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UPC - Universitat Politecnica de Catalunya

A forgotten presentation we did last year.

Just found it thanks to Arinto Murdopo :) http://www.slideshare.net/arinto

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- 1. Quantum CryptographyArinto MurdopoMaria StylianouIoanna Tsalouchidou13/12/2011
- 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 ofgood 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 theoremPolarized Wave Applet! http://surendranath.tripod.com/Applets/Waves/Polarisation/PW.html
- 6. Theoretical BackgroundFilter to distinguish polarized photons.Correct FilterappliedWrong Filterapplied
- 7. Quantum Key Distribution - BB84● First quantum cryptography protocol● Goal: describe a scheme of two users who want tocommunicate and exchange data securely.● Idea: distribute a key securely, based on the laws ofphysics.● Security proofs:○ If someone reads the state of photon -> state changes○ Not possible to copy the photon in order to encode it withall possible ways (basis)
- 8. Quantum Key Distribution - BB84
- 9. Quantum Key Distribution - BB84Step 1● Alice has two choices, key (a) & basis (b), chosenrandomly● Combine bits of a and b, 1-1,● Four different states of qubit (photon polarization)● Sent through public quantum channels:○ Optical Fiber○ Free SpacePhoton Source
- 10. Quantum Key Distribution - BB84Step 2● Bob receives qubit from Alice● Bob measures it by choosing random basis usingBeam 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 tothe correct detector● Otherwise, the photon can head randomly to any of thewrong 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 publicchannel● They compare the basis used to encode and measurethe 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 lengthbecause the probability of Bob choosing the same basisas Alice is 50%
- 14. Quantum Key Distribution - BB84Step 4● Check if someone has intruded the communication or ifsome imperfection of the devices or channel hasintroduced noise that distort the outcome● If Eve has intruded the communication, she willDEFINITELY left some traces due to HeisenbergUncertainty 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 intrudedthe 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 aresame● The problem is, in Step 4, Eve manages to find out someportions of their key● Privacy Amplification comes into the rescue!
- 17. Quantum Key Distribution - BB84Step 5● Alice and Bob apply Hash function to compress the keyinto the final one. And they should use the same Hashfunction.
- 18. Vulnerabilities - Photon number attack● Sending more than one photon for each bit leads to photonnumber attack.○ Eve can steal extra photons to extract thestolen photons information.● Ensure photon spitter only sends exactly ONE photon eachtime.● Single photon ensures quantum mechanic laws aresatisfied.
- 19. Vulnerabilities - Spectral attack● If photons are created by four DIFFERENT laser photodiodes, they have different spectral characteristics.● Eve performs spectral attack by measuring COLOR, and notpolarization.
- 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 provenmathematically○ Algorithms generate "random" sequences by followingspecific 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 Evehas 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 timeto 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 tocreate 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. Putting them all together!Faked-state attack
- 35. Faked-state attackResult of the Attack: Impressive!Bob@V Bob@-45 Bob@H Bob@+45Eve@V 99.51% 0 0 0Eve@-45 0 99.66% 0 0Eve@H 0 0 99.80% 0Eve@+45 0 0 0 99.95%
- 36. The end!Questions?

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