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A Quantum Fuzzy Logic for a Secure and Safe

Wireless Network Communication

Varun Pande, Khaled Elleithy, Wafa Elmannai, Elham Geddeda

Department of Computer Science and Engineering

University of Bridgeport, Bridgeport, USA

vpande@my.bridgeport.edu, elleithy@bridgeport.edu, welmanna@my.bridgeport.edu, egeddeda@my.bridgeport.edu

Abstract—Due to the wireless network’s features and the

flexibility that it provides over the communication, it has

become the most common used network. That motivates many

researchers to introduce and discover new techniques in order

to improve this environment. However, the huge use of

wireless networks leads to lack of secure communication.

Especially, with wireless local area networks (WLAN); where

many public places such as airports and banks are equipped

with those networks. In order to transmit the secrete key

between two parties, quantum cryptography uses a new

method called quantum key distribution (QKD). It has been

created to solve the problem of secret key distribution. In this

paper we provide a secure and safe wireless network

communication using quantum logic (QKD) and fuzzy logic;

where fuzzy logic is an approximation process, in which crisp

inputs are turned to fuzzy values based on linguistic variables,

set of rules and the inference engine provided. This process is

called fuzzification which is a process that enables us to

determine a value within sets. Similarly in quantum

computing we determine the probability of a qubit inclined

towards the 1 or 0. Since a qubit can be a function that is

closely related to fuzzy logic, our protocol creates a rule based

engine that implements fuzzy logic to show the output on a

quantum based rule engine during the communication. The

algorithm detects an intruder who tries to intercept the

communication.

Keywords— Wireless Networks, Communication, Security,

Fuzzy Logic, Quantum key distribution.

I. INTRODUCTION

Nowadays, wireless networks are used over the world

due to its rapid advancement during past years. The number

of its users is being increasing every day [1, -3]. Therefore,

it would not be long when the industry’s communications

will be controlled by the wireless network due to its appealing

features. Although the wireless networks and their

applications became the most popular ones to provide a

smooth communication; security of information remains a

major concern. Therefore, in this paper we address this

problem by introducing an algorithm that provides a high

level of security over the wireless networks using Quantum

Key Distribution (QKD) and fuzzy logic.

Radio frequency signals makes wireless

communications are more exposed and vulnerable to the

attackers than its corresponding wired communications.

Most of wireless networks’ security applications such as

encryption and protocols become widespread; that increases

the security risk with such applications [4, 5]. Several

methods can used by the attackers such as man-in-the

middle attacks, Identity theft (MAC spoofing), denial of

service attack (DOS), and ARP poisoning.

Quantum Key Distribution (QKD) technique is used to

distribute the secret key between the two communicating

parties. Recently, optical communications have used QKD

protocols with optical fiber schemes [6]; for example, six-state

[7], B92 and BB84 [8]. In particular, BB84 is considered as the

most used technique [9]. In optical networks, QKD shows

noteworthy improvements [10, 11].

In 1965, Lotfi A. Zadeh introduced Fuzzy logic at the

University of California in Berkeley [12, 13]. However, it was

a long debate between the thoughts of multivalued logic and

the notion in the field of Fuzzy Logic which was considered as

multivalued logic; that permits moderate values such as:

true/false, right/wrong, big/small, yes/no, and so on. While,

other methods were described as notions; that can be processed

mathematically using computers. It can be applied as human

way of thinking through programming of computers.

Furthermore, the developed ideas of Fuzzy logic yielded a

profitable tool for the steering and controlling of complex

systems in serial processes, households and many other

applications in our daily life [14].

II. RELATED WORK

In this section we are presenting some techniques that have

been used to support security over the wireless networks

using fuzzy logic and QKD. The two dimensional fuzzy

dynamic switching is the main focus in [6]; where it

switches between the sender and receiver through long

distance. The authors provide a solution for Line-Of-Sight

(LOS) issue using Fuzzy logic. The authors used QKD

system using fuzzy logic with the IEEE 802.11i protocol for

wireless network. The authors argue that their work would

provide secure communications over the network.

Based on the privacy amplification phase of IEEE 802.11,

the authors tested their results using quantum cryptography

[15]. They have tested their application based on obtained

data from a quantum station against combinations of inputs.

Their analysis showed that the adjustment which they made

on IEEE 802.11 protocol does not have any major effect on

general key distribution system. The results displayed the 4-

phase handshake was finished within rational time limits

even under high error rate. In the end, they have claimed

that their suggested solution is resourceful enough to be

combined in the IEEE 802.11 standard.

