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Abstract— In this paper we propose a new protocol for

multiparty secret key sharing by using quantum entanglement

swapping. Quantum Entanglement swapping is a process that

allows two non-interacting quantum systems to be entangled.

Further, to increase the security level and to make sure that the

users are legitimate, authentication for both parties will be

required by a trusted third party. In this protocol, a trusted third

party will authenticate the sender and the receiver and help them

forming a secret key. Furthermore, the proposed protocol will

perform entanglement swapping between the sender and the

receiver. The result from the entanglement swapping will be an

Einstein-Podolsky-Rosen (EPR) pair that will help them in

forming and sending the secret key without having the sender to

send any physical quantum states to the receiver. This protocol

will provide the required authentication of all parties to the trusted

party and it will provide the required secure method in

transmitting the secret key.

Index Terms—cryptography, entanglement, EPR, multiparty,

quantum swapping

I. INTRODUCTION

QUANTUM Mechanics unique properties and laws are the

keystone to quantum computing and quantum information

theory. Quantum computing have been providing prom-

ising solution to the difficult problems in classical computing.

For instance, quantum teleportation, entanglement and paral-

lelism are contributing in computing by providing new

techniques that differ from the current techniques in classical

computing [1-4].

Many protocols based on quantum entanglement and

quantum teleportation have been proposed to provide solutions

to the different challenged in classical computing networks and

data security [5-11]. Quantum entanglement is the basic

element in quantum teleportation which is a significant protocol

in quantum cryptography for secure data transmission. The

aim from the different proposals in quantum cryptography

protocols is to find new unconditional security protocols instead

of the current security protocols in the classical cryptography.

Which depend on the computing difficulty to compute the

secret key.

Transmitting an arbitrary unknown state from a sender

named Alice to a receiver named Bob where there is a

significant distance between them. Yet, teleportation require a

quantum channel to send the unknown state and a classical

communication channel. The need for classical channel in

teleportation is when Alice send the unknown state to Bob, the

Alice will have to send codes through the classical channel to

help Bob recovering the state. Note that in quantum copying

of a state is not possible without disturbing the original state.

Therefore, the process of teleportation moves the state from one

location to another and do not copy the state because copying

of quantum state is not possible due to the no-cloning theorem

[12]. Since the teleportation uses two different type of

channels, an eavesdropper could try to manage to be on these

communications path to perform malicious activities. Thus,

the routing path will no longer be secure for sending and

receiving messages [12, 13].

Remote state preparation (RSP) of quantum state is an

interesting protocol to send a known to the quantum state to the

sender and prepare it to the receiver was presented by Lo [13].

RSP depends on the benefits that the EPR pairs provide using

the prior entangled states. RSP is similar to quantum

teleportation with some differences. For example, in

teleportation the sender send an unknown state where in RSP

the sender send a known state. Further, there are two

communication channels required in teleportation however, in

RSP it require only one classical communication channel. Pati

[14], Bennett et al [15] have investigate RSP and other

researchers have continue to study and provide new theoretical

types of RSP [16-24]. Moreover, experiment on RSP have

been conducted by Peng et al [18] and Xiang et al [20].

In this protocol we assume that Alice and Bob want to share

a secret key. However, a trust between Alice and Bob need to

be established so Alice can share her secret state with Bob and

Bob want to make sure that Alice is a legitimate user and not an

intruder. Therefore, a trusted party for Alice and Bob will be

required to authenticate them to each other’s. As a result, Alice

will have enough trust to form and share a secret key to Bob.

After the authentication process, the trusted party will create

and EPR pair between Alice and Bob to be used in their

communication. The communication between Alice and Bob

will be based on Alice measurement to her qubit in the EPR.

The organization of this paper will be as follow. After we

started with introduction in section I we will cover some of the

basics and background of quantum computing in section II.

Then we will cover the related work in the literature in section

III. After that, the proposal protocol with the steps required

to process it in section IV. Finally the conclusion and the final

remarks in section V.

Authenticated Multiparty Secret Key Sharing

Using Quantum Entanglement Swapping

Muneer Alshowkan, Student Member, IEEE, Khaled Elleithy, Senior Member, IEEE

Q

Muneer Alshowkan, Department of Computer Science and Engineering,

University of Bridgeport, Bridgeport, USA; malshowk@bridgeport.edu.

Khaled Elleithy, Department of Computer Science and Engineering,

University of Bridgeport, Bridgeport, USA; elleithy@bridgeport.edu.

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II. QUANTUM COMPUTING PRELIMINARIES

A. Quantum bits

Quantum computing takes the advantages of the laws of

quantum mechanics to efficiently solve the difficult problems

in classical computing. Having the bit as the fundamental unit

in classical computers to represent and store data. Where, the

name of the same unit in quantum computing is called qubit.

