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Proceedings of 2014 Zone 1 Conference of the American Society for Engineering Education (ASEE Zone 1)
978-1-4799-5233-5/14/$31.00 ©2014 IEEE
Abstract—The advances in hardware speed has being rapidly
increased rapidly in the recent years, which will lead to the
ability to decrypt well known decryption algorithms in short
time. This motivated many researchers to investigate better
techniques to prevent disclosing and eavesdropping of
communicated data. Quantum Cryptography is a promising
solution, since it relies on the prosperities of quantum physics
that ensure no change in the quantum state without the
knowledge of the sender/receiver. Quantum Communication
Scheme for Blind Signature with Two-Particle Entangled
Quantum-Trits was proposed by Jinjing et al. [1] That scheme
uses qutits during the communications and the process of the
encryption is not clearly defined. In this paper we suggest a
modification of Jinjing et al. protocol using qubits and qutrits
during the encryption and decryption which proposed by Zhou et
al. [2] The proposed algorithms enhances the efficiency of that
scheme and creates a quantum cryptosystem environment to
exchange the data in a secure way. During the communications,
all the messages are encrypted using the the private key of the
sender and a third party verifies the authenticity and the
blindness of the signature.
Keywords— Quantum communication; Blind signature; Quantum
signature; Quantum cryptography
I. INTRODUCTION
The security of information, either local or being
transmitted over the internet, is a main goal for individuals or
organizations because it contains private or valuable data that
could be used by intruders in a way that affect their life in
different aspects. Cryptography is a field that is concerned on
how to protect and secure the information from attackers and
unauthorized users. In general, cryptography is divided into
two parts; symmetric encryption and asymmetric encryption.
For symmetric encryption, the same key is used for cipher and
decipher by sender and receiver, which implies that this key
Manuscript received February 10, 2014. Manuscript revised February 27,
2014.
A. Abu Malluh is with the Computer Science and Engineering Department,
University of Bridgeport, Bridgeport, CT 06604, USA (e-mail:
aabumall@bridgeport.edu ).
K. M. Elleithy is the Associate Dean for Graduate Studies in the School of
Engineering at the University of Bridgeport. He is with the Computer Science
and Engineering Department, University of Bridgeport, Bridgeport, CT
06604, USA (e-mail: elleithy @bridgeport.edu ). He is IEEE senior member.
A. Alanazi is with the Computer Science and Engineering Department,
University of Bridgeport, Bridgeport, CT 06604, USA (e-mail:
aalanazi@bridgeport.edu ).
R. J. Mstafa was with the Computer Science Department, University of
Zakho, Duhok, Iraq. Now he is with the Computer Science and Engineering
Department, University of Bridgeport, Bridgeport, CT 06604, USA (e-mail:
rmstafa@bridgeport.edu ).
must be kept secured. For asymmetric encryption, there are
two different keys; private and public. Both techniques’
strength is inversely related with the computational power.
That means that encryption fails under brute force attack with
sufficient powerful computers.
Quantum Cryptography was introduced in 1984 by
Charles Bennett and Gilles Brassard [3]. The authors proposed
a new algorithm (BB86) based on Quantum Communication
Networks, where the transmission depends on photons.
Quantum cryptography utilizes Heisenberg’s Uncertainty
principle which states that when a quantum state is measured,
then it is disturbed and leads to incomplete information about
the system. Eavesdropping on a quantum communication
alerts legal users and this feature is the main advantage of
quantum cryptography[4].
A digital signature is used to insure the authenticity and
the validity of who sent the message and signed the
transmitted document. It ensures that the original message has
not been changed by someone who tries to break the security
of the message [5].
The signature in classical cryptography has some
characteristics including identifiability, undeniableness and
unforgeability which provide a mechanism to decide who
verifies that signature. David Chaum [6]introduced the idea of
a blind signature as an electronic signature where the content
of a message is blinded prior the process to sign it. Blind
signature is involved in privacy-related protocols where the
party that signs the message and party who writes it are
different[7]. Several algorithms that use Quantum
Cryptography were proposed in literature. They differ
essentially in the choice of the parameters between the
communicating parties such as the number of states that a
quantum bit has, and the key process forming. In this paper we
present an ideal environment of quantum communication
scheme for blind signature with two-particle entangled
quantum qubits and qutrits.
II. RELATED WORK
Jinjing et al. [1] proposed a quantum communication
scheme for blind signature with two-particle entangled
quantum-trits (qutrit). The authors introduced a third fully
trusted participant Trent (the arbitrator and proxy) which is
responsible to help Alice and Bob trust each other before
communication verify the legalization and authenticity of the
blind signature and provide a batch of efficient proxy blind
signatures to Alice. Their model utilizes public key principle
with qutrit usage; transformation of a message to qutrits.
