∎

# Network Coding-based Routing and Spectrum Allocation in Elastic Optical
Networks for Enhanced Physical Layer Security

*Giannis Savva  Konstantinos Manousakis  Georgios Ellinas This work has been partially supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 739551 (KIOS CoE) and from the Government of the Republic of Cyprus through the Directorate General for European Programmes, Coordination and Development. It was also partially supported by the Cyprus Research and Innovation Foundation under project CULTURE/AWARD-YR/0418/0014 (REALFON).Giannis Savva, Konstantinos Manousakis and Georgios Ellinas are with the Department of Electrical and Computer Engineering and the KIOS Research and Innovation Center of Excellence, University of Cyprus, Nicosia 1678<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

In this work, an eavesdropping-aware routing and spectrum allocation approach
is proposed utilizing network coding (NC) in elastic optical networks (EONs).
To provide physical layer security in EONs and secure the confidential
connections against eavesdropping attacks using NC, the signals of the
confidential connections are combined (XOR-ed) with other signals at different
nodes in their path, while transmitted through the network. The combination of
signals through NC significantly increases the security of confidential
connections, since an eavesdropper must access all individual signals,
traversing different links, in order to decrypt the combined signal. A novel
heuristic approach is proposed, that solves the combined network coding and
routing and spectrum allocation (NC-RSA) problem, that also takes into account
additional NC constraints that are required in order to consider a
confidential connection as secure. Different routing and spectrum allocation
strategies are proposed, aiming to maximize the level of security provided for
the confidential demands, followed by an extensive performance evaluation of
each approach in terms of the level of security provided, as well as the
spectrum utilization and blocking probability, under different network
parameters. Performance results demonstrate that the proposed approaches can
provide efficient solutions in terms of network performance, while providing
the level of security required for each demand.

##  1 INTRODUCTION

Elastic optical networks (EONs) provide improved transmission performance and
more flexible spectrum allocation compared to conventional WDM optical
networks. In EONs, the C-band can be separated in slices (frequency slots) of
$25$, $12.5$, and $6.25$ GHz. Subsequently, a connection can be allocated to a
number of frequency slots to satisfy its required bit rate. To establish a
connection in EONs, a viable solution to the RSA problem must be found, which
consists of finding a path (routing - R) from the source to the destination,
along with the allocation of the required spectrum slots (spectrum allocation
- SA). To find a feasible RSA solution, three basic constraints must be
satisfied: (i) the spectrum continuity constraint, where each demand must be
allocated the same frequency slots on each link of the selected path, (ii) the
non-overlapping constraint, where a frequency slot can only be allocated to
one demand at a time, and (iii) the spectrum contiguity constraint, where the
slots serving each demand must be contiguous EONs1 ; RSA .

Optical networks are considered one of the most important critical
infrastructures, as many services (e.g., cloud computing) and critical
applications (e.g., national security, public health) rely on these networks
for data exchange. Due to the type and the amount of data transmitted, the
security of optical networks is of paramount importance, since even attacks
over a short time period can still compromise large amounts of critical data.

There are numerous real-world scenarios where optical networks were breached
(e.g., utilizing tapping devices to access the signal transmitted via optical
fibers). Hence, optical layer security has received considerable attention in
recent years. Optical layer security can be divided into different categories
based on the type and the purpose of the threat. Such security threats include
the observation of the existence of communication (privacy), the unauthorized
use of spectrum (authentication), the manipulation or destruction of data
(integrity), the denial of service (availability), and the unauthorized access
to information (confidentiality) Sec1 ; Sec3 ; Furdek16 ; Sec2 ; Savva182 ;
JAM1 ; SavvaJocn ; Bei18 ; Singh16 . The focus of this work is on
confidentiality, where an adversary tries to and can have undetected access to
confidential data from an optical communication channel (i.e., eavesdropping)
for a prolonged period of time.

Network coding (NC) is a technique where data of different connections are
combined and transmitted through the network Manley10 . In this work, NC is
used to provide security in EONs against eavesdropping attacks by encrypting
the confidential data. Thus, with the use of NC, it is extremely difficult for
an adversary to compromise any confidential connection, since a number of
different connections that traverse different routes will have to be
compromised, in order for the attacker to make sense of the accessed
confidential data. This work significantly extends the concept presented in
Savva19  by providing an extended analysis of NC within optical networks,
followed by novel policies for allocating a path and spectrum slots for the
confidential demands. Further, additional properties are considered for the
paths used in the XOR operations, which are subsequently incorporated within
the heuristic algorithms. Finally, extensive simulations are performed to
compare all policies in terms of spectrum utilization, blocking probability,
and the level of security provided for the confidential demands.

