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QKD protocol based on entangled states by trusted third party

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QKD Protocol Based on Entangled States
By Trusted Third Party
Abdulbast A. Abushgra Khaled M. Elleithy
Computer Science & Engineering Department Computer Science & Engineering Department
Unversity of Bridgeport Unversity of Bridgeport
USA USA
aabushgr@my.bridgeport.edu Elleithy@bridgeport.edu
Abstract— Quantum cryptography is considered a solution
for sharing secret information in a secure mode. Establishing a
quantum security platform into an exciting system requires a
package of stable processes. One of these processes is based on
creating a Quantum Key Distribution (QKD) protocol or sharing
a secret key. This paper presents a QKD protocol that utilizes
two quantum channels to prepare a shared secret key. The first
communication channel will be initiated by entanglement states,
where the entangled photons will be emitted by a trusted third
party. The second communication channel utilizes the
superposition states that will be initiated by the one of the
communicated parties. Moreover, the protocol produces a string
of random qubits after verifying the communicated legitimate
parties during entangled state channels. The produced string will
reflect the shared secret key between the users.
Keywords- Entangled State, Superposition State, Qubits, Decoy
State, and Bell’s States.
I. INTRODUCTION
Flowing enormous data through various communication
channels causes leaks of important information through
classical communications by eavesdroppers. Classical
cryptography has several algorithms that defend against many
information attacks (these algorithms are still secure as long as
the quantum computer is conceptual). Furthermore, quantum
cryptography provides security of information with some
challenges that are determined in quantum attacks or natural
noise. In 1984, Charles Bennett and Gilles Brassard invented
[1] the most sparkling quantum key distribution protocol,
which is called BB84 protocol. Several QKD protocols then
were invented (such as B92 protocol [2], SARG04 protocol [3],
EPR protocol [4], and DPS protocol [5]).
Any quantum key distribution protocol technically uses
different channels to submit qubits (Quantum Bits) for data
transmission, with and regular bits for either confirming or
reconciling the submitted qubits. Each quantum channel is
initiated in varying environments that specifies the type of
platforms and used tools (such as transformers and detectors).
First of all, the quantum channel should utilize either Viper-
Optics or Free-Space to transfer a qubit from one side to
another; both cannot be protected totally from eavesdroppers.
The quantum mechanics is the only factor that makes quantum
communication unconditionally secure [6]. Moreover, the rules
of physics keep the whole system that is used active (as long as
no attempts to break the system). Therefore, any illegal alien
will be detected by destroying the system.
Furthermore, using multiple polarized states of a particle
and the measurement process of the same particle determine
the stability and efficiency of each QKD protocol. Fulfilling an
authentication between two or more communicators is one of
the challenges that cause an enormous leak of information if
the communicators cannot verify each other. This paper
presents a new algorithm that is designed to prove the
authentication within an entangled channel. The presented
protocol is based upon two quantum channels: one channel is
EPR channel (entangled states channel) and second channel is
quantum channel (qubits channel). The protocol will be
terminated in case the authentication between the
communicated parties is interrupted.
II. THE PROPOSED PROTOCOL MECHANISM
A. The EPR Preparation
Initiating an EPR connection should be done by submitting
EPR photons to the receiver (Bob). The source of EPR photon
would be from the sender (Alice) or a third party; but in this
proposed protocol, the third party will be confirmed. The
submitted EPR string S
EPR
contains several characters, which
are considered an open key for the whole scheme. These
characters involve a sequence of information (such as initiation
time t
1
, number of matrices n (if any), matrix size m, parity
diagonal p, state dimension s, matrix indices R, and termination
time t
2
) as in figure (1).
Fig. 1 The EPR string prepared by the sender.
The sender (Alice) is supposed to start talking with the third
party by sending a copy of the plaintext into a classical
2
channel. Next, the trusted third party will convert the plaintext
to encoded information

to be transferred into
entanglement states. Both of the communicated parties (the
sender and receiver) will receive a copy of the entangled
photons at the same time. The EPR string S
EPR
is the encoded
plaintext that will be shared between the sender and receiver.
The string contains particles of Pauli states (
,
,
)[7].
Each photon has two states|, where | should be sent to
Alice and the | will be sent to Bob. Based upon the
theoretical measurement and the fact of EPR photons, both
parties can initiate the communication in safe mode.

