Department of Software
The University of Babylon
LECTURE NOTES ON Quantum Cryptography
By
Dr. Samaher Hussein Ali
College of Information Technology, University of Babylon, Iraq
Samaher_hussein@yahoo.com
17 December 2012
Introduction
• One: hard problems in mathematics
– Breaking the system requires an efficient algorithm for
solving a hard problem – e.g. Factoring large numbers,
discrete logarithms
– Examples: RSA, El Gamal
– Used in public key systems
– Slow
• Two: information theory
– Texts scrambled by repeated application of bit shifts and
permutations
– Examples: DES, AES
– Used in private key systems
– Fast
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Technology Determines What is Breakable
RSA
Cryptosystem
C = Me mod n
d = e-1 mod ((p-1) (q-1))
RSA vs. supercomputer: 40 Tflop/s (4 x 1012
flop/sec)
– RSA wins!
RSA vs. Quantum Computer
– computer wins!
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Modern Ciphers
vs. Quantum Computer
• “Hard problem” variety
– Exponential speedup – easily breaks
algorithms such as RSA
– If information requires long term protection
(e.g. 20+ years), these algorithms are already
dead
• “Information theory” variety
– Quadratic speedup (so far)
– Longer keys can keep them useful
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Quantum Crypto – Why?
Quantum Cryptography
• is one of the new field in the cryptography to design the system
promises of new level of security in the communication system
• Protect against attack by quantum computer
– or any future machine
• Eavesdropping detection
– Hard to do now
• High volume key distribution
– If it can be made fast enough
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Quantum Mechanics for Cryptography – Measurement Basis
• Basis – frame of reference for quantum
measurement
• Example – polarization
vertical/horizontal vs. diagonal
– Horizontal filter, light gets through = 0
– Vertical filter, light gets through = 1
– 45 deg. filter, light = 0
– 135 deg. filter, light = 1
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
No cloning theorem
• It is not possible to create perfect copies of a quantum state in
transit for the purpose of measurement, while sending on the
original. Consequently, current practical quantum cryptography setups are point to point based or at best within a Local Area Network
since optical fiber amplifiers cannot be used.
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Entanglement
• Two or more quantum systems can be
entangled
Causality and Superposition
Causality, together with the superposition principle can be used for
secure key distribution. If the two terms that constitute a
superposition state are sent with a time delay relative to each other,
and if they are not essentially connected, then Eve cannot spy on
them.
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
A Quantum Key Distribution with Single Photons
• The transmitter is traditionally called Alice and the receiver Bob,
while the intruder is called Eve.
Single photons

Quantum key distribution with single polarized photons was
originally proposed by Bennett and Brassard in 1984 (BB84
protocol).

There are two data transmission channels involved: the
classical (high density) and quantum (low density) channels.
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
BB84 protocol
•
Alice sends randomly one of the four quantum states
Bit value ‘0’
0 ,
1
2
Bit value ‘1’
1 ,
1
2
 0  1 
 0  1 
•
with equal probability,
•
When Bob receives a state from Alice, he chooses randomly either
0 ,
1 ,
• And also Bob result correlates with the bit Alice sent only when he
picked the right basis i.e. the one used by Alice. After Bob has
measured the necessary number of states, Alice communicates with
Bob via the classical channel and tells him when she used which basis.
They discard the cases in which they used different bases, and
therefore establish a secret key, called the sifted key.
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Comparing measurements
Alice’s Bit
0
1
0
1
1
Alice’s
Basis
+
×
×
+
×
Bob’s
Basis
+
+
×
+
×
Bob’s Bit
0
0
0
1
1
Photon
The test bits allow
Alice and Bob to test
whether the channel
is secure.
17 December 2012
Dr. Samaher Hussein Ali
Test bits
Notes of Lecture 12
Getting the Final Key
Alice’s Bit
0
1
0
1
1
Alice’s
Basis
+
×
×
+
×
Bob’s
Basis
+
+
×
+
×
Bob’s Bit
0
0
0
1
1
Photon
Test bits
discarded
Final Key = 01
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
Quantum Eavesdropping
•
It is impossible for Eve to gain perfect knowledge of the quantum state
sent by Alice to Bob. However, Eve can gain partial knowledge via a
probing auxiliary quantum system in contact with the signal so that they
interact, and then perform a projection measurement on the auxiliary
system to retrieve some information.
•
Ideally we can always identify Eve by the occurrence of errors during
transmission. But this is not that easy in the real world. There will always
be detector noise, misalignments of detectors and transmission losses. It
is not even possible in principle to distinguish errors due to noise from
errors due to intrusion. We therefore have to assume that all errors are
due to eavesdropping.
•
Since it is necessary that Alice and Bob share an identical string of bits,
they must rectify any discrepancy in their sifted key. This concerns error
correction and uses the public channel.
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12
QKD vs. Public/Private Key protocols
17 December 2012
Dr. Samaher Hussein Ali
Notes of Lecture 12