One of the most profitableness of fuzzy Logics is to

convert heuristic control rules to be operated automatically

instead of being operated manually [12, 13]. Modern

applications of technologies and science are greatly

benefited and developed by fuzzy logic techniques. For

example, steam engine controller, complex systems signal

processing and many other fields of science and

technologies cannot ignore the parole that played by the

importance of fuzzy logic [14]. There are still some

difficulties that need to be overcome such as the

interference of inputs and outputs in engine maps for

instance.

The modern science of cryptography is used to as a

safe guard for protecting private information from the

attackers, as well as authentication and insuring data

integrity. By using key distribution quantum (KDQ)

technique, the eavesdropping can be detected [16].

However, authentication needs a partner in communication

progression who could share some amount of secret

information. However, for an unlimited secret key growing,

quantum cryptography will be essential. Recently,

Heisenberg uncertainly was suggested to provide secure

communications [17].

The authors in [18] used quantum cryptography

mechanism which is called fuzzy logic controller (FLC)

over the social networks. Thus, its purpose is to prevent the

attacker of being involved inside the network. They have

compared their proposed fuzzy quantum cryptography

method with PKI methods. This approach showed

improvement in the results compared to PKI methods. The

main reason of the proposed method is to recognize the

irregular behavior over the networks.

III. PROPOSED WORK

A. Proposed Algorithm:

In this section, we introduce an algorithm to provide a

high level of security over wireless networks using quantum

fuzzy logic. Our algorithm is based on Gaussian principal

and membership sets of fuzzy logic. In order to demonstrate

the security level of this algorithm, an application was

developed using C sharp programming language.

As we demonstrated in previous sections, fuzzy logic is

an estimate process, in which crisp values are turned to

fuzzy values based on semantic variables, set of rules and

the inference engine provided. This method is called

fuzzification. Fuzzification is a method that allows us to

control a value within sets. Likewise in quantum computing

we define the probability of a qubit inclined towards the 1

or 0. Furthermore, the qubit has a rotation that defines its

positive or negative attribute. Since a qubit can be a

function that is closely related to fuzzy logic, we are going

to use the fuzzy logic’s features of maximizing qubit value

to be optimized. Our main goal is to get the closed values to

determine whether the qubit is 0 or 1. Therefore, the

optimization model of fuzzy can be presented over multi-

objective software design issues as following:

Such that ,

Our goal is to maximize the minimum qubit value of all

delay which is donated by D and the difference between the

measured and recommended values donated by U.

At-Norm T: [o,1]2 -> [0,1] is a commutative and associative

function satisfies:

T(a,1) = a and a ≤ b => T(a,c) ≤ T(b,c)…(1)

A t-Conorm: [0,1]2 -> [0,1] is a commutative and

associative function satisfies:

(a,1) = a and a ≤ b => (a,c) ≤ (b,c)……(2)

From equations 1 and 2, we understand that the spin

sets of a single qubit can be derived. Once the spin value is

derived, then n subsets will be stored under the probability

set. The Gaussian principal allows us to determine the point

of access between any of the two qubits. Thus, it is enabling

us to determining a path without overwhelming it.

Theoretically, we can determine the spin function based on

each node that is adjacent other nodes. That is to make

subsequent sets as showing in equation 3 in order to define

the number of qubit sets having the same spin state. Since it

is an exponential function, a delta spin value is generated

from the total set of qubits. This enables us to determine

three sets of spinning qubits. One of the sets that have a

positive spin and flow towards path is more probable to

have the value one. One set of qubits that have a spin in the

negative direction and flow towards the value 0 in a

probability function. Finally a set of qubits that have no

spin function determined. A vice versa case again gives

output to multiple probabilities. Thus, this process makes

the whole communication faster, and more secure without

overwhelming and creating a large overhead.

Our main goal is to show the possibility of deriving a

quantum based rule engine that implements fuzzy logic to

determine the possibility of multiple logical outputs to

provide a secure wireless communication. Figure1

demonstrates a logic based interference engine which we

are going to use. We are showing how a number of

probable if statements and a number of if else statements

logic, all go to a main interference engine.

Figure 1: A Logic Based Interference Engine’s Architecture

B. System Architecture:

Figure 2 presents an overview of the. The algorithm

receives a set of quantum based inputs and fuzzy logic

based inputs into our interference engine. Then we

determine the sets based on the fuzzy logic for the inputs.

