Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
Managing Security Levels in a Cognitive Radio
Network
1
Kan Chen, 2Balasubramaniam Natarajan
Department of Electrical & Computer Engineering, Kansas State University, Manhattan, Kansas, USA
1
[email protected]; 2 [email protected]
Abstract- The open network architecture commonly envisioned for cognitive radio networks (CRNs), while offering flexibility, increases
vulnerability from a security standpoint. Therefore, understanding and managing the trade-off between CRN performance and security is critical for practical operation. In this paper, we attempt to design a secure CRN by optimizing the total throughput performance
subject to constraints on expected security level. We employ block cipher as the security mechanism, vulnerability level as the security
metric, and consider an exponential adversary attack model. In order to balance physical layer security and throughput in CRNs, we
propose a security level adjustment (SLA) algorithm based on the idea of water-filling. The SLA algorithm can distribute the optimal
security levels as well as the optimal cipher block length for each communication link in the CRN depending on the corresponding
channel quality. Simulation results for throughput show that our SLA algorithm outperforms conventional fixed block length cipher.
Keywords-Cognitive Radio Networks; Physical Layer Security; Encryption; Optimization.
I.
INTRODUCTION
Unlicensed users (cognitive users) have the ability to sense and identify white spaces in licensed spectrum and then opportunistically utilize these white spaces by operating with tolerable interference to primary users (PUs). For example, IEEE 802.22
standard on Wireless Regional Area Networks (WRANs) includes the idea of cognitive radio to allow sharing of unused channels
allocated to television broadcast services, and consequently brings broadband access to hard-to-reach low-population-density
areas (e.g., rural environments) [1]. Cognitive radio networks (CRNs) are modeled as open architecture networks, making CRNs
more vulnerable from a security perspective. An eavesdropper can easily capture the communication by snooping on transmit
data. Therefore, successful deployment of CRNs is dependent on the implementation of proper security mechanisms. Implementing a security strategy in a CRN requires adequate understanding of its effect on network performance. Typically, achievable
throughput is considered as a key metric in wireless communication. While a number of distinguished studies have been conducted on achievable throughput in CRNs [2–6], security issues have always been overlooked in these studies. Since securing
communications against the adversary typically consumes network resources in terms of bandwidth [7], it is not possible to study
these issues in isolation. The objective of this study is to find a balance between physical layer security and throughput in order
to build a more efficient and secure CRN.
A.
Related Work
In [2–6], the authors present a plethora of results related to achievable throughput in CRNs. In [2], a CRN model based on
two-sender, two-receiver interference channel is considered with sender 2 having knowledge of the encoded message sender 1
plans to transmit. The authors derive the achievable rate for both genie-aided cognitive radio channel case and additive Gaussian
noise case. Goldsmith et al. survey fundamental capacity limits and associated transmission techniques for different wireless
network design paradigms based on CRNs in [3]. [4] considers a communication scenario in which the primary and the cognitive
radios wish to communicate to different receivers, subject to mutual interference. The highest rate at which the cognitive radio
can reliably communicate under the constraint that no rate degradation occurs for the primary user is derived. The variation
of capacity when constraints are placed on the channel output signal (as well as generalizations thereof) is investigated in [5].
In [6], Liang et al. study the problem of designing the sensing duration to maximize the achievable throughput for the secondary
network under the constraint that the primary users are sufficiently protected. They formulate the sensing-throughput tradeoff
problem mathematically and use energy detection sensing scheme to prove that the formulated problem indeed has one optimal
sensing time which yields the highest throughput for the secondary network. However, all the above efforts related to CRN
performance assume a perfectly secure environment.
Clancy et al. in [8] introduce a class of attacks specific to CRNs, such as, manipulation of spectral and self-propagating
articial intelligence virus. They also propose a mitigation method for some of these attacks and a road-map for implementing
these ideas in the network stack. Shu et al. explore the existing attacks to physical layer of CRNs and discuss how to defend
against these attacks in [9]. Nevertheless, the throughput performance of CRNs is ignored in both these efforts.
