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- 1. Quantum Cryptography Arinto Murdopo Maria Stylianou Ioanna Tsalouchidou 13/12/2011
- 2. Outline● Quantum Cryptography● Theoretical Background● Quantum Key Distribution (QKD) ○ BB84 Protocol● Vulnerabilities & Attacks ○ Faked - state attack
- 3. Quantum Cryptography- How it came up● Cryptography => Secure Communication => Secure Data Transmission● Two techniques ○ Symmetric - key encryption (shared key) ■ Key - distribution problem ○ Asymmetric - key encryption (pair of public&secret keys) ■ Success based on hardware limitations, absence of good algorithms and non-use of quantum computers. Quantum Cryptography!
- 4. Quantum Cryptography● Quantum Cryptography is ○ the use of laws of quantum physics, to: ■ perform cryptographic functionalities ■ break cryptographic systems● Examples: ○ Quantum Key Distribution (next section) ○ Quantum Computers to break existing protocols
- 5. Theoretical Background● Quantum - minimum amount of any physical entity● Photon Polarization - Quantum Superposition ○ Vertical-Horizontal 2 orthogonal ○ Diagonal +-45 degrees states● Heisenberg Uncertainty Principle ○ “observation causes perturbation” ○ no-cloning theorem Polarized Wave Applet! http://surendranath.tripod.com/Applets/Waves/Polarisation/PW.html
- 6. Theoretical BackgroundFilter to distinguish polarized photons. Correct Filter applied Wrong Filter applied
- 7. Quantum Key Distribution - BB84● First quantum cryptography protocol● Goal: describe a scheme of two users who want to communicate and exchange data securely.● Idea: distribute a key securely, based on the laws of physics.● Security proofs: ○ If someone reads the state of photon -> state changes ○ Not possible to copy the photon in order to encode it with all possible ways (basis)
- 8. Quantum Key Distribution - BB84
- 9. Quantum Key Distribution - BB84Step 1 ● Alice has two choices, key (a) & basis (b), chosen randomly ● Combine bits of a and b, 1-1, ● Four different states of qubit (photon polarization) ● Sent through public quantum channels: ○ Optical Fiber ○ Free Space Photon Source
- 10. Quantum Key Distribution - BB84Step 2● Bob receives qubit from Alice● Bob measures it by choosing random basis using Beam Splitter (BS), practically it could be 50/50 mirror● PBS sends qubit to certain detector using some rules
- 11. Quantum Key Distribution - BB84Step 2How PBS of a specific basis works ● Let photon that polarized on that basis to pass through to the correct detector ● Otherwise, the photon can head randomly to any of the wrong detectors
- 12. Quantum Key Distribution - BB84Step 2Example of how PBS combining with detector works!
- 13. Quantum Key Distribution - BB84Step 3 ● 1st communication between Alice and Bob in public channel ● They compare the basis used to encode and measure the qubit ● If Bob.basis == Alice.basis ○ Keep the bit! ● Else ○ Discard the bit ● The length of the initial key is reduced to half of its length because the probability of Bob choosing the same basis as Alice is 50%
- 14. Quantum Key Distribution - BB84Step 4 ● Check if someone has intruded the communication or if some imperfection of the devices or channel has introduced noise that distort the outcome ● If Eve has intruded the communication, she will DEFINITELY left some traces due to Heisenberg Uncertainty Principle (HUP) and non cloning theorem
- 15. Quantum Key Distribution - BB84Step 4 ● Alice and Bob performs MANY parity-checks ● In this way, they can find out whether Eve has intruded the communication ● Very simple example: ○ Calculate parity of blocks of 4-bits ● Alice sends the parities of her blocks and Bob checks them
- 16. Quantum Key Distribution - BB84Step 5 ● Now Alice and Bob have the same keys, all the bits are same ● The problem is, in Step 4, Eve manages to find out some portions of their key ● Privacy Amplification comes into the rescue!
- 17. Quantum Key Distribution - BB84Step 5 ● Alice and Bob apply Hash function to compress the key into the final one. And they should use the same Hash function.
- 18. Vulnerabilities - Photon number attack● Sending more than one photon for each bit leads to photon number attack. ○ Eve can steal extra photons to extract the stolen photons information.● Ensure photon spitter only sends exactly ONE photon each time.● Single photon ensures quantum mechanic laws are satisfied.
- 19. Vulnerabilities - Spectral attack ● If photons are created by four DIFFERENT laser photo diodes, they have different spectral characteristics. ● Eve performs spectral attack by measuring COLOR, and not polarization.
- 20. Vulnerabilities - Random numbers● Are our random numbers really "Random"?● Bob side, randomness is determined by BS.● Alice side, randomness if a bit stream cannot be proven mathematically ○ Algorithms generate "random" sequences by following specific patterns => NOT that random! ○ Eve can use same algorithm to extract information. Entangled Photon Pairs comes to the rescue!
- 21. Entangled photon pairs
- 22. BB84 with photon pairs
- 23. Faked-state attackGeneral scheme
- 24. Faked-state attackPractical Implementation - Detector replica ● Eve has replica of Bobs detector ● To capture the photon and measure it like Bob always does
- 25. Faked-state attackPractical Implementation - Fake Stated Generator ● Blind Bobs detector ○ Insensitive to photon ● Forces Bobs detectors to have same "click" as what Eve has measured ○ Bob and Eve have same information
- 26. Faked-state attackPractical Implementation - Blind all Bobs detectors ● QKD detectors use Single Photon Avalanche Diode (SPAD)
- 27. Faked-state attackSingle Photo Avalanche Diode ● Has two modes ○ Geiger Mode ○ Linear ModeHence, SPAD in Linear Mode can be considered asblind-to-photon.
- 28. Faked-state attackSingle Photo Avalanche Diode ● How to make SPAD behaves in Linear Mode?
- 29. Faked-state attackSingle Photo Avalanche Diode ● SPAD in Linear Mode ● Bright illumination causes the capacitor has not enough time to recharge and re-balance the voltage value at point 2 ● SPADs bias voltage below VBreakdown -> Linear Mode
- 30. Faked-state attackSingle Photo Avalanche Diode ● SPAD in Linear Mode ●
- 31. Faked-state attackPractical Implementation - Force Bobs detector to click ● Blinding Bobs detector is not enough ● Eve needs to force specific Bobs detector to "click" according to the measurement result in Eves detector
- 32. Faked-state attackPractical Implementation - Force Bobs detector to click ● SPAD in linear mode ("blind SPAD) -> easily forced to create a "click" ● Sending pulse of light with intensity power "I0"
- 33. Faked-state attackPractical Implementation - Blind the detector ● Correct light pulse intensity is important ● (2*I0) is the answer!
- 34. Faked-state attackPutting them all together!
- 35. Faked-state attackResult of the Attack: Impressive! Bob@V Bob@-45 Bob@H Bob@+45 Eve@V 99.51% 0 0 0 Eve@-45 0 99.66% 0 0 Eve@H 0 0 99.80% 0 Eve@+45 0 0 0 99.95%
- 36. The end! Questions?

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