Based on the fuzzy sets, a logic based decision is taken via

logic engine and a probability of location or spin is derived.

The value need to be checked for each qubit. These output

values help define a path in the unlimited network, and then

the data transmission begins under secure communication.

Figure 2: The Flowchart of Proposed System

Figure 3 is the presentation of the node network. We can

call it a quantum spin or qubit spin node network. As each

of the nodes in the network transmits data to each other

based on the qubit’s spin which is presented in the data

stream based on [19]. Basically the presence of the nodes

shows how the data is passed across the network based on

the qubit’s spin and its position between 1 and 0. It is a

similar concept to the P2P [20] networking for data

transmission across a node network, but we define the set of

data value to be transmitted based on the spin notation and

the probability of the location of the qubit between 0 and 1.

Thus, the path determination for the data transmission is

based on the probability of the qubit location which is

between 0 and 1.

Figure 3: Presentation of a Purposed Node Network

C. Results:

Based on our implemented idea, we could provide a secure

communication between the nodes. Figure 4 shows to the

implementation that creates create an interference engine

using quantum and fuzzy logic.

Figure 4: Fuzzy Logic Interference for the sensor nodes communication

We first use a fuzzy based logic for using multiple

attributes of a sensor node in a network to generate the

value ranges between 0 and 1. Then we define a condition

or expression to classify how the transmission process will

occur throughout the network. Although the choice can be

defined by the user, default definitions can be selected to

access the whole network.

Figure 5 shows that the data transmission decreases as

the number of nodes increases as well as the energy and the

transmission power were not at maximum value. Thus,

based on the node properties, we can determine the amount

of input data transmitted. Theoretically, based on quantum

computation this should not be an issue even with infinite

nodes as the transmission packets will be qubits, since the

log function cannot be displayed in relation to other

attributes. We show that the transmission power will not be

at its maximum.

The final result which is based on the fuzzy logic is that

the data is transmitted. That is the data is sent completely

without any loss of packets of any data size and any

condition. There was no packet loss throughout the network

in either scenario as showing in figure 6.

The quantum logic function window is allowed us to

see and modify the attributes of the individual qubits. We

can determine the qubit sets based on the fuzzy logic here

and determine the number of qubits that have a positive

negative and no spin. We tend to reach a crossover point via

fuzzy logic to determine sets before the transmission of the

qubit data as shown in Figure 7.

Detla spin basically determines the difference between

the number of qubits in the whole network whether or not it

is ready to be transmitted against the amounts that are

having the positive spin and the negative spin. Again using

fuzzy logic as a subset of qubits are defined based on the

probability of these bits toward the whole binary value 1 or

whole binary value 0 as showing in figure 8. Qubit’s

position displays the result of the number of qubits and their

final probable locations as showing in Figure 9.

Figure 5: The Scenario of Transmission Rate Vs the Number of the Nodes

Figure 6: Scenario of Data Transmission without Lose

IV. CONCLUSIONS

In this paper, we have shown a novel and secure way using

quantum logic and fuzzy logic over wireless network. The

development of an interference engine was demonstrated

using an application developed in C# programing language

which determines how the fuzzy logic can support secure

communication over a network of unlimited nodes without

loss of data using qubits of quantum logic and set theory

derived via fuzzy logic. Since there is no quantum machine

to actually determine the ability of such an engine, we

statistically used the properties of both functions to verify a

fast and secure method using a quantum fuzzy logic

interference engine. In the future we plan to apply this logic

on large node network sizes and observe how the behavior

of fuzzy logic changes based on set determination and the

path selection as a network grows exponentially.

Figure7: Quantum Logic Interference for the sensor nodes communication

Figure8: Defining Subset of qubits based on the Probability of these Bits

Figure9: The Presentation of Final Probable Locations of Qubit

REFERENCES

[1] Xu Huang, Shirantha Wijesekera, and Dharmendra Sharma,

“Implementation of Quantum Key Distribution in Wi-Fi (IEEE

802.11) Wireless Networks,” IEEE the 10th International Conference

on Advanced Communication Technology, Feb 17-20, 2008 Phoenix

Park, Korea. Proceedings ISSN 1738-9445, ISBN 978-89-5519-135-

6, Vol. II, p865.

[2] Tom Karygiannis, Les Owens, Wireless Network Security, 802.11,

Bluetooth and Handheld Devices, NIST, Special Publication 800-48,

November 2002.