The difference between a bit and qubit is that a bit represents

one of two different disjointed states such as a signal to be high

or low, a switch to be on or off or logical value true or false.

However, a qubit can represent one state or two states

simultaneously such as a switch to be on and off or logical value

to be true and false at the same time. The notation of one qubit

is for zero and for one. When a qubit is in both states

and it state is called a superposition and it can be

represented as a linear combination of both stats as:

(1)

The coefficients and the coefficient are complex

numbers in Cn and the states and are an orthonormal

basis in the two-dimensional vector space. The value

determination in classical and quantum computers are different.

For instance, we can easily examine a classical bit and

determine if it in state 0 or 1. However, in qubits we examine

the coefficients and instead. After measuring a qubit the

result become either 0 with probability or 1 with

probability resulting in:

(2)

Having both probabilities sums to one geometrically

indicates that the qubit state must be normalized to length one

in the two-dimensional vector space.

Two qubits in quantum systems can be represented by four

states using classical bit for instance, 00, 01, 10, 11. At the

other hand, two qubits can be represented by four basis states

denoted by ,,,. Moreover, the two qubits

can also be in a superposition by forming a linear combination

of states with their complex coefficient which often called an

amplitude.

(3)

After the measurement of this multi qubit state, the result will

be similar to a system with only one qubit, as the probability of

having one of the four states is can be donated by

B. Quantum gates

Classical systems depends on the wires and the logic gates in

the digital circuits to carry and manipulate the information. For

instance, the NOT gate in classical system perform a specific

operation which is manipulating the stats 0 and 1 by

interchanging their values in which state 0 to be 1 and state 1 to

be 0. Similarly, the NOT gate in quantum systems interchange

state to state and state to state .

(4)

Moreover, another convenient way to represent quantum

gates is in matrix form. For instance, quantum gates I, X, and

H which represent the Identity, NOT and Hadamard gates

respectively can be represented in term of matrices as:

(5)

C. Quantum Teleportation

Quantum teleportation [7] is a technique of transferring a

quantum state from one location to another with the absence of

physical quantum channel between the sender and the

receiver[25]. However, this process of transferring the state

from one location to another doesn’t conflict with the no-

cloning which states that it is impossible to clone an exact state

without destroying the original state. That means it is possible

to move a state from one location to another but not copying.

Providing that, the teleported state will necessarily be destroyed

Teleportation uses the EPR pairs which is also called Bell

states and Bell basis to archive its goal. Bell Basis consist of

two entangled qubits in a noncanonical basis:

(6)

The Bell basis or the noncanonical basis consists of four

entangled vectors as follow:

(7)

(8)

By using Bell basis, if Alice would like to teleport a qubit to

Bab and the qubit is in an arbitrary state.

To accomplish the teleportation process Alice perform some

operations denoted in the quantum circuit in Fig 1.

Fig. 1. Quantum Teleportation Circuit

After applying the required operations Alice qubits will be

result to one of the four states which

will indicate the state of Bob’s qubit as follows:

(9)

(10)

(11)

(12)

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Alice will sends to Bob her measurement and depending on

Alice’s qubits Bob will have to fix the state in his possession by

applying one of the quantum gates. Receive state will

require Bob to apply I gate, receiving state will require him

to apply X gate, receiving state will require him to apply

the Z gate and receiving state will require Bob to apply X

and Z gates which is often called Y gate.

(13)

III. RELATED WORK

An enhancement of multiparty quantum secret sharing (QSS)

algorithm [26] was proposed in [27]. The authors proposed

two algorithms taking advantage of the entanglement swapping

operation. The first proposed algorithm requires the sender to

release the encoded classical bits to help the receiver to deduce

intended classical bits from a qubit state. However, in the

second proposed scheme the sender and the receiver need to

physically meet and exchange the classical bits. However, the

new algorithms improve the amount of data the original QSS

protocol transmit by the reducing it twice. Further, the new

algorithms are more efficient in term of the performance

compared to the original QSS. In addition, a reused scheme

was also proposed to reuse some qubits from previous round in

new round.

A protocol for quantum authentication using entanglement

swapping was proposed in [28]. The aim in this paper is to

securely exchange messages between the participating parties.

The proposed protocol provides mutual authentication for the

sender and the receiver when using unsecure routing path.

Further, the authentication protocol depends on four sequence

numbers called Si generated by a third party with the following

functions for each number: Quantum key generation by S1,

eavesdropping detection by S2, identity identification by S3 and

message transferring using S4 . In order to obtain the secret

key, the eavesdropper on the channel need to successfully break

S3. However, the eavesdropped on the routing path cannot

break the entanglement swapping technique and cannot have

access to the controlled qubits.