=

(1)
|EP
R

=1
2(|00

±|11

)
(2)
|EP
R

=1
2(|01

±|10

)
(3)
|=|0
±|1
(4)
Fig. 2 The communication between the third party with Alice and
Bob.
B. The Qubits Preparation
To create a secret (shared) key, Alice is supposed to know
the information that will be submitted to the other party. The
plaintext should be converted to qubits (data), and the third
party then sets up the converted plaintext into a designed
matrix. The matrix matches the length of the plaintext n as
follows:
 = log
,
(5)
where DM is the size of the used matrix and n is the length
of the converted plaintext.
Next, the third party will fill up the lower and upper
triangles (the diagonal line is not included) by the converted
qubits of the plaintext. The filling scenario starts from up to
down in the lower triangle and from down to up in the upper
triangle, as shown in figure (2). The whole matrix will be filled
as a result except the diagonal line, where the third party
adjusts the diagonal cells based on the summation of each row.
If the summation of the row is odd, the third party will add (1)
to the empty cell to make the row even. On the other hand, if
the summation of the row is even, it will be added (0) bit to the
cell. Therefore, the third party prepares the whole matrix with
even row’s summation; this will be an extra protection against
PNS attacks [8], where Alice and Bob will know if the
upcoming qubits were interrupted by eavesdroppers or
environment.
Fig. 3 The prepared matrix into three sections: lower triangle, upper
triangle, and diagonal line.
III. COMMUNICATION CHANNELS
A. EPR Channel
In 1935 [9], Einstein, Podolosky, and Rosen came up with
their fabulous paper that opened a huge argument about the
wave function and incompleteness of quantum mechanics. The
main concept of EPR is a photon submission from the source
(X) to two different destinations (e
1
, e
2
). The measurement, in
the case of no interruption, will demonstrate a different state at
each side. Moreover, if Alice (one of the communicators or the
sender) received|0, then Bob (one of the communicators or
the receiver) should have |1after his measurement. The
presented algorithm is initiated by creating an EPR channel and
the protocol will be described as follows:
Alice sends n bits of the plaintext (the length of the
plaintext) to a third party.
The third party converts the plaintext to EPR states
(,|Ψ) based on the plaintext, and then sends the
EPR states into separate channels (where one state is
sent to Alice EPR
A
and the other state is sent to Bob
EPR
B
).
Alice creates an unknown photon (e.g.|=
|0+
|1), which is in the superposition state.
3
Calculating both the entangled state and
superposition state (

⨁|
) to produce a three-
dimension particle state.
Alice separates the three states, where | will
become||.
The first outcome of | becomes entangled and |
is separated (or became in superposition).
Alice submits two classical bits
(|00,|01,|10,|11) for the used gates at both
sides.
Fig. 4 The photon emits from the source, and the measurement
will be same color if one side measured.
Therefore, the authentication between the communicated
parties should either be approved to move on or to start over.
After that, Bob should have the proper quantum gates as
well as the photon states.
Algorithm .1 QKD Protocol
1. Submit n bits to well-known third party (p) by A
2. n (|Ψ|Φ) // First loop
3.


