decoding secret messages. • Most common form: Symmetric Cryptography • Message M,Key K • Encryption: enc(M,K) = c • Decryption: M = dec(c,K)

5. Classical Cryptography [2] • We assume that the key has been already secretly shared between sender/receiver. Sender enc(M,K) = c Receiver M = dec(c,K) Eavesdropper dec(c,???)

6. Perfect Cryptosystems • In order to decipher the message M, the eavesdropper needs to know the key K. • Assuming K is completely secret, a perfect cryptosystem can be used. • Perfect cryptosystem: H(C|K)=H(C) • Example: One-Time Pad • Use a different key each time, equal in length to the message

7. Key Distribution • How do you exchange the key securely in the first place? Sender K Receiver K Eavesdropper K

8. QKD • Quantum mechanics gives us a way of ensuring that an eavesdropper, if present, is always detected. • This is called Quantum Key Distribution. • Main Idea: • Encode each bit of the key as a qubit.

9. Photons as Qubits • A qubit holds a single quantum state. • Can be in any mixture of basis states. • The polarization of a single photon can be used as a qubit. Rectilinear Basis  or  or 

10. or  or  The Diagonal Basis • We can also encode a qubit as a photon in the diagonal basis: Diagonal Basis 

11. Quantum Measurement • Observing a photon changes its state. Calcite Crystal

12. Measurement [2] • If a photon is measured using the wrong polarization angle for the crystal, then the result will be • Correct with probability 50% • Incorrect with probability 50% • Therefore, if an eavesdropper made a measurement in the wrong basis, his result would be random and he would be detected.

13. Review of QKD • The basic idea is that each bit in the key is mapped to a photon with a specific polarization. • e.g.: 0 1 0 1 0 1 1 • Bases:      • Photons:    

14. Eavesdropping • An eavesdropper can choose a basis for decoding at random. For previous example: • Photons received:     • Bases chosen:    • Result: ? ? 0 1 ? ? ? • To get all of n bits correctly, probability is only 0.5n • So for 64 bits, eavesdropper only has chance 5.410-20 of getting the right answer.

15. Breaking Classical Codes Peter Shor, ATT Labs If computers that you build are quantum, Then spies of all factions will want 'em. Our codes will all fail, And they'll read our email, Till we've crypto that's quantum, and daunt 'em. • Invented a quantum algorithm for efficiently finding the prime factors of large numbers. • Classical factoring algorithms: O((log N)k) • Shor’s algorithm: O(log N)

16. Afterword “Einstein was a giant. His head was in the clouds, But his feet were on the ground. But for those of us who are not that tall, We have to choose somewhere inbetween.” - Richard Feynman, on quantum mechanics