The rest of the paper is organized as follows. The general concept of network
coding and its implementations in optical networks are discussed in Section 2.
The combined NC-RSA problem is described in Section 3, followed by the
proposed heuristic algorithm in Section 4. Next, the performance results are
presented in Section 5, while Section 6 offers some concluding remarks.

##  2 Network Coding Implementations in Optical Networks

The application of NC to optical networks from the algorithmic and
infrastructural perspectives has been investigated by the authors in Manley10
. Furthermore, using NC in conjunction with the RSA process, several
connections can combine their transmitted data, enabling protection,
multicasting, and security functionalities within the optical network. In the
following, a short description of how these functionalities can be achieved,
along with a discussion on the physical implementation of NC in optical
networks are presented.

(a) NC-based Protection in Optical Networks
NC-based protection in optical networks has been widely studied Manley10 ;
Ramirez14 ; Kamal14 ; Hai17 . For such an approach, intermediate network nodes
process a set of signals such that a destination node will receive a linear
combination of signals over several disjoint paths. Then, in the case of a
failure in the primary path, the destination node will still be able to
recover the failed signal from the rest of the received combined signals
arriving at the destination from paths that are not affected by the failure.
For instance, consider the network shown in Fig. 1(a). In this example,
connections $1-4-6$ and $2-5-6$ transmit datastreams $a$ and $b$,
respectively. To provide protection for the primary paths, using network
coding, source nodes $1$ and $2$ also transmit their datastreams to node $3$,
which performs an XOR operation ($a\oplus b$). Subsequently, the resulting
signal ($a\oplus b$) is transmitted to the destination (i.e., node $6$). In
the case that connection $1-4-6$ fails, datastream $a$ can still be recovered
by the destination node as $a=(a\oplus b)\oplus b$. Similarly, in the case
that path $2-5-6$ fails, datastream $b$ can still be obtained as $b=(a\oplus
b)\oplus a$.

Figure 1: Utilizing NC for (a) protection, (b) multicasting, and (c) security.

(b) NC-based Multicasting in Optical Networks
NC can also be used for multicasting in optical networks. Authors in Manley10
; Agarwal04 ; Yang16  demonstrate the utilization of network coding for
multicasting connections to improve network throughput. The concept of NC in
multicasting is to divide the original traffic into different lower-rate sub-
streams and design trees in such a way that the destination nodes will be able
to decode the incoming signals based on specific XOR operations. In Fig. 1(b),
assume that node $1$ is the source node and needs to transmit datastreams $a$
and $b$ to both destination nodes $5$ and $7$. One possible solution using
network coding is to transmit datastream $a$ to node $5$ and datastream $b$ to
node $7$, perform the XOR operation $(a\oplus b)$ at node $4$, and transmit
the resulting datastream $(a\oplus b)$ to both destination nodes through paths
$4-6-7$ and $4-6-5$. Hence, each node can obtain both $a$ and $b$ by using the
received signals. For example, node $5$ receives datastream $a$ and $(a\oplus
b)$. Then, $b$ can be obtained through the process $b=a\oplus(a\oplus b)$. A
similar procedure can also be performed at node $7$ to obtain datastreams $a$
and $b$ Kim09 ; Yang16 .

(c) NC-based Security in Optical Networks
Authors in Engel16  studied the effectiveness of linear network coding (LNC)
in optical networks to protect connections from security threats such as
eavesdropping and jamming attacks. To enhance the network with security
capabilities, a confidential connection can transmit a coded version of its
data. Hence, in the case of an eavesdropping attack, the attacker must have
knowledge of both the coded version of the signal and all connections used to
perform the XOR operations in order to access the confidential data. Recently,
work in Savva19  investigated the problem of network security in elastic
optical networks using NC through a heuristic approach. This is also the main
topic of this work, in which a significant extension of the approach presented
in Savva19  is provided.

Fig. 1(c) presents a simple example where network coding can be used to
provide security for a confidential connection in an optical network. As shown
in this figure, the confidential datastream $a$ is transmitted using path
$1-2-6$. Also, two non-confidential connections are established in the network
using paths $1-3-6$ and $2-5-6$, and transmit datastreams $b$ and $c$,
respectively. To provide security for the confidential connection using path
$1-2-6$, source node $1$ transmits a coded version of datastream $a$, namely
$a\oplus b$, over link $1-2$, and additional security is provided at link
$2-6$ by also using connection $2-5-6$ and datastream $c$. Thus, ($a\oplus
b\oplus c$) is transmitted at the second link of the confidential path. To
acquire the confidential datastream $a$ at node $6$, the receiver can perform
the operation $a=b\oplus c\oplus(a\oplus b\oplus c)$. Hence, an eavesdropper
must also gain access to both datastreams $b$ and $c$ in the network in order
to be able to make sense of the confidential datastream $a$. In other words,
the eavesdropper must simultaneously tap $3$ different links at different
network locations to compromise datastream $a$.