Network cryptographic protocol based on entanglement

swapping key management center was proposed in [29]. The

goal was to securely distribute the secret keys between parties

with prior sharing of entanglement pairs. However, this

protocol only requires channels between the users and the key

manger center and not between the users themselves. This

protocol preserve the networks resource by only allowing the

physical communication channels between the users and the

key management center and eliminating user-to-user channels.

Also, this protocol performs well even if the users are far away

from each other’s.

Quantum direct communication (QDC) for mutual

authentication based on entanglement swapping was proposed

in [30]. There are two phases in this protocol. First phase is

used to provide mutual authentication and the second phase is

used for direct communication. The identification between

Alice and Bob can be performed by testing the Einstein-

Podolsky-Rosen (EPR) pairs. Moreover, the properties of

entanglement swapping allows Bob to decode Alice’s message

by just performing exclusive-or operation on both of Alice’s

public key and Bob’s measurement. Further, the authentication

process and the direct communication process are proved to be

secure because there is no physical transmitting of qubits in

both operations. The public key for Alice will consist of two

classical bits. Alice will have to send it to Bob using the public

classical channel. However, that will not reveal any

information about the secret key Alice holds because they are

irrelative to each other.

In [31] a study of quantum cryptography was conducted

including in details description of protocol BB84. Also,

described key reconciliation, distillation, security measure and

level of security. Security measure is a probability that

indicates if the distributed key was intercepted or not by

unauthorized third party. Two security measures were defined

as in (14) and (15) where log is the natural logarithm, k is the

number of the compared bits in the public channel and n is the

length of the key.

(14)

(15)

In J(k) the first 20% of bits have more effect on the result

compared to the last 30% of the bits in the key. And dividing

S(k) by n gives maximum value of 0.1 which is equivalent to

37% of the bits in the key.

Travis Humble discussed securing quantum communication

in the link layer [32]. Besides, describing the basics of

quantum communications and quantum optical communication.

As well as, described the quantum seal Fig. 2 to provide

integrity and monitoring to quantum communication.

Fig. 2. Quantum Seal [31]

As illustration, an entangled pair of photons are created by

SPDC and passed through an active and reference fiber

channels.

An attempt to change a photon by an attacker will result in

destroying the correlation between these two photons and will

result in losing the entanglement. On the other hand, Cyber-

Physical security is implement using quantum seal. Detecting

any violation will be by setting threshold stating if the

communication is safe or not when the threshold value will be

the result of quantum seal process.

Quantum determined key distribution scheme was proposed

in [33] and it is based on quantum teleportation. In this

protocol the sender and the receiver will share predetermined

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key by taking the advantage of quantum teleportation instead of

random string as in the other key distribution protocols.

Moreover, because of quantum mechanics properties, the

system will be unconditionally secure. In fact, the protocol

consists of two major steps. First step, building the shared EPR

pairs. Second step, building the secret key. In the first step

Alice create EPR pairs in state and share them with Bob.

(16)

First qubit A will belong to Alice and the second qubit B will

belong to Bob. Then, Bob measures his qubit in one of three

basis. After that Alice and Bob declare the basis they used in

their measurements and compare their results. If both used

different basis they discard the EPR pair. However, if they find

they are many disagreement when they used the same basis,

they can conclude that there is an eavesdropper on the channel.

Building the will be based on quantum teleportation using the

EPR pairs were previously built.

IV. PROPOSED ALGORITHM

In this process we assume that each party shares N EPR pairs

with the trusted party named Charlie and not sharing EPR pairs

with the other parties. The first step in this protocol will be

establishing an EPR-pair between the sender and the receiver

by the help of the trusted node Charlie. After that Charlie will

act as generator for EPR-pairs between the sender and the

receiver to allow them to communicate with each other’s. The

first step require Charlie to help the sender (Alice) and the

receiver (Bob) to form an EPR pair. The shared EPR pair

between Alice and Charlie will be as follows:

(17)

And the shared EPR pair between Charlie and Bob is as

follows:

(18)

(19)

(20)

Applying CNOT to C:

(21)

Applying Hadamard gate to C in the first EPR-pair:

(22)

Rearrange and group C:

(23)

Depending on the result of Charlie’s measurement, Alice and

Bob can build their entangled qubits after applying Pauli-X,

Pauli-Z, both or no gate. For the particles in Alice’s and Bob’s

possessions, the result of the process will be one of the

following EPR pairs:

(24)

(25)

(26)

(27)

After forming the EPR pair between Alice and Bob, they

have the option to measure their EPR pair using one of the basis

. When Alice measure her qubit (first qubit

in the EPR pair) using one of these basis, Bob’s qubit (second

qubit in the EPR pair) will be collapsed to the opposite of the

result of Alice’s state. However, for Bob to have the correct

opposite state, he needs to measure his qubit using the same

basis Alice used to measure her qubit.

