Quantum Cryptography

Arinto Murdopo Maria Stylianou

Ioanna Tsalouchidou

13/12/2011

Outline

● Quantum Cryptography● Theoretical Background ● Quantum Key Distribution (QKD)

○ BB84 Protocol● Vulnerabilities & Attacks

○ Faked - state attack

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

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

Theoretical Background

Filter to distinguish polarized photons. Correct Filter applied Wrong Filter applied

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 - BB84

Quantum Key Distribution - BB84

Step 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 - BB84

Step 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 - BB84

Step 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 - BB84

Step 2Example of how PBS combining with detector works!

Quantum Key Distribution - BB84

Step 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 - BB84

Step 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!

Entangled photon pairs

BB84 with photon pairs

Faked-state attack

General scheme

Faked-state attack

Practical Implementation - Detector replica● Eve has replica of Bob's detector ● To capture the photon and measure it like Bob always does

Faked-state attack

Practical Implementation - Fake Stated Generator

● Blind Bob's detector○ Insensitive to photon

● Forces Bob's detectors to have same "click" as what Eve has measured

○ Bob and Eve have same information

Faked-state attack

Practical Implementation - Blind all Bob's detectors● QKD detectors use Single Photon Avalanche Diode (SPAD)

Faked-state attack

Single Photo Avalanche Diode● Has two modes

○ Geiger Mode○ Linear Mode

Hence, SPAD in Linear Mode can be considered as blind-to-photon.

Faked-state attack

Single Photo Avalanche Diode● How to make SPAD behaves in Linear Mode?

Faked-state attack

Single 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

● SPAD's bias voltage below VBreakdown -> Linear Mode

Faked-state attack

Single Photo Avalanche Diode● SPAD in Linear Mode

●

Faked-state attack

Practical Implementation - Force Bob's detector to click● Blinding Bob's detector is not enough● Eve needs to force specific Bob's detector to "click"

according to the measurement result in Eve's detector

Faked-state attack

Practical Implementation - Force Bob's 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 attack

Practical Implementation - Blind the detector● Correct light pulse intensity is important ● (2*I0) is the answer!

Putting them all together!

Faked-state attack

Faked-state attack

Result 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%

The end!

Questions?