(d) Physical Layer Implementation of NC in Optical Networks
In opaque networks, NC can be easily implemented, since signals can be
received, combined, and transmitted by the intermediate nodes, providing an
encrypted version of the signal at each link. However, for such a technique to
work in transparent optical networks, the nodes must be equipped with
additional hardware in order to perform the XOR operation at the physical
(optical) layer. Furthermore, all involved signals must use the same spectrum
resources in order for network coding to be enabled. It was shown that NC in
all-optical networks can be realized by all-optical XOR logic gates.
Specifically, a review of an optical implementation of all-optical XOR gates
was performed in Zhang05 . All-optical XOR gates are typically based on
semiconductor optical amplifiers (SOAs) that offer low-power consumption, easy
deployment, and short-latency. Experimental works have also demonstrated NC
using XOR operations that can be performed at line speed for transmission
above $10$ Gbps and up to $100$ Gbps with different modulation formats Kong13
; Chen15 ; Lu16 . In addition, authors in Li14  proposed and experimentally
demonstrated a coherent optical layer network coding scheme on polarization-
multiplexed differential quaternary phase-shift keying (PM-DQPSK) signals, in
which the two PM-DQPSK signal components in the network-coded signal occupy
the same channel and cannot be separated by conventional demultiplexing means.
Finally, authors in Liu13  demonstrated, using OFDM signals, that the NC
technique does not require symbol-level synchronization. Thus, the feasibility
of optical NC was clearly demonstrated and is a technology that could be
implemented in EONs to provide security at the physical layer against
eavesdropping attacks.

##  3 Problem Description

To provide security for confidential connections in the network against
eavesdropping attacks, the combined NC-RSA problem must now be solved. More
specifically, in order to find the path and the spectrum required for a
confidential connection, the path is chosen so as to take advantage of the
existing connections established in the network, that are utilized to perform
a number of XOR operations in the nodes that traverse the confidential path.
Further, it should be noted that the spectrum slots selected for the
confidential connection can significantly affect the choice of existing
connections that can be involved in the XOR process. To consider a
confidential connection as secure when using network coding, the following
constraints must be satisfied.

  * •

Encrypted Transmission (ET): All links of the path allocated to a confidential
connection must transmit an encrypted version of their data with at least one
XOR operation with other currently established connections in the network.

  * •

Frequency Slot Matching (FSM): At least a subset of the frequency slots
utilized by the confidential connection must have the same id with the slots
of the rest of the already established connections used in the XOR operations.

To satisfy the ET constraint, an existing connection must have at least two
common nodes with the confidential connection (the first node will be used to
encrypt the confidential connection and the second node will be used to
decrypt it). Thus, an existing connection with at least two common nodes with
the confidential connection can either be used to provide security for the
entire path of the confidential demand (i.e., when the source and destination
nodes are common nodes), or it can be used to provide security for a segment
of the confidential connection (i.e., source/intermediate to
intermediate/destination node). Also, in this work, the order in which the
common nodes are traversed by the connections involved in the XOR process must
be the same, which will also ensure that the direction of the connections
traversing the nodes are the same. Finally, the ET constraint ensures that for
a secure confidential connection, the selected existing connections must
collectively secure all links of the path allocated to that connection.

To satisfy the FSM constraint, at least a subset of the frequency slots
utilized by the confidential connection must have the same id with the
frequency slots of the rest of the existing connections used in the XOR
operation. This is the case, since it is assumed that no frequency conversion
is performed at intermediate nodes, and therefore, the signals used for the
XOR operation must be on the same frequency. However, the confidential
connection is considered as secure even when only part of the signal (a subset
of the frequency slots) is XOR-ed, since the eavesdropper would still have to
access all connections used in the encryption process in order to decrypt and
make sense of the accessed confidential data.

Finally, it is important to note that to satisfy both constraints, all
connections involved in the encryption process (i.e., both the confidential
and the currently established connections used in the XOR operation) must be
link-disjoint. This is the case, since the connections used in the XOR
operation must transmit signals that are at least partially utilized on the
same frequency. Thus, considering also the non-overlapping constraint of the
RSA problem, all paths involved in this process must be link-disjoint.

The following example (Fig. 2) provides an illustration of the aforementioned
constraints in combination with the establishment of a secure confidential
connection. In this example, $4$ connections ($p_{2},p_{3},p_{4}$, $p_{5}$)
are currently established in the network, provisioned as shown in Table 2,
where each connection, $p_{x}$, transmits datastream $c_{x}$. Further, a
confidential connection $p_{1}$ must be established in the network, requiring
$2$ spectrum slots and using path $1-4-5$.

Figure 2: Example of network coding for the establishment of a secure
confidential connection.