(28)

(29)

(30)

(31)

Alice can start to measure her qubit in one of these basis and

get the measurement result. After that Alice can meet Bob on

the classical channel and inform him about the basis she used

in measuring her qubit without disclosing her measurement

result. Then, Bob can measure his qubits using the same basis

Alice used. The result of Bob’s measurement will be the

opposite of Alice’s result in the same basis. For example, if

Alice used basis and her measurement results state

then the result of Bob measurement will be And if

Alice used basis , for her measurement, if the result of

her first qubit is then the result of Bob’s second qubit will

be . Alice and Bob perform this process until they meet

their key length. Once they finish with the process of

measurement, Bob can start to reverse all of his measurement

result which will make his measurement result identical to

Alice’s measurement results and this will be the secret key.

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A. The steps of the Protocol:

Step 1: When Alice want to securely communicate with Bob,

Alice contact Charlie. Since Charlie have prior entangled pairs

with Alice, Charlie can Authenticate Alice identity.

Step 2: Charlie authenticate Bob’s identity as they share prior

entangled pairs. Further, Charlie communicate with Bob and

inform him about Alice request. Bob can accept or reject

Alice’s request.

Step 3: If Bob accept to securely communicate with Alice,

Charlie start the entanglement swapping process and inform

both Alice and Bob when the process is successful and provide

the gate code so Alice and Bob perform to make the correct EPR

pair. On the other hand, if Bob rejected the request. Charlie

inform Alice and do not process the entanglement swapping.

Step 4: When Alice receive the confirmation from Charlie,

Alice start her measurement using one of the basis. Then, Alice

inform Bob about the basis she used in her measurement.

Step 5: After Bob receive the message from Alice, Bob can

measuring his qubit using the same basis Alice used in her

measurement.

Step 6: When Bob measures all the qubits, Bob will have to

reverse the stats of his measurement. This process will make

Bob’s state identical to Alice’s states and will be the key they

can use to encrypt their information.

Alice and Bob will not use and quantum or classical channels

to transmit the physical quantum states. Instead, they are

depending on the EPR pairs they started to share by the help of

the trusted center Charlie. Once Charlie Authenticate the

identity of both parties in the beginning of the process then we

can have confident that the following process will be secured

because the states will not be able to compromise.

V. CONCLUSION

We have presented a multiparty quantum secret key sharing

using quantum entanglement swapping. This protocol solves

the problem of trust between sender and receiver. Where there

will be a trusted third party who can authenticate each party to

the other. This protocol requires each party to have an EPR

pair shared with the trusted party. However, and EPR pair

between the parties themselves will not be required. For a

sender to share a secret key with the another party who shares

only EPR pair with the trusted party, the sender will request a

permission to contact the receiver and the trusted party will

handle the authentication process with the receiver as they share

and EPR pair and they can easy be verified using their entangled

qubits. Once the authentication process is completed, the

trusted party perform the entanglement swapping process and

have both parties sharing EPR pair. Where the sender

measures his own qubit and inform the receiver and about the

measurement basis. When the receiver measure his qubit with

the same basis that will result in having the opposite result of

the sender. Then receiver can just reverse the result which will

in the same state as the sender. The sender and the receiver

will not use any quantum channel to send and receive states and

will only depend on classical channel to share the basis without

sharing any state result. Sharing the basis has wouldn’t affect

the security because there will be no states in any medium that

can be intercepted and channel. Thus, this protocol is secure.

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Muneer Alshowkan is currently pursuing a Ph.D. degree in Computer Science

and Engineering at the University of Bridgeport. In 2011, he received his

Master’s degree in Information, Network and Computer Security at New York

Institute of Technology, and received his B.S. in Computer and Management

Information Systems at King Faisal University in Kingdom of Saudi Arabia.

His research interest in Quantum Computing, Computer Networks Security and

Wireless Communication. He is currently an active member of IEEE.

Dr. Khaled Elleithy is the Associate Dean for Graduate Studies in the School

of Engineering at the University of Bridgeport. He has research interests are in

the areas of network security, mobile communications, and formal approaches

for design and verification. He has published more than two hundred fifty

research papers in international journals and conferences in his areas of

expertise. Dr. Elleithy is the co-chair of the International Joint Conferences on

Computer, Information, and Systems Sciences, and Engineering (CISSE).

CISSE is the first Engineering/Computing and Systems Research e-Conference

in the world to be completely conducted online in real-time via the internet and

was successfully running for four years. Dr. Elleithy is the editor or co-editor

of 10 books published by Springer for advances on Innovations and Advanced

Techniques in Systems, Computing Sciences and Software.