In [2], the authors introduced a new algorithm to qubit
with hybrid keys .The encryption and decryption operations
A Highly Secure Quantum Communication Scheme
for Blind Signature using Qubits and Qutrits
Arafat Abu Malluh, Khaled M. Elleithy, Adwan Alanazi, Ramadhan J. Mstafa
uses a quantum key and classical key which are shared
between Alice and Bob before starting the communication
between the two parties. Alice and Bob are communicating
through a classical channel which is also used to check the
presence of Eve who is trying to attack the communication.
The encryption and the decryption operations use the basic
Hadamard gate and Controlled-NOT gates. To start the
communication, Alice adds random bits to her message
and encrypts it with quantum block encryption
algorithm. Then, Bob decrypts the cipher text that was
received from Alice. After that, Alice declares her check bits
and their corresponding positions to Bob who is going to
compare the received check bits with the bits that Alice
already declared. If the bits are the same, they continue the
communication. Otherwise, if the bits are different, which
means someone attacked the channel, the shared keys are
canceled and they must establish new keys to continue the
communication in safe way.
In[8] a quantum signature in service-oriented vehicular
networks was proposed. In the initial phase, the sender and the
receiver share a quantum key and generate EPR pairs to
construct a special correlation between each other. In the
signature phase, the signatory produces the signature by using
EPR pairs and sends it to Bob. In the verification phase, the
receiver has the capability to identify the signature by using a
quantum key and EPR pairs. Based on this relation, the
receiver can reconstruct the original quantum states to verify
whether the signature is derived from initial quantum
entangled state or not. Also, two quantum unitary operations
are used, I gate and X gate, to represent classical bits 0 and 1.
In[9], the authors proposed a quantum digital signature
scheme based on quantum mechanics. The security in the
protocol depends on the quantum one-way function that
should be easy to compute and hard to invert. An arbitrator
was introduced to authenticate and validate the signing
message. Public quantum keys are used to ensure the validity
of the signature and one time pad to verify the security of
quantum information. There are three algorithms in a digital
signature scheme, a key generation algorithm which randomly
selects the private key, a signing algorithm and a verifying
algorithm. The proposed scheme provides some security
services such as security against repudiation since Alice
cannot deny her signature because Bob will return to the
arbitrator who has a copy of the signature. Also, the arbitrator
tests if the signature has been forged or not by comparing that
with its current information. Also, it provides Security against
forgery. In this case any attempt to alter the signed quantum
states or to recover Alice’s private keys and generates a
“legal” signature will be detected.
Wen and Liu [10], proposed a quantum message signature
scheme without an arbitrator. This scheme has N-pairs M and
M’ of particles that are created by Alice to carry the quantum
message. Bob creates N-pairs of particles A and B in EPR
(Einstein-Podolsky-Rosen) states. Alice saves the particle M
and transmits the particle M’ to Bob. When Bob receives the
particle M’ he sends particle A to Alice and keeps particle B.
Then the state with triplet particles Ai, Bi, and Mi is produced.
For each triplet state, Bell-base measurement is implemented
by Alice on both Mi and Ai and her result will be recorded as
Ri. Each Bell state Ri represents two classical bits which Alice
encrypted those states by using Vernam algorithm to make
signature S. Bob decrypts the signature that was received from
Alice through the classical channel. Unitary operations Ui
have to be applied on Bob’s particle Bi to extract the initial
state Mi. Then Alice’s signature S is accepted by Bob only
when both Bi and M’
i states are equivalent. This kind of
scheme has a private symmetric key for both sender and
receiver without having to share it with the third party which
means that the arbitrator is not needed in this system.
In [11], the authors discuss three problems of the scheme
presented in [9]. First, the quantum one way function is not
defined clearly. Second, the private key was not used for
signing the message and third, there are some problems during
the signing and the verification phases of the algorithm. While
generating the key, the authors do not specify the quantum
states. During the generation process, we know the signer’s
public key and its corresponding private key. If we combine
the signing process we can see the signer Alice does not use
her private key which is a significant security flaw.
III. QUANTUM COMMUNICATION FOR BLIND SIGNATURE
The classical blind signature algorithm contains three
parties: Alice, Bob and the third Party Trend. Alice who is the
sender is able to generate a signature for her message. Bob
who is the receiver can identify if the signature is from Alice
or not by the third party Trend whose main task is the
authentication of the signed message[12]. The quantum
communication scheme for blind signature is shown in Fig. 1
and works as follows:
(1) Alice sends a message that is encrypted by her private key
to the receiver Bob.
