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Simultaneous Initiating EPR and Quantum
Channel by Quantum Key Distribution Protocol
Abdulbast Abushgra α & Khaled Elleithy σ
Abstract-
Cryptography is the background of protecting the
flowed information between various communicated parties.
Quantum cryptography gives the extreme trust to transferred
information by creating a unique secret key that is based upon
the law of physics. This paper will discuss a novel algorithm
that is presented through quantum key distribution (QKD)
protocol. This QKD protocol depends on parallel quantum
communications between participants within EPR and
quantum channels. The proposed protocol utilizes the EPR
channel to prove the authentication while the quantum channel
to transfer the shared key. Moreover, the proposed protocol
initiates the verification of the participant’s identity between the
communicators by the EPR channel. After that the transferred
data
into quantum channel will create the secret key that
contains a string of qubits as well as no need to communicate
into classical channel.
Keywords: entangled states, epr pair paradox, intercept-
resend attack (IRA), open-key string (OKS), and pauli-
matrices measurement.
I.
Introduction
ccording to several studies in the quantum
cryptography, approving the stability of quantum
key distribution protocol (QKDP) is based upon
resisting the QKD protocol to quantum security attacks.
These attacks have different algorithms and
mechanisms that are generally used to tap or eavesdrop
transferred data between various parties. The robust
scenario in using quantum cryptography is its
independency to utilize the law of physics through the
quantum channel, which can detect an error as long as
it occurs
during an eavesdropper or fiber-optics noise.
For instance, Intercept-Resend-Attack (IRA) is the well-
known quantum attack that threatens the submitted
photons from the sender to the receiver (Acín,
Masanes, & Gisin, 2003; Curty
&
Lütkenhaus, 2005). In
this scenario, Eve will mask itself as one of the legal
parties where she will measure the first particle of the
submitted entangled state, and she will try to resend the
new created qubit back to Bob. First, the EPR pairs are
anticipated to be located with Alice and Bob, but Eve will
not be detected at first check. However, because of the
property of EPR pairs, Eve will be detected during the
second error check that is because EPR pairs have
collapsed (Li & Zhang, 2006; Long & Liu, 2002).
The majority of QKD protocols face a difficulty
of identity’s determination, where the communicators
sometimes are not exactly sure who is the sender (or the
receiver). Several quantum attacks take this advantage
of missed identification between the communicated
parties. Therefore, the run time execution will suffer a
delay due to much time to restart a new communication
or errors correction, every time when the participants
find a noise in the quantum channel. On the other hand,
the shared data will be lacked if the connected parties
ignore the error rate that usually happens during many
quantum attacks.
Furthermore, using an authentication procedure
at the beginning of the communication between two or
more parties will rise the security rate of data
transmission. It can also avoid the Intercept-Resend
Attack (IRA) or Man-In-Middle Attack (MIM) (Gao, Qin,
Guo, & Wen, 2011; Peev et al., 2005) that are based
upon impersonating the sender or receiver or both. On
the other hand, making a separation between the
authentication phase (e.g. EPR channel) and the data
submission stage (e.g. Quantum channel) will increase
the live time execution that causes a chance for Eve to
catch or interrupt even a few communication qubits.
Therefore, merging the authentication and the
submission of data have the possibility to reduce any
eavesdropping chance.
This paper will introduce a new quantum key
distribution algorithm, which uses the two quantum
channels to ful fil the authentication between the
participants by EPR channel. Then the quantum channel
will be prepared at the same time of EPR
communications to submit a qubits (secret key data).
There will be early decision available to both
communicators to finish or keep the connection. First
part of this paper will demonstrate the initiation of EPR
and Quantum channels, and then will show the
measurement techniques that will be used at the
receiver side.
II. THE INITIATION OF THE EPR CONNECTION
In 2015, a quantum key distribution algorithm
(Abushgra &Elleithy, 2015) was presented, where it was
designed to be robust against common quantum
attacks. One such quantum attack was the Man-In-
Middle (MIM) attack, which causes an enormous leak of
A
Author
α
: He is PhD candidate at Computer Science and Engineering
Department, University of Bridgeport.
e-mail: aabushgr@my.bridgeport.edu
Author
σ
: He is Professor at Computer Science and Engineering
Department, University of Bridgeport. e-mail: elleithy@bridgeport.edu
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data into the quantum communication between Alice
and Bob. The proposed protocol prevents the MIM
attack according to the rules of MIM attacks. The MIM
attack relies on the fact that the MIM attack will lie or
pretend to be a sender or a receiver to both legitimate
parties (Yong, Huadeng, Zhaohong, &Jinxiang, 2009).
