Implementation of Practically Secure
Quantum Bit Commitment Protocol
Ariel Danan
School of Physics Tel Aviv University
September 2008
Project Members:
 Ariel Danan, Yoav Linzon
(With a lot of help from Ezra Shaked- electronic workshop)
Academic supervisors:
 Lev Vaidman and Shimshon Barad
Outline









Introduction
Bit Commitment
Practically Secure Quantum Bit Commitment
Phase Encoding with Optical Fibers
Experimental Setup
Demonstration (Q.O. lab)
Security Discussion
Final Results
Future Prospects
Introduction

Quantum Information → Quantum computers

(Grover's quantum search , Shor's quantum factoring ….)
Quantum Key Distribution ↔ ‘No Cloning Theorem’


Unconditionally Secure Quantum Bit Commitment → ‘No Go Theorem’
Practically Secure Quantum Bit Commitment
Based on the limitation of current technologies
(Non-demolition measurement and long quantum memory)
Introduction

Lev’s Practically Secure Quantum Bit Commitment Protocol
Patent Pending → The term Non Demolition measurement was not used
in the thesis

Implementation of Practically Secure Quantum Bit Commitment using low
cost quantum optics devices
What is Bit Commitment?

Committing phase:
Alice select a bit, put it in a strong box and sends
0
or
it to Bob
1
Alice

Bob
Opening Phase:
Alice sends the key to Bob and he reveals her commitment
Alice
Bob
Both Classical and Quantum Unconditionally Secure bit
commitment is impossible!
0
or
1
Applications
‫רק לא‬
@!‫גיידאמק‬
#

Secure Commercial Biding

User Authentication

Lon distance coin Tossing

Oblivious Transfer (Two party secure computation)
?
‫אתמול היה‬
‫לי יותר‬
Conjugate observables

Photon has 2 bases of polarization that don’t commute.
Rectilinear basis:
eigenstates of σz
Diagonal basis:
eigenstates of σx
Practical secure QBC protocol
Committing phase:

Bob sends photons prepared randomly in one of the 4 polarization
{



} to Alice.
Bob keeps the record of when and what he sent to Alice.
Alice measures all photons in one of two bases which manifests her
commitment
{
} =0 {
} = 1.
She announces immediately the time of detection of the photons.
Pulse No. 1042 (0,0)
b =0
or
b =1
Pulse No. 1043 (1,1)
Pulse No. 1044 (0,1)
Pulse No. 1045
Alice
Pulse No. 1045 (1,1)
Bob
Opening Phase:
-Alice reveals her commitment (measurement base) and the measurements
outcomes.
-Bob checks Alice’s answers.
Alice
Bob
Advantages
1.
2.
3.
4.
5.
Cheating tasks (long-time Qubit memory, Perfect Nondemolition Measurement) are beyond current technology
No need for high fidelity (the security increase exponential
with the number of Qubits per commitment).
Short distances possibility (unlike Classical bit commitment)
Since Alice don’t control the information she gets, it’s more
difficult for her to cheat.
Bob cannot gain information about Alice's commitment or
measurements outcomes before she announces them.
Phase Encoding with Optical Fibers
Sent
Qubit
Meas.
Basis
D0
D1
0,0
0
25%
0%
1,0
0
12.5%
12.5%
0,1
0
0%
25%
1,1
0
12.5%
12.5%
1
12.5%
12.5%
1,0
1
25%
0%
0,1
1
12.5%
12.5%
1,1
1
0%
25%
0,0
Phase Encoding Principle. Two pulses exit Bob apparatus,
and interfere on Alice’s side.
{1  0}   {1   }  
{1 

2
}
{1 
3
}
2
Φ1
Φ2
0
0

2

3
2
0

2
0
0
0

2

2


3
2

2
2
Experimental Setup
Transmitter
Bob
2X2 fiber coupler
(Beam splitter)
-0.25 0.000.25
Pulse modulator
Laser
Encoder
ND
filter
1
-0.25 0.000.25
Trigger Card
SPD(1(
-0.25 0.00 0.25
SPD(0)
2
-0.25 0.00 0.25
-0.25 0.00 0.25
-0.25 0.00 0.25
-0.25 0.00 0.25
Optical fiber
P.C.
-0.25 0.000.25
Synchronizer
Serial com.
Receiver
Encoder
Alice
-0.25 0.000.25
-0.25 0.00 0.25
Nanosecond
pulse laser
Phase shifter
(Piezoelectric
mount)
P.C.
Data
Acquisition
Single photon
detector (~25%
efficiency )
Polarization
controller
Optical line performance
Visibility
L-S + S-L interference pulse
L-L pulse
S-S pulse
Classical regime
Quantum regime
Low Fidelity Source
Michelson interferometer measurement with short pulses: (a) without
interference; (b) & (c) interference with two different phase shifts
The system's Stability - ~0.3s
Photon losses – path transmissivity
Let’s Go To The Q.O. Lab
For a Demonstration
Security Discussion

Bob’s Cheating:
1.
Look for correlations between detection efficiency and
sent qubit base.
2.
Alice has different setting time for different measurement
base.
3.
Trojan Horse Attack

Alice’s Cheating:
1.
Non Demolition and Quantum Memory Attack
('no go theorem' ); not feasible with today's technological limit.
2.
Random Base Attack
Imposes 25% quantum bit error rate (QBER)
3.
Photon Number Split Attack
To prevent this kind of attack the ratio of the probability
for having two photon (or more) in a pulse and Alice's
supposed detection probability must be smaller than one.
4.
Combined Attack
Imposes
Security Discussion with Low Fidelity source

Bob has a low fidelity output which imposes an additional
QBER ( )
1.
Random Base Attack:
Imposes
3.
Photon Number Split Attack:
Will not effect PNS like attack
4.
Combined Attack:
Imposes
Final Results
Opening stage results (1 photon per pulse
•Each protocol took about two hours to be complete
•All QBC protocol results do not exceed the standard deviation range
and are acceptable commitments.
)
Final Results
Opening stage results(0.2 photon per pulse
)
•Each protocol took about a day to be complete.
•All QBC protocol results do not exceed the standard deviation range
and are acceptable commitments.
Fragile Security- to increase security the number of sent qubits per
commitment must be increased (2000)
Probably the first practically secure
QBC system in the world
Future Prospects

Improve Quantum Bit Error Rate
1.
Single photon source
(Spontaneous parametric Down-Conversion)
2.
Improve pulse coherence

Faster
1.
Real time Labview \ Design DSP circuits
Change Piezo with Crystal for E-O modulation (LiNbO3)
2.
Q&A
What did he
say?
You
don’t
say!