(2) Bob adds his information to the received message which
he encrypts by the key that is shared between him and
Alice.
(3) Bob sends that message as well as his information to Alice
which is considered as the blind signature.
(4) Alice receives the blind signature and decrypts it with the
shared key with Bob and checks if the received message
has not been changed.
(5) Now, the two parties Alice and Bob send a message to the
third party Trend containing the result of the signature
and Trend checks and validate the signature.
(6) If the result of the validation of the signature is positive,
Alice sends a message to Trend.
(7) Trend checks those messages by applying Bob’s personal
information and Trend’s random checking photons
A. Initialization of the Communication
We assume that the secret keys Kab, Kac, Kbc are
distributed for Alice and Bob; Kab is the secret key between
Alice and Bob and can be used in two cases twice for Bob’s
encryption and Alice’s decryption in the first communication.
However, Kac and Kbc are used for the communications
between Alice and the third party Trend and between Bob and
Trend. Alice has her key Ka which can be used for encrypting
the received message that Bob signed it before. Fig. 2 shows
the relationship in the communications between Alice, Bob
and Trend. Furthermore, Alice has amount of message that
Bob should sign. We annotate the message
as
, where every message has n trits.
, where M1 is selected initially as
the first attempt for trying quantum blind signature.
Fig. 1: Quantum communication protocol for blind signature.
Fig. 2: Distribution of the quantum keys for blind signature.
B. Trying Blind Signature
Alice generates a qutrit string |ψM1> to be used for trying
message. Alice converts the trying message M1 into a qutrit
string |ψM1> that we have in the following string n qutrits,
where:
Also, |ψM1> has a single qutrit |ψ1j> where can be shown as:
, where α0, α1, α2 are
complex number where .
Then, Alice generates a secret string of qutrits |T> and the
private key is related with measurement operators where:
and
measurement operators
.
After that, the secret string qutrits is measured with the
related key measurement operators, this value will be used
later to compare with the signer value to check whether it was
changed during signing.
To sign the secret message, Bob inserts his private
information in to it without knowing that the contents of the
message. Bob generates a qutrit string of his own personal
information |ψp>, where n qutrits in the string, can be shown
as:
Also, Bob assume that Alice does not know the content of
his personal information and cannot access it. |ψp> is
encrypted using Kbc which will be combined with a sequence
of measurement operators Mkbc, where:
The key
Bob should check his qutrits |ψp> and gets:
In order to have a quantum blind signature for the secret
trying message, Bob will use kab, to encrypt |T> and |P> to
obtain the blind signature:
Finally, Bob sends Sb to Alice and waits for the signature
Verification.
C. Verifying the signature
First, Alice got Sb as shown before and he decrypts it
using kab. Alice obtains |T’> and |P’>, then she can get |ψ’
M1>
by decrypting |T’> using her private key Ka.
Second, Alice checks if the signature is blind. She verifies
that by comparing |ψ’
M1> to her |ψM1> that chosen in the first
trying quantum blind signature. If |ψ’
M1> does not equal |ψM1>,
then the message has been compromised by someone who was
trying to reveal part of the content of the secret message. This
will lead to dropping the message and start again. However, if
they are equal, we can assume that the content of the message
were not compromised and at this stage the blind signature has
started. Then, |P> will be sent by Bob to Trend. It can be
obtained by encrypting |ψp> using Mkbc . Bob will send it to
Trend through the quantum channel since no other than them
can know |P>. After that, Alice sends |P’> to Trent.
Finally, since Trend has |P> and |P’>, he will verify the
authenticity of the signature. He checks if |P> = |P’>, and
decrypts |P> and |P’>, using Kbc. Trend has already |ψp> and
|ψ’
p> and he will check if |P> = |P’>, |ψM1>= |ψ’
M1> and |ψp> =
|ψ’
p>, which means we got successfully the trying blind
signature. Since we got the trying blind signature authentic
and blindness, Trend sends a message to Alice and Bob about
the result and can communicate safely. However, if one of the
previous conditions has not been met, the communication will
be dropped.
IV. PROCESS OF ENCRYPTION AND DECRYPTING OF QUBIT
As shown in Fig. 3, we have a string of n qubit that can
be expressed as:
Also, the hybrid key contains two types of keys, quantum
key and binary key that are involved in the process of
encryption and decryption. The quantum key can be
represented as follow:
Binary key as: K2=k21k22…k2s {0, 1}
We assume that the two keys are distributed in advance to
Alice and Bob in a secure way and can be used for future
communications if it has not been hacked. The purpose of the
classical channel is to detect the presence of Eve who wants to
access the information. We will apply Hadamard gate and
Controlled-NOT gate in the encryption and decryption.
