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Authenticated Multiparty Secret Key Sharing Using Quantum Entanglement Swapping

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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.
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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 Termscryptography, 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.
2
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.
5
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.
... In the protocol of Liu et al. [16], they shared the quantum state through measuring the GHZ state with the BELL-base. Zhang et al. [17] measured the multiple EPR pairs with the BELL-base to share the quantum state, and Elleithy and Alshowkan [18] used the similar method to realize the authenticated classical information sharing. Besides, Song et al. [19] proposed an attack method on QSS based on entanglement swapping. ...
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