Slide 1 Introduction to Quantum Cryptography Nick Papanikolaou

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

Slide 3 This Talk About Cryptography About Cryptography Making Quantum Codes Making Quantum Codes Breaking Classical Codes Breaking Classical Codes Announcement: Nicks office hours (Rm 327): Tuesdays 3-4pm Thursdays 2-3pm

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

Slide 5 Classical Cryptography [2] We assume that the key has been already secretly shared between sender/receiver. 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,???)

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

Slide 7 Key Distribution How do you exchange the key securely in the first place? How do you exchange the key securely in the first place? SenderK ReceiverK Eavesdropper K

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

Slide 9 Photons as Qubits A qubit holds a single quantum state. 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

Slide 10 The Diagonal Basis We can also encode a qubit as a photon in the diagonal basis: We can also encode a qubit as a photon in the diagonal basis: Diagonal Basis or

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

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

Slide 13 Review of QKD The basic idea is that each bit in the key is mapped to a photon with a specific polarization. The basic idea is that each bit in the key is mapped to a photon with a specific polarization. e.g.: e.g.: Bases: Bases: Photons: Photons:

Slide 14 Eavesdropping An eavesdropper can choose a basis for decoding at random. For previous example: An eavesdropper can choose a basis for decoding at random. For previous example: Photons received: Photons received: Bases chosen: Bases chosen: Result: ? ? 0 1 ? ? ? Result: ? ? 0 1 ? ? ? To get all of n bits correctly, probability is only 0.5 n To get all of n bits correctly, probability is only 0.5 n So for 64 bits, eavesdropper only has chance of getting the right answer. So for 64 bits, eavesdropper only has chance of getting the right answer.

Slide 15 Breaking Classical Codes Invented a quantum algorithm for efficiently finding the prime factors of large numbers. Classical factoring algorithms: O((log N) k ) Shors algorithm: O(log N) 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 , Till we've crypto that's quantum, and daunt 'em.

Slide 16 Afterword Einstein was a giant. 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