Fig. 3: Qubit of encryption and decryption
V. PROCESS OF DECRYPTION OF QUBIT WITHOUT HAVING EVE
IN BETWEEN
Trend Decrypts Bob’s Qubits (Original Data) using BC
key (part1), after that, Trend Decrypts Bob’s Qubits that was
send by Alice by BC key (part2). The process is shown in
Table 1.
TABLE1: DECRYPTION OF QUBITS WITHOUT EVE
Part1 Part2
M α 0 α 1 M α 0 α 1
Q1 0.4 0.6 Q1 0.4 0.6
Q2 0.3 0.7 Q2 0.3 0.7
Q3 0.2 0.8 Q3 0.2 0.8
Q4 0.1 0.9 Q4 0.1 0.9
Q5 0.7 0.3 Q5 0.7 0.3
Q6 0.8 0.2 Q6 0.8 0.2
Q7 0.9 0.1 Q7 0.9 0.1
Q8 0.3 0.7 Q8 0.3 0.7
Q9 0.2 0.8 Q9 0.2 0.8
Q10 0.4 0.6 Q10 0.4 0.6
Q11 0.5 0.5 Q11 0.5 0.5
Q12 0.8 0.2 Q12 0.8 0.2
VI. THE PROCESS OF THE DECRYPTION OF QUBIT HAVING EVE
IN BETWEEN
Trend Decrypted Bobs Qubits that was send by Alice by BC
key as in Table 2.
TABLE2: DECRYPTION OF QUBITS WITH EVE
M α 0 α 1
Q1 -0.2 0.0
Q2 -0.1 0.3
Q3 -1.1 -0.5
Q4 -0.4 0.4
Q5 0.3 -0.1
Q6 0.2 -0.4
Q7 0.6 -0.2
Q8 -0.1 0.3
Q9 -1.1 -0.5
Q10 -0.4 -0.2
Q11 0.0 0.0
Q12 -1.7 -2.3
VII. PROCESS OF DECRYPTION OF QUTRITS WITHOUT HAVING
EVE IN BETWEEN
Trend decrypts Bob’s Qutrits (original data) using BC key
(Part1), after that, Trent Decrypted Bobs Qutrits that was send
by Alice by BC key (part2) as shown in Table 3.
TABLE3: DECRYPTION OF QUIRITS WITHOUT EVE
Part1 Part2
M α 0 α 1 α 2 M α 0 α 1 α 2
Q1 0.1 0.6 0.3 Q1 0.1 0.6 0.3
Q2 0.3 0.4 0.3 Q2 0.3 0.4 0.3
Q3 0.2 0.6 0.2 Q3 0.2 0.6 0.2
Q4 0.3 0.6 0.1 Q4 0.3 0.6 0.1
Q5 0.2 0.3 0.5 Q5 0.2 0.3 0.5
Q6 0.2 0.2 0.6 Q6 0.2 0.2 0.6
Q7 0.6 0.1 0.3 Q7 0.6 0.1 0.3
Q8 0.3 0.4 0.3 Q8 0.3 0.4 0.3
Q9 0.3 0.5 0.2 Q9 0.3 0.5 0.2
Q10 0.3 0.6 0.1 Q10 0.3 0.6 0.1
Q11 0.2 0.3 0.5 Q11 0.2 0.3 0.5
Q12 0.2 0.2 0.6 Q12 0.2 0.2 0.6
VIII. THE PROCESS OF THE DECRYPTION OF QUTRITS HAVING
EVE IN BETWEEN
Trend Decrypts Bobs Qutrits that was send by Alice by
BC key as shown in Table 4.
TABLE4: DECRYPTION OF QUTRITS WITH EVE
M α 0 α 1 α 2
Q1 -1.6 -1.1 -1.4
Q2 -2.2 -2.1 -2.2
Q3 -1.5 -1.1 -1.5
Q4 -1.4 -1.1 -1.6
Q5 -3.1 -3 -2.8
Q6 -4.8 -4.8 -4.4
Q7 -9.4 -9.9 -9.7
Q8 -2.2 -2.1 -2.2
Q9 -1.7 -1.5 -1.8
Q10 -1.4 -1.1 -1.6
Q11 -3.1 -3 -2.8
Q12 -4.8 -4.8 -4.4
IX. ANALYSIS OF THE PROPOSED ALGORITHM
The scheme introduced in [1] is using qutrits during the
communication and the encryption is not discussed clearly in
the paper. In this paper we propose that during the
communication, the qubit and qutrits should be encrypted to
improve the security of the scheme. Also we have shown that
the new development can make it easier to detect any attempt
by any illegitimate node to change the original content at any
phase with the help of Trend who is responsible for
authentication and verification of the signature during the
communication.