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Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
Ruiliang et al. in [10] propose a new security mechanism that deploys helper nodes (HN) near the primary transmitter to
protect CRNs from primary user emulation (PUE) attack. However, the system and HN implementation requires additional cost
as well as energy. The secrecy capacity (defined as the difference of the Shannon capacity of the channel between the source and
destination and the Shannon capacity of the channel between the source and eavesdropper) of CRNs is studied in [11]. However,
in secrecy capacity efforts, the emphasis is not on ways to protect the communication, but rather, understanding the fundamental
limits on communication in the presence of eavesdropper. In [12], the authors present a framework to maximize the throughput
under a specified security condition. However, their approach is focused on the data-link layer of a point to point communication
network. Wang et al. concentrate on the security of physical layer spectrum sensing in [13]. They investigate collaborative
sensing of cognitive radio networks under malicious attacks, and analyze the spectrum sensing performance in a generalized
framework. Nonetheless, the goal of [13] is to improve efficiency of spectrum access.
In spite of all these efforts, there is still a fundamental unanswered question: how can we balance physical layer security
and throughput in a CRN? That is, how much information can a user transmit safely under the exponential adversary attack.
Encryption at the physical layer is one way of securing communication. Physical layer encryption offers a number of advantages
over encryption at higher layers [14] and it is easily integrated with traditional upper layers encryption techniques [15, 16]. In
this work, we will focus our attention on physical layer encryption and evaluate the tradeoff between security and throughput.
B.
Contributions
In this work, we restrict ourselves to security of the primary tier since only primary users are licensed in a CRN. We assume
a two-tier underlay cognitive radio network with all PUs and cognitive users (CUs) distributed as Poisson Point Process (PPP).
Then, we employ block cipher as the security mechanism and use vulnerability level as the security metric to evaluate our CRN
model. The secure CRN is studied under an exponential adversary attack. Based on this secure CRN model, we formulate the
security-throughput tradeoff problem mathematically, and aim to optimize throughput with constraints on vulnerability level for
each link. In order to solve the constrained throughput maximization problem, we propose a security level adjustment (SLA)
algorithm based on water-filling. Results show that our SLA algorithm performs much better than the conventional fixed block
length cipher. The contributions of this paper can be summarized as follows:
• The optimal trade-off between security and throughput is quantified via a constrained throughput maximization problem.
• A simple and efficient security level adjustment (SLA) algorithm based on water-filling is proposed to achieve balance
between security and throughput.
• To the best of our knowledge, this is the first work to demonstrate the effectiveness of security level management on CRN
throughput.
The remainder of the paper is organized as follows: Section II describes the system model and the security metric used in this
paper. The formulation of constrained optimization problem and its analysis is given in Section III. In Section IV, the simulation
results are presented. Section V summarizes the conclusions and future work.
II.
A.
SYSTEM MODEL
CRN Model
We consider a two-tier underlay cognitive radio network with all PUs and CUs using the same frequency band. The CRN is
modeled as a bipolar network [17], as shown in Fig. 1, in which each transmitter is at a fixed distance from corresponding
receivers. The PTs are distributed as a homogeneous PPP: Ψp = {pt1 , pt2 , . . .} ⊂ R2 with density λp , and the location of
potential CTs follows another homogenous PPP: Ψc = {ct1 , ct2 , . . .} ⊂ R2 with density λc (independent of PTs). Since we
assume all primary receivers (PRs) and cognitive receivers (CRs) are located at a fixed distance from corresponding PTs and
CTs, PRs and CRs also follow a PPP with density λp and λc . To protect the quality of primary user communication, we set up
exclusive regions, which are circular with radius D. Within the exclusive regions, CUs cannot be active in order to limit the
interference to PUs. The activation of CTs is highly dependent on exclusive regions, and distribution of active CTs follows a
Poisson Hole Process [18]. In this work, we assume that CUs have complete information regarding PU locations.
B.