|0
|1 // P sent a pair to both A&B
4. if (A == 0) then (B == 1) // Second loop
5. B 1
6. else: error
7. end; // ending the loop
8. A |
9. for: 1 n //Measuring & reconciliation
10. (|Ψ⊕|) // Third loop
11. end; //use the data collected by EPR
12. B {0,1} // B gets the secret key
The proposed algorithm runs through three loops that are
involved in submitting a plaintext to a third party, initiating an
EPR connection by the third party, and the quantum
communications between the sender and receiver.
B. The Classical Communication
To ensure that Bob has the right quantum gates (as in figure
(5)) Alice initiates a communication into a classical channel.
Two bits have the needed information that Alice should send to
Bob. Each two bit has a meaning of a certain quantum gate; the
(00) bits mean using the unitary operator, (01) Z gate, (10) X
gate, and (11) X and Z gates. These gates are the only classical
operation that Alice and Bob need to use during the entire
system procedures.
Fig. 5 The three quantum gates (X, Y, and Z) used into
exchanging channel.
00−−−−→
01−−−−→
10−−−−→
11−−−−→&
Moreover, interrupting the classical communication will not
impact the protocol processes because the receiver will get
unmatched qubits during the preparation of the upcoming
qubits. Also, the decoy states (diagonal line) will show some
huge variations.
C. Quantum Channel
After an authentication proof, both parties start exchanging
qubits (data) into the quantum channel. The submitted qubits
will be in two bases (,|+) and four states
(|0,|45,|90,|135). Alice creates the qubits based on
the EPR
A
that was submitted by the third party; and Bob will
use Pauli-matrices with prior knowledge to measure the
upcoming qubits from Alice into the right states [10]:
=
01
10
,
(6)
=
0−
0
,
(7)
=
10
0−1
.
(8)
The physical measurements should all be correct because
Bob has already agreed on the EPR
B
confirmation. Moreover,
the mechanism of data organization into a matrix setup will
assist to protect qubits from any quantum attack. On the other
hand, Bob can realize any changes in the received qubits and he
can figure out the error by diagonal decoy states.
4
Fig. 6 The whole mechanism for the proposed scheme in two quantum
channels.
IV. THE PROPOSED PROTOCOL SIMULATIONS
A. The Runtime-Execution
To test the simplicity of the proposed protocol, it was
simulated technically by measuring the run time execution
during the generation of a secret key by two legitimate parties.
The simulation is considered a test of the time taken from
initiation the communication to generation of the secret key.
Even the loops that were required for some function will be
included, as well as the reconciliation phase. The following
equation will simply explain the calculation of the run time
execution:
 = 
(9)
where P is the required loop for each function process
into the entire algorithm initiation.
The proposed protocol runs in a low time rate if there is no
error created by eavesdropper. On the other hand, applying an
error during the communications between the legal parties will
increase the rate of time taken to create a secret key.
B. The Efficiency
Based upon the measurements that were applied on the
proposed protocol, the efficiency can be approved by
measuring the Qubit Error Rate (QBER). The total of used
qubits at the beginning of the communication will be different
at the end for many reasons. The environment is one reason
that causes a qubit drop or weak light. Quantum attacks can
also cause several damages to the submitted qubits, either by
splitting the state of the photon or by interrupting and
resending a photon.
The efficiency measurement was applied by counting the
QBER, where correcting errors should be realized by the
following equation [11, 12]:
 =
(10)
where n is the total of the submitted qubits, and r is the
qubits that were measured and successfully uncovered. The
results show the proposed protocol is efficient even if the
quantum attacks are applied. Therefore, there is no leaked
information even if the eavesdropper tried to use one of the
attacks scenarios.
Fig. 7 The correlation between submitted and received qubits
measured with 50 qubits.
The correlation in the figure (7) between the submitted and
received qubits reflects the difficulties of finding out the
relation between the two parties. Hence, the main point is
utilizing a matrix either in sorting submitted qubits or re-
sorting received qubits; this usually is considered as an
advantage to hide the core of a created secret key.
C. The Security
The security measurement is applied by several methods, but