In general we can say that the current scheme is more
secure and more efficient. Also, it provides many security
features such Impossibility of forgery and prevention of denial
by the receiver. These two features are explained in this
section
A. Preventing forgery
During the communication steps that we have discussed
before, there are two eigenstate for qubit bit and three
eigenstate for qutrits. This is a main feature that enables us to
make it impossible for Eve to attack the communication. Also,
if one of the communicating parties turns to be malicious and
wants to access unauthorized, it can be detected. If Alice tries
to sign one of Bob's messages pretending by forging Bob’s
personal signature, she will be detected in the verification
phase. If Trend compares |Ps> and |P>, he will find out they
are different which leads to abolishing the signing phase.
Also, if an attacker tried to imitate Bob's signature, he will be
detected in the initial phase.
B. Preventing repudiation by the receiver
Another feature that is supported by this scheme is
preventing denial by the receiver. Let's assume Alice tried to
deny Bob's signature. In the Verification phase, Alice obtains
|P> and |T> by encrypting Sb using Kab. If |P’> is fake
information of Bob. when Trend finds |P> = |P’> and |ψp> =
|ψ’
p>, in this case, Trend will send the result to Alice and Bob
telling them that trying blind signature is authentic but if one
of the conditions is missing, the process will stop at this stage.
In other words, Alice and Bob are not able to deny the
signature of one of them. However, if one of them denies the
signature, Trend will detect it that and they will stop the
communication.
TABLE5
Hadamard and C-Not Gates Sizes (Matrices) for Qubits and
Qutrits (After Tensor Product Between Encrypted Qubit
and Quantum Key)
Hadamard C-not
Qubits Qutrits Qubits Qutrits
4 X 4
16 X 16
4 X 4
16 X 16
8 X 8
64 X 64
8 X 8
64 X 64
X. CONCLUSIONS
In this paper, we have improved the communication
Scheme for Blind Signature with Two-Particle Entangled
Quantum-Trits. We have applied a two-particle entangled
quantum-qubits and qutrits. The new implementation
improves security of the scheme where it is harder for
attackers to break. Furthermore, implementation of encryption
t using encrypted qubits and qutrits during the communication
provides higher efficiency. Finally, the scheme has several
new enhanced security features such as preventing forgery
within the parties and eliminating the possibility of
repudiation of a signee.
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Arafat Abu Mallouh
Arafat Abu Mallouh is originally from Jordan. He is pursuing his
Doctorate in Computer Science and Engineering at the University of
Bridgeport in Bridgeport, Connecticut, USA. He received his Bachelor’s
degree in Computer Science from The Hashemite University, Zarqa, Jordan.
Mr. Abu Mallouh received his Master’s degree in Computer Science from
Amman Arab University for Graduate Studies, Amman, Jordan. His research
interests include artificial intelligence, image processing, Machine Learning,
and Data Mining.. Currently Mr Abu Mallouh works on new techniques for
voice processing.
Khaled M. Elleithy
Dr. 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 and 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 six years. Dr. Elleithy is the
editor or co-editor of 12 books published by Springer for advances on
Innovations and Advanced Techniques in Systems, Computing Sciences and
Software.
Adwan Alanazi
Adwan Alanazi is originally from Saudi Arabia He is pursuing his
Doctorate in Computer Science and Engineering at the University of
Bridgeport in Bridgeport, Connecticut, USA. He received his Bachelor’s
degree in Computer Science from University of Hail, Hail, Saudi Arabia. Mr.
Alanazi received his Master’s degree in Computer Science from University of
Missouri Kansas City. His research interests include Wireless Sensor
Networks and Network Security.
Ramadhan J. Mstafa
Ramadhan Mstafa is originally from Dohuk, Kurdistan Region, Iraq. He is
pursuing his Doctorate in Computer Science and Engineering at University of
Bridgeport, Bridgeport, Connecticut, USA. He received his Bachelor’s degree
in Computer Science from University of Salahaddin, Erbil, Iraq. Mr. Mstafa
received his Master’s degree in Computer Science from University of Duhok,
Duhok, Iraq. His research interests include image processing, mobile
communication, security and steganography.
