A Quantum Fuzzy Logic for a Secure and Safe Wireless Network Communication

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.

Full text

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

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