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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.

REFERENCES

[1] S. Jinjing, et al., "Quantum communication scheme for blind

signature with two-particle entangled quantum-trits," in

Advanced Communication Technology (ICACT), 2012 14th

International Conference on, 2012, pp. 558-561.

[2] N. Zhou, et al., "Novel qubit block encryption algorithm with

hybrid keys," Physica A: Statistical Mechanics and its

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[3] G. B. C.H. Bennett, "Quantum cryptography:Public key

distribution and coin tossing," Proc. IEEE Int. Conf. on

Computers, Systems, and Signal Processing, 1984.

[4] W. Tittel, et al., "Experimental demonstration of quantum secret

sharing," Physical Review A, vol. 63, p. 042301, 2001.

[5] S. William, "Cryptography and Network Security: Principles and

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[6] D. Chaum, "Advance in Cryptography, Proceedings of Crypto’82

Springer- Verlag, Berlin," p. 267, 1982.

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networks using entangled states," in Security Technology

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79, 1996

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.