[3] IEEE Std 802.1X, 2004, IEEE Standard for Local and metropolitan

area networks, Port-Based Network Access Control.

[4] Floriano De Rango, Dionogi Lentini, Salvatore Marano, Statis and

Dynamic 4-Way Handshake Solutions to Avoid Denial of Service

Attack in Wi-Fi Protected Access and IEEE 802.11i, June 2006.

[5] Changhua He, John C. Mitchell, Security Analysis and Improvements

for IEEE 802.11i.

[6] Huang, Xu, Shirantha Wijesekera, and Dharmendra Sharma. "Fuzzy

dynamic switching in quantum key distribution for Wi-Fi networks."

In Fuzzy Systems and Knowledge Discovery, 2009. FSKD'09. Sixth

International Conference on, vol. 3, pp. 302-306. IEEE, 2009.

[7] Dagmar Bruß, Optimal Eavesdropping in Quantum Cryptography with

Six States, Physical Review Letters, 81.3018, October 1998.

[8] C.H. Bennett, Quantum cryptography using any two

nonorthogonalstates, Physical Review Letters, 68 (1992) 3121-3124.

[9] Tobias Schmitt-Manderbach, Henning Weier, Martin Fürst, Rupert

Ursin, Felix Tiefenbacher, Thomas Scheidl, Josep Perdigues, Zoran

Sodnik, Christian Kurtsiefer, John G. Rarity, Anton Zeilinger, Harald

Weinfurter, Experimental Demonstration of Free-Space Decoy-State

Quantum Key Distribution over 144 km, Phys. Rev. Lett. 98,

010504, January 2007.

[10] M.S. Goodman, P. Toliver, R.J. Runser, T.E. Chapuran, J. Jackel, R.J.

Hughes, C.G. Peterson, K. McCabe, J.E. Nordholt, K. Tyagi, P.

Hiskett, S. McNown, N. Nweke, J.T Blake, L. Mercer, H. Dardy,

Quantun Cryptography for Optical Networks: A Systems

Perspective.

[11]http://www.computerworld.com/securitytopics/security/story/0,10801,

96111,00.html , Quantum cryptography gets practical.

[12] L.A. Zadeh, Toward a theory of fuzzy information granulation and

itscentrality in human reasoning and fuzzy logic, Fuzzy sets

andsystems, 90 (1997) 111-127.

[13] E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with

afuzzy logic controller, International journal of man-machine studies,

7(1975) 1-13.

[14] L.A. Zadeh, Outline of a new approach to the analysis of

complexsystems and decision processes, Systems, Man and

0pCybernetics, IEEE Transactions on, (1973) 28-44.

[15] R.Lalu Naik, Dr.P.Chenna Reddy , U.Sathish Kumar,

Dr.Y.V.Narayana, “Quantum Cryptography with Key Distribution in

Wireless Networks on Privacy Amplification ,” IRACST –

International Journal of Computer Networks and Wireless

Communications (IJCNWC), Vol. 1, No. 1, December 2011.

[16] M. Dušek, N. Lütkenhaus, M. Hendrych, Quantum

cryptography,Progress in Optics, 49 (2006) 381-454.

[17] P. Busch, T. Heinonen, P. Lahti, Heisenberg's uncertainty

principle,Physics Reports, 452 (2007) 155-176.

[18]Javidnia, Hossein, Shahaboddin Shamshirband, and Miss Laiha Mat

Kiah. "Cooperative Multi-agent System Based on Fuzzy Quantum

Cryptography." International Conference on Computer and

Intelligent Systems (ICCIS’2012) & International Conference of

Electrical,Electronics, Instrumentation and Biomedical Engineering

(ICEEIB’2012) Dec. 28-29, 2012 Bangkok (Thailand).

[19] Wafa Elmannai, Khaled Elleithy, Varun Pande, Elham Geddeda,

“Quantum Security Using Property of a Quantum Wave Function,”

Accepted at 2014 IEEE LISAT 10th Anniversary Conference, 2014.

[20] Umezaki, Kouhei, Evjola Spaho, Keita Matsuo, Leonard Barolli,

Fatos Xhafa, and Jiro Iwashige. "A Fuzzy-Based System for

Evaluation of Trustworthiness for P2P Communication in JXTA-

Overlay." In Information Technology Convergence, pp. 451-460.

Springer Netherlands, 2013.