Quantum Cryptography and Possible Attacks

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

- 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 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)

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

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

Step 2
How 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

Step 2
Example of how PBS combining with detector works!

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%

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

Step 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

Step 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!

Step 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 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
● How to make SPAD behaves in Linear Mode?

Faked-state attack
● 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
● 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%

Quantum Cryptography and Possible Attacks

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