this proposed protocol utilizes Shannon Entropy [13, 14] to
measure the level of security. The probability in the next
equation shows the rate of corrupted qubits of the received
qubits:
=−
log
(11)
where P
i
is the probability of the shown character (certain
qubits) in i numbers.
The security measurement can be applied into the entropy
of security in general, where it can measure the rate of
uncovered qubits .
()=−
×log(
)
(12)
where log represents the natural logarithm (the
logarithm with the base e). The constant e is called Euler’s
number and it is equal to an approximately:  ≈ 2.71828
[15]. Moreover, k is the uncovered qubits that should be
5
measured by Bob and n is the total of qubits that are submitted
by Alice.
Fig. 8 The entropy of security measured for the proposed protocol
that confirmed by a third party.
The figure (8) demonstrates the S(k) function to calculate the
entropy of security, where the used key length is 32 qubits.
The rate of uncovered qubits will be approx. 0.53 qubits of the
secret key.
I. CONCLUSION
The proposed scheme presents a quantum key distribution
protocol that is essentially designed in two quantum channels.
The EPR channel (confirmation channel) uses the entangled
states rather than states in superposition, which has a low risk
and certain probability. The second channel is utilized to
transfer data from sender to receiver with the ability to detect
any interruption. Generally, the proposed scheme treats
missing authentication between legitimate parties in most
well-known quantum key distribution protocols. Also, it uses
qubit preparation in matrix (or matrices if any) by the sender,
which is considered a powerful procedure to ignore PNS and
IRA attacks. The proposed scheme has approved its stability
against the Man-In-The-Middle attack, where there is no
chance to impersonate the sender or the receiver.
V. REFERNCES
[1] C. H. B. G. Brassard, "Quantum Cryptography:
Public Key Distribution and Coin Tossing "
International Conference on Computers, Systems &
Signal Processing, p. 5, December 10 - 12, 1984
1984.
[2] C. H. Bennett, "Quantum cryptography using any two
nonorthogonal states," Physical Review Letters, vol.
68, p. 3121, 1992.
[3] V. Scarani, A. Acin, G. Ribordy, and N. Gisin,
"Quantum cryptography protocols robust against
photon number splitting attacks for weak laser pulse
implementations," Physical Review Letters, vol. 92,
p. 057901, 2004.
[4] A. Einstein, B. Podolsky, and N. Rosen, "Can
quantum-mechanical description of physical reality
be considered complete?," Physical review, vol. 47,
p. 777, 1935.
[5] K. Inoue, E. Waks, and Y. Yamamoto, "Differential-
phase-shift quantum key distribution using coherent
light," Physical Review A, vol. 68, p. 022317, August
27 2003.
[6] H.-K. Lo, X. Ma, and K. Chen, "Decoy state quantum
key distribution," Physical Review Letters, vol. 94, p.
230504, June 16 2005.
[7] A. Abushgra and K. Elleithy, "QKDP's comparison
based upon quantum cryptography rules," in 2016
IEEE Long Island Systems, Applications and
Technology Conference (LISAT), 2016, pp. 1-5.
[8] M. Elboukhari, M. Azizi, and A. Azizi, "Quantum
key distribution protocols: A survey," International
Journal of Universal Computer Sciences, vol. 1, pp.
59-67, 2010.
[9] A. K. Ekert, "Quantum cryptography based on Bell’s
theorem," Physical Review Letters, vol. 67, p. 661,
1991.
[10] A. Abushgra and K. Elleithy, "Initiated decoy states
in quantum key distribution protocol by 3 ways
channel," presented at the Systems, Applications and
Technology Conference (LISAT), IEEE Long Island,
New York, 2015.
[11] D. Gottesman, L. Hoi-Kwong, Lu, x, N. tkenhaus,
and J. Preskill, "Security of quantum key distribution
with imperfect devices," presented at the
International Symposium on Information Theory.
ISIT 2004. Proceedings., Chicago, IL, USA, 2004.
[12] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and
W. K. Wootters, "Mixed-state entanglement and
quantum error correction," Physical Review A, vol.
54, p. 3824, 1996.
[13] D. J. MacKay, Information theory, inference and
learning algorithms: Cambridge university press,
2003.
[14] Y. Huang, "Computing quantum discord is NP-
complete," New Journal of Physics, vol. 16, p.
033027, 2014.
[15] M. Niemiec and A. R. Pach, "The measure of security
in quantum cryptography," in Global
Communications Conference (GLOBECOM), 2012
IEEE, 2012, pp. 967-972.
... Schere et al. [34] implemented the ES− BBM92 protocol in experimentally rely on existing technology. Since then, some attention has been devoted to entangled-based QKD [35][36][37][38][39]. ...
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