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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

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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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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.

ReferencesRéférences Referencias

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Curty, M., &

Lütkenhaus, N. (2005). Intercept-resend

attacks in the Bennett-Brassard 1984 quantum-key-

distribution protocol with weak coherent pulses.

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Ekert, A. K. (1991). Quantum cryptography based

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