Cipher Mode
All primary transmissions are protected via a cipher. In this work, a block cipher is used. There are five basic modes of operation
for a block cipher: Electronic CodeBook (ECB) mode, Cipher Block Chaining (CBC) mode, Cipher FeedBack (CFB) mode,
Output FeedBack (OFB) mode and the CounTeR (CTR) mode. ECB mode and CBC mode are defined as block modes because
plaintext is independently encrypted into a block at a time to produce corresponding ciphertext. Stream mode, including CFB
mode, OFB mode, and CTR mode, encrypt one bit at a time. As a result, in these modes, there is no propagation error across
transmissions. However, for block modes (ECB mode and CBC mode), a single bit error in the received ciphertext block may
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Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
CRN Model
0.6
primary transmitter
primary user
cognitve transmitter
cognitive user
0.4
0.2
0
−0.2
rc
−0.4
−0.8
−1
D
rp
−0.6
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Fig. 1 Bipolar network model. The stars are primary transmitters and the circles are primary receivers. The primary transmitter-receiver pairs
are represented by lines with arrows pointing to the receivers. The distance between a primary transmitter-receiver pair is rp . The rhombuses
are active cognitive transmitters and the triangles are active cognitive receivers. We have eliminated the inactive cognitive communication pair
which is located in the exclusive region, and denoted as a large circle with radius D. The cognitive transmitter-receiver pairs are also represented
by lines with arrows pointing to the receivers, and the distance between a cognitive transmitter-receiver pair is rc .
result in an error in every bit of the decrypted block (error propagation), which leads to a fundamental trade-off between security
and throughput in encryption based CRN security. Thus, our study primarily focuses on block mode cipher [19].
C. Exponential Adversary Attack Model
There are several ways using which one can quantify the strength of an encryption scheme. One way is to use the brute force
technique, i.e., for a given ciphertext, try decrypting with all possible encryption keys until it decrypts to the corresponding plaintext [20]. In practice, however, encryption systems are frequently subject to vulnerabilities which ultimately lead to short-cut
attacks. Such vulnerabilities indicate that it is reasonable to model the attacker strength as a random parameter using some probability distribution. We define the attacker strength as α. The probability of cracking a cipher with block length N corresponds
to Pr (α = N ). This implies that the attacker with strength α has the ability to crack any cipher with block length less than α
within reasonable constraints related to cost and time required to crack the cipher. In our work, we employ exponential adversary
attack model. Here, an exponential distribution is used to describe the attacker strength. Therefore, the protection probability of
an exponential adversary attack model can be written as [12]:
ϕi = Pr (α ≥ Ni ) = e−kNi ,
(1)
where, Ni is the block length of the cipher for ith communication link and k > 0 is a constant.
III.
A.
SECURITY AND THROUGHPUT TRADE-OFF
Analysis of the CRN
As indicated above, we model a CRN as a two-tier bipolar network: primary tier and cognitive tier. The transmitters in each
tier differ in terms of transmit power (denoted as Pp and Pc ), data rate (Cp and Cc ), and spatial density (λp and λc ). Without
loss of generality, we consider the ith primary user located at the origin. Distance between the j th primary transmitter and ith
primary transmitter and the distance between the k th cognitive transmitter and ith primary transmitter are denoted by dpp (j, i)
and dcp (k, i). The corresponding power fading parameters hpp (j, i) and hcp (k, i) are assumed to be i.i.d exponential distribution
−α
(Rayleigh fading). The standard path loss function is given by l (x) = kxk , where α > 2 is the path loss exponent. Therefore,
−α
(i) (i,i) (i,i) (i,i)
the received power of the ith primary receiver from the ith primary transmitter is Pp hpp . dpp , where hpp ∼ exp (1)
(i)
and Pp is transmit power of the ith primary transmitter. The resulting SINR at the ith primary receiver is:
SIN R(i) =
−α
(i) (i,i) (i,i) Pp hpp . dpp n0 + Ipp + Icp
16
,
(2)
Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
where, n0 is the background noise power. Ipp is the interference from other primary transmitters, given by:
m
X
Ipp =
−α
(j,i) (j,i) Pp(j) hpp
. dpp .
(3)
j∈Ψp \i
The interference generated by other cognitive transmitters is represented as:
Icp =
n
X
(k,i) −α
Pc(k) h(k,i)
.
