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!
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
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)
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
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
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
Quantum Key Distribution - BB84Step 2Example of how PBS combining with detector works!
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%
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
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
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!
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.
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.
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.
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!
Faked-state attackPractical Implementation - Detector replica ● Eve has replica of Bobs detector ● To capture the photon and measure it like Bob always does
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
Faked-state attackPractical Implementation - Blind all Bobs detectors ● QKD detectors use Single Photon Avalanche Diode (SPAD)
Faked-state attackSingle Photo Avalanche Diode ● Has two modes ○ Geiger Mode ○ Linear ModeHence, SPAD in Linear Mode can be considered asblind-to-photon.
Faked-state attackSingle Photo Avalanche Diode ● How to make SPAD behaves in Linear Mode?
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
Faked-state attackSingle Photo Avalanche Diode ● SPAD in Linear Mode ●
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
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"
Faked-state attackPractical Implementation - Blind the detector ● Correct light pulse intensity is important ● (2*I0) is the answer!