Moreover, the MIM attacker plays on the weaknesses of
verification identities between the communicated
participants.
The proposed protocol is initiated by a
communication into the EPR channel, where Alice (or
third party) submits a string of entangled states
|± |± as well as an unknown state|. The
unknown state is considered to be the identification
state, where the identification state includes initiated
strings of time t1, size of matrix m, and number of
matrices n, parity strings p, number of states s, raw
index R, and determinate time t2. The EPR
communication will not take a long time of execution
because the string of entangled states should be sent in
short. After that Bob measures the upcoming string
based on EPR theory (Entangled states) (Bell, 1964;
Ekert, 1991; Li & Chen, 2007), and then after tensor EPR
state (in random) with unknown state (Alice knows) Bob
receives a separate code to apply the proper gate,
which are one of the quantum gate (x, y, and z gates).
Bob will use these gates to measure the states in the
superposition. Next, Alice now knows that Bob had
received a portion of the right qubits if the percentage of
matched qubits is over 70%. Hence, Alice starts
negotiations with Bob to make sure there is no
eavesdropper. If Alice finds the matched qubits less
than 70%, she will announce Bob to restart another
communication.
In case, Alice accepts the EPR communication
outcomes, she will submit the string of qubits (data) as
in (Abushgra & Elleithy, 2015) into the quantum channel.
When Alice initiates the quantum communication within
the quantum channel, she knows that Bob has already
produced Open-Keys such as (t1, n, m, s, p, R, and t2).
On the other side, Bob measures the upcoming qubits
based on the number of states (s). He will have
enormous amount of measured qubits, where these
qubits will be reset in a number of matrices (n) based
upon the raw index (R). After that Bob inserts the parity
diagonal string (p) into the matrix to start correcting the
error phase. If the total of matrix raw summation was
even, it means there is no interruption. On the other
hand, if the total of the matrix raw was odd, Bob will
initiate reconciliation phase.
={1,,,,,,2}.
Fig.1 :
Shows the initiated open-key string that will be
submitted by Alice to Bob through EPR channel.
Fig.
2
:
Shows the proposed scheme between two
legitimate parties (A and B).
The submitted Open-Key (OK) string provides
the authentication by EPR entangled states, where each
photon is prepared by the sender or third party to be
merged with an unknown state (e.g. two dimension
state). Measuring an electron at the same time gives an
opposite result at each participant’s side by
conservation of linear momentum (Hwang & Lee, 2007).
Therefore, these electrons are employed in the
authentication phase because physically the photons
that represent the Open-Key travel faster than the light
speed. Moreover, the Open-Key string in the proposed
protocol includes the following characters that are used
to authenticate the communication between Alice and
Bob as follows:
• t1 is the initiated time.
• n is the used matrices that can be any number (i = 1,
2,… N).
• m represents the size of the matrix (or matrices) that
must be (a = b).
• p is the string of parity diagonal, which it should be
prepared simultaneously with EPR connection.
• s is the number of states that are bounded in two
types: orthogonal states, or non-orthogonal states.
• R is the row indices sequentially.
• t2 is termination time.
These characters must be submitted into the
Open-Key (OK) string by the EPR channel, and both of
the participants should know the included qubits by the
theory of entangled states. To measure the upcoming
qubits, it is necessary to use the Pauli-Matrices
(,,)(Shor & Preskill, 2000) in Bob’s circuit’s
Global Journal of Computer Science and Technology Volume XVI Issue V Version I
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Simultaneous Initiating EPR and Quantum Channel by Quantum Key Distribution Protocol
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side. Moreover, when Alice desires to share a classical
bit 0 with Bob, she initiates the EPR pairs in the state of
|. Also, Alice creates | state, if she wants to
share classical bit 1(Li & Zhang, 2006).
|=|0+|1
|=1
2(|0
|0 |1
|1)
|=1
2(|0
|1 |1
|0) .
Hence, the submitted particle should be
initiated in the previous entangled state, where the
position of eigenstate in the | are first |0, |1 and
second |0, |1. Then Alice keeps one of the qubits in her
quantum memory and submits the other qubits into EPR
channel. To figure out how the size of the used matrix
(or matrices), Bob must calculate the upcoming qubits
during the EPR channel in the equation as follows:
= |
=1
×.