,
d
cp
cp (4)
k=1
(k)
where, Pc is the transmit power of k th cognitive transmitter.
The Shannon Capacity of the wireless communication channel between the ith primary transmit and the ith primary receiver
can be evaluated from function (2) as:
(5)
Ci = log2 1 + SIN R(i)
Pm
Thus, the total capacity of the entire primary tier is: Ctotal = i=1 Ci .
B.
Security Metric
In this section, we introduce a security metric of interest in this work: average vulnerability level. We consider this as the metric
for managing security in the CRN. If each communication link is encrypted with a distinct block length, the expression of average
vulnerability level can be defined as:
Pm
Pr (α ≥ Ni )
(6)
Φ = i=1
m
where, m represents that there are m communication pairs in the primary tier, and the ith communication link is encrypted using
block length Ni . It is important to mention that the average vulnerability level has an inverse relationship to the security level as
defined in [12].
C. Problem Formulation
As we have mentioned in section II B, in block cipher model, an error in the received ciphertext block will result in the loss
of the entire block due to error propagation after decryption. Hence, it will lead to communication failure. Therefore, the
throughput of communication channel i can be written as Ci (1 − pi )Ni , where pi denotes the bit error probability of the ith
communication channel; Ni is the block length of corresponding cipher for ith communication pair; Ci stands for the capacity
of ith communication channel. The goal of our work is to maximize overall throughput while simultaneously guaranteeing a
certain average vulnerability level for each communication link in the CRN. Therefore, the throughput for the whole primary
communication tier is:
m
X
T =
Ci (1 − Ni pi ) .
(7)
i=1
In the exponential adversary attack model, we can substitute for Ni from (1) to rewrite (7) as:
maximize : T =
ϕi
m
X
pi
Ci 1 + ln ϕi
k
i=1
(8)
subject to:
ϕi − ϕmin ≥ 0
(C1)
ϕmax − ϕi ≥ 0
Pm
ϕi
Φ0 − i=1
=0
m
(C2)
(C3)
As we have derived that the optimal solution ϕi should be ϕmin 6 ϕi 6 ϕmax . The first constraint C1 and the second constraint
C2 mean the optimal solution should be greater than or equal to the minimum protection probability and should be less than or
equal to the maximum protection probability. Φ0 denotes the maximum allowable overall vulnerability level and i = 1, 2, . . . , m.
The equality in (C3) results from the following argument. We have m communication channels in our CRN model. For each of
the channels we have different channel quality. Hence, we should employ different security levels for the channels. We observe
that the increase in security level will lead to a decrease in throughput. Thus, in order to achieve the maximum throughput, we
17
Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
should use the maximum allowed overall vulnerability level, which has an inverse relationship to the security level. Therefore,
we have this constraint in place to guarantee the maximum throughput.
The Lagrangian corresponding to (8) can be written as:
m
X
m
X
pi
Ci 1 + ln ϕi +
νi (ϕi − ϕmin )
k
i=1
i=1
!
m
m
X
X
ϕi
vi (ϕmax − ϕi ) + u mΦ0 −
+
L=
(9)
i=1
i=1
where, νi , vi and u, i = 1, 2, . . . , m are the Lagrange multipliers. Using the KKT conditions, we have:
Primal feasible condition:
Pm
ϕi
Φ0 − i=1
=0
m
Dual feasible condition:
νi ≥ 0, vi ≥ 0, u ≥ 0
(10)
(11)
Complementary slackness condition:
νi (ϕi − ϕmin ) = 0
(12)
vi (ϕmax − ϕi ) = 0
(13)
Ci pi
k (u + νi + vi )
(14)
Stationary condition:
ϕi =
In order to solve (8) via KKT condition, we need to optimize the throughput for every communication link in primary tier of our
CRN model. Therefore, for i = 1, 2, . . . , m, we have only three cases to consider, namely,
• Case 1: νi = 0, vi 6= 0, we have ϕi = ϕmax
• Case 2: νi 6= 0, vi = 0, we have ϕi = ϕmin
• Case 3: νi = 0, vi = 0, ϕi =
Ci pi
ku
Using these cases, we can develop an efficient algorithm to solve our optimization problem as described below:
First, by observing the role of optimization parameters, we have:
T =
m
X
Ci (1 +
i=1
m
m
X
1X
pi
lnϕi ) =
Ci +
Ci pi lnϕi
k
k i=1
i=1
(15)
Pm
Here, since ϕi is the variable, only the
part ( i=1 Ci pi lnϕi ) influences the total throughput. Therefore, in order to find
Psecond
m
the optimalP
ϕi that maximizes T = i=1 Ci (1 + pki lnϕi ), we can solve the equivelent problem of finding the optimal ϕi that
m
maximizes i=1 Ci pi lnϕi .