Based on the received qubits, Bob can organize
the qubits into a matrix (or matrices) by the above
equation of Mxy where the whole received qubits are put
in the number of matrices n. Also, the|
=1is an
Open-Key string that represents the tensor of all
received qubits. Then Bob begins multiple sequential
steps to decide if the qubits are zero eavesdropping or
there was a noise during the communication.
III. THE MEASURED QUBITS INTO EPR CHANNEL
To re-sort the proper indices in their positions,
Bob should match the measured indices (Rj) with the
OKP (Ri) indices, which usually will be raw by raw. The
concluded matrix will be filled in by qubits either |
or | as well as the diagonal of the matrix (LEFT to
RIGHT) that will be filled by a parity string. The parity
string (p) is the qubits that should be located at the
matrix’s diagonal (UP to DOWN). Later, Bob sums the
qubits in each raw; if the summation is (0) that means
the first correcting phase is secure. Otherwise, Bob will
know that there is a noise or an eavesdropping when he
finds (1) as a summation of the matrix raw.
()= ()
where R is the index number of the matrix, and
{1, 2 … }).
The abovementioned security checks are not
the only security procedures into the proposed protocol,
where the implemented decoy states during Alice’s
preparation is a type of security protection against MIM
attacks. The decoy states are located in the upper-
triangle of the matrix ( {|0, |1, |, |}), where
it has a limited tolerance to lose some qubits through
the communication phase.
11 1
1×=11 1
1,
where | is the real qubits that will create the key,
| is the parity states that are placed diagonally in the
matrix, | is decoy states that usually are created
similar to real data in random, and | is the resorted
matrix’s rows after the measurement by Bob (
{1, 2 … }) as shown in figure (3).
The submitted qubits will not be effected by
eavesdroppers, in case, Eve tried to interrupt the
channel. The reason of standing against any Eve’s
interruption is involved through inability of realizing the
real qubits of the decoy qubits. Moreover, the string of
qubits will be such as one string of data, and there is no
variation between each photon.
IV. TRANSFERRED QUBITS INTO THE QUANTUM
CHANNEL
Alice initiates the qubits that she desires to
share with Bob at the same time while preparing the
EPR channel. Also, Alice should have the created qubits
in her memory to start submitting one by one in a string
mode. Although the participants are looking to
exchange secure data, the EPR connection, at first, is
used to solve the authentication phase. Moreover, both
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Simultaneous Initiating EPR and Quantum Channel by Quantum Key Distribution Protocol
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Fig. 4:
Shows the prepared qubits in one matrix by
three classifications, shared data, decoy states, and
parity states resorted from up to down and left to right
sequentially, where |⟩is the parity diagonal states, |⟩
is the data thatwill build the secret key, and |⟩is the
decoy states. (= ∈{1,2 … }).
Fig. 3 :
Shows re-sorting the received rows by Bob in the
proposed protocol between two matrices, where these
rows were received such as one string and sequentially
resorted in equal matrix.
Early View
parties now attempt to obtain correct data rather than
interrupted qubits by the eavesdropper or environment
noise. The submitted qubits will be in four states and
two non-orthogonal bases.
|=1
2(|0+|1),
|=1
2(|0+|1).
There are multiple options available to transfer a
qubit through quantum channel and make the
submission secure. One such option is that Alice can
communicate with Bob in multi-states |, where Alice
decides through the EPR channel the dimension of the
used photon that will be submitted to Bob (e.g. two
dimension or more). This is an optional technique that is
used; especially, when the secret key should be created
to match big data such as in OTP.
Therefore, the proposed algorithm proved its
stand against two common quantum attacks. These
attacks as mentioned above are IRA and MIM attacks,
which both of these attacks are still considered the most
concerns around submitting a data through a quantum
channel. Also, there is ability to create a huge secret key
to match the whole data as long as the quantum
memory is available.
V. CONCLUSION
The proposed QKD algorithm has proved its
stability of trusted communication through the quantum
channel as well as it is robust against MIM and IRA
attacks. The protocol was built, in general, to fulfill the
authentication between the communicated parties
through the quantum channel. Moreover, the QKD
protocol has employed simultaneous exchanges either
into the EPR channel (authentication) or quantum
channel (sharing a secret key) that maximally sustains
the flowing of data into secure phase. As a result, the
proposed protocol has been tested and simulated
mathematically by MATLAB in classical system and has
proved its security against common quantum attacks.
Therefore, the proposed protocol is specified by using
two parallel quantum channels to prove the
authentication between the communicated parties
before exchanging secret key plain-text.
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Lütkenhaus, N. (2005). Intercept-resend
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