Thus, we can rewrite the objective function as:
maximize : t =
ϕi
m
X
Ci pi · ln ϕi
(16)
i=1
subject to: (C1)-(C3). Since each element in t is concave, the solution to (16) can be solved via water-filling approach as
presented in security level adjustment (SLA) algorithm (see Algorithm 1). Our SLA algorithm is extended from the standard
water-filling algorithm in [12] and briefly described below: let ti = Ci pi ln ϕi , the first order derivative of ti with respect to ϕi
∂ti
Ci pi
is:
=
. We sort the channels in nonincreasing order of Ci pi . Then, starting from ϕ1 = ϕmin , each ϕi is updated based
∂ϕi
ϕi
Pm
ϕi
ϕi
on the water level
. This procedure to find the optimal ϕi allocations is continued until the constraint Φ0 − i=1
=0
Ci pi
m
is reached.
18
Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
Algorithm 1 SLA algorithm to find the optimal security allocation
1) Sort the communication links in non-increasing order of Ci pi , i = 1, 2, . . . , m.
ϕmin
2) Let j = 1, compute α =
.
Ci pi
3) Then ϕi P
= αCi pi , for i = 1, 2, . . . , m; if ϕi < ϕmin , let ϕi = ϕmin ; if ϕi > ϕmax , let ϕi = ϕmax .
m
ϕi
4) If Φ0 < i=1 , set j = j + 1 and go to step 2); otherwise proceed to step 5).
m
Pm
ϕi
5) If Φ0 = i=1 , the current set of ϕi , i = 1, 2, . . . , m are solution; otherwise proceed to step 6).
m
6) Suppose the optimal α is between αj and αj−1 , set α = αj−1 . Let l be the index of the largest Ci pi , i = 1, 2, . . . , m such
that ϕl < ϕmax , and imin is the index of smallest Ci pi , i = 1, 2, . . . , m such that ϕi > ϕmin .
ϕmin
ϕmax
, set ϕi = αCi pi , for i = 1, 2, . . . , m; ϕi (ϕi < ϕmin ) = ϕmin ; ϕi (ϕi > ϕmax ) =
; if α <
7) Let α =
Cl pl
Cimin+1 pimin+1
ϕmax ; go toP
step 8); otherwise set l = l − 1 and go to step 9).
Pm
m
ϕi
ϕi
8) If Φ0 = i=1 , the optimal set is found; otherwise if Φ0 < i=1 , set l = l + 1 go to step 7); otherwise set l = l − 1
m
m
and go to step 9).
1
9) The optimal α is found as α = Pl
(mΦ0 − (m − imin ) ϕmin + (l − 1) ϕmax ); set ϕi = αCi pi , for i =
i=imin Ci pi
1, 2, . . . , m, ϕi (ϕi < ϕmin ) = ϕmin ; ϕi (ϕi > ϕmax ) = ϕmax .
Parameter
Path loss exponent: α
The transmit power of PTs: Pp
The transmit power of CTs: Pc
The background noise power: n0
The radius of protect region: D
The distance between PTs and PRs: rp
The distance between CTs and CRs: rc
The exponent: k
The density of PTs: λp
The density of CTs: λc
Fading function: h
Modulation method:
Value
4
1W
0.1W
0.05W
0.45
0.25
0.10
0.0001
4,5,6,7,8,9
12,15,18,21,24,27
∼ exp (1)
BPSK
TABLE I Simulation Parameters
IV.
SIMULATION RESULTS
In this section, we evaluate our proposed security level management strategy using simulations. The CRN parameters associated
with our simulation are presented in Table I. We employ the ECB block cipher with target, maximum and minimum block cipher
length of 128, 1024 and 16 corresponding to the target (Φ0 ), maximum (Φmax ) and minimum (Φmin ) security level in our CRN
model. The optimal security block lengths of each communication link are determined based on security level adjustment (SLA)
algorithm.
We define two metrics for evaluating the impact of our proposed security level adjustment (SLA) algorithm on throughput.
Tnew − Tf ix
The first metric is the throughout gain, G =
, where, Tnew and Tf ix represent the throughput of optimal block
Tf ix
length allocation and the throughput of fixed block length allocation (i.e., no security management). The second metric is the
T
normalized throughput TN =
, where T is normalized by the maximum transmission rate Cmax = max {Ci }. The
mCmax
first metric, i.e., throughput gain enables us to differentiate between the performance of the CRN with our proposed security
management algorithm and the performance of the CRN without using a security management algorithm. The second metric,
i.e., normalized throughput provides a measure of the standalone individual performance of the security strategies considered in
the CRN.
Fig. 2 indicates that we can vary the average SINR by changing the densities of PUs (e.g., as PU density increases, the
average SINR decreases as interference increases). It is important to note the meaning of average SINR in this context. We set
the PU densities and CU densities to obtain a realization of the CRNs. This sets the number of PU links m. The average SINR
is the instantaneous SINR (define in (2)) averaged over these m links.
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Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
Trade−off between density of PUs and average SINR
18
16
Average SINR
14
12
10
8
6
4
5
6
7
Density of PUs
8
9
Fig. 2 The relationship between average SINR of primary tier and the density of PUs.
Trade−off between gain in throughput and average SINR
0.24
0.22
Gain in throughput
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
6
8
10
12
Average SINR
14
16
18
Fig. 3 Trade-off between throughput gain and average SINR generated by our CRN model using BPSK modulation with exponential adversary
attack model.
Fig. 3 illustrates the variation of throughput gain G as a function of average SINR. It shows that the throughput gain
decreases with increasing SINR. This can be explained based on Eq. (7). For high average SINR (i.e. lower bit error probability),
throughputs
Pm of optimal block length allocation and fixed block length allocation are both close to the achievable throughput
(T = i=1 Ci ). At lower SINR, (i.e. higher bit error probability), the throughput of optimal block length allocation performs
significantly better than the fixed block length allocation.
Fig. 4 demonstrates the effect of security management on normalized throughput TN . Once again, we vary the average SINR
and observe TN for the cases when we use security management and when we use a fixed security level, respectively . Figure
4 shows that the security level adjustment (SLA) algorithm enhances the throughput of the system relative to the fixed security
level algorithm. Combining results from Fig. 3 and Fig. 4, we observe that as communication quality improves, the performance
gap between these two methods reduces.
V.
CONCLUSIONS
This paper focuses on managing security levels in CRNs to build more efficient and secure networks so as to optimize the
throughput of every link while simultaneously maintaining necessary security levels for them. We employ block cipher as the
security mechanism and use vulnerability level as the security metric. The secure CRN is studied under an exponential adversary
attack. In order to balance the tradeoff between physical layer security and throughput in CRNs, we propose a security level
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Journal of Communications Engineering and Networks
Jan 2014, Vol. 2 Iss. 1, PP. 14-22
Comparison of normalized throughputs
0.38
Tnew
Tfix
0.36
Normalized throughput
0.34
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
6
8
10
12
Average SINR
14
16
18
Fig. 4 Comparison of system normalized throughput using our new algorithm allocation and fixed block length allocation for BPSK with
exponential adversary attack model.
adjustment (SLA) algorithm based on water-filling. The SLA algorithm can distribute the optimal security level as well as the
optimal cipher block length for each communication link in our CRN model corresponding to their channel quality. Results
show that our SLA algorithm performs much better than the conventional fixed block length approach. Future work involves the
exploration of alternative security mechanism and optimization the trade-off between security and throughput.
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