As also discussed previously, only the existing connections with two common
nodes with the confidential connection can be used to provide security for
$p_{1}$ using NC. Thus, $p_{4}$ and $p_{3}$ cannot be used to provide security
for $p_{1}$, as $p_{4}$ does not have two common nodes with $p_{1}$ and
$p_{3}$ traverses its common nodes with $p_{1}$ in the opposite order compared
to $p_{1}$. Further, the group of spectrum slots that will be assigned for
connection $p_{1}$ is very important, since at least a subset of the frequency
slots utilized by the confidential connection as well as the already existing
connections that take part in the XOR process must be the same (FSM
constraint). Thus, if spectrum slots $4-5$ were used for $p_{1}$, then only
$p_{5}$ can be used to provide security for the connection, while if spectrum
slots $2-3$ are used, then both $p_{2}$ and $p_{5}$ can be used to provide (a
higher level of) security for $p_{1}$. Table 2 presents the transmitted
datastreams for each link of the confidential connection, if allocated using
spectrum slots $2-3$. As shown in Table 2, an encrypted version of the
confidential signal is transmitted at all links of the path, satisfying also
the ET constraint. In this example, the destination node can successfully
decrypt the data, whereas the eavesdropper must gain access to multiple
additional connections that are allocated at link-disjoint paths (i.e.,
$p_{2}$ and $p_{5}$) apart from the confidential one, in order to make sense
of the accessed confidential datastream.

Table 1: Paths and spectrum slots allocated to existing connections in the network. | Connection
---
Id
| Path
---
Selected
| Spectrum
---
Slots Allocated
$p_{2}$ | $6-4-2-3-5$ | $1-3$
$p_{3}$ | $5-3-4$ | $1-4$
$p_{4}$ | $1-2$ | $1-2$
$p_{5}$ | $1-6-7-5$ | $2-5$

Table 2: Datastream transmitted at each link of the confidential connection $p_{1}$. Link |  | Transmitted
---
datastream
$1-4$ | $c_{1}\oplus c_{5}$
$4-5$ | $c_{1}\oplus c_{2}\oplus c_{5}$

##  4 Proposed Heuristic Algorithm

To solve the combined NC-RSA problem, the proposed heuristic algorithm is
divided into the routing (R) and spectrum allocation (SA) sub-problems. A
network planning scenario is considered, where all demands are known a priori
and each demand is described by a $4$-tuple (s,d,B,c), denoting the source,
destination, bit-rate, and confidentiality, respectively. Confidentiality in
this case is defined as a binary variable which describes the demand as
confidential ($1$) or non-confidential ($0$). It is noted that different
classes of confidential connections could be utilized based on the minimum
threshold of XOR operations (designated as $T$ in this work) required per
link. However, in this work, only the case of confidential ($T=1$) and non-
confidential demands will be considered.

###  4.1 Pre-processing Phase

Prior to the utilization of the heuristic approach, a pre-processing phase is
required that pre-calculates the candidate paths for each $s$-$d$ pair. Also,
a node-matching procedure takes place, to ascertain whether two paths have at
least two common nodes traversed in the same order, so as to satisfy the ET
and FSM constraints, that are required for a feasible NC-RSA solution for the
confidential demands.

First, a set of $k$ candidate paths is pre-calculated for each $s$-$d$ pair.
Subsequently, to implement NC, the security level that each candidate path can
provide to the rest of the candidate paths must be calculated. According to
the ET constraint, all links traversed by a secure confidential connection
must transmit an encrypted version of the data. This means that at least one
XOR operation with the established connections must be performed for all links
in the path used by the confidential connection. Let $P$ be the set of all
candidate paths, $p$ the path under consideration ($p\in P$), and $P^{\prime}$
the set of the rest of the candidate paths that may be used by path $p$ to
provide encryption over specific links of path $p$ ($P=P^{\prime}\cup p$).
Also, let $\delta_{p^{\prime}l}^{p}$ be a coefficient which is equal to $1$ if
paths $p\in P$ and $p^{\prime}\in P^{\prime}$ have two common nodes and the
$l^{th}$ link of path $p$ can be “covered” (i.e., encryption is provided) by
path $p^{\prime}$, and $0$ otherwise.

Figure 3 provides an example of the $\delta$ coefficients for $3$ paths
$\\{3-1-2-4,2-5-6-4,2-3-5\\}$ utilized by $3$ connections in the network.
Hence, the links that are covered for each pair of connections must be
calculated ($\delta$ coefficient), with regards to the common nodes of each
pair of paths.

Figure 3: Example of $\delta$ coefficient calculation
for $3$ connections established in the network.

Table 3: $\delta$ coefficients for $3$ paths established in the network.

$\delta_{p^{\prime}l}^{p}$ | $\delta_{p^{\prime}1}^{p}$ | $\delta_{p^{\prime}2}^{p}$ | $\delta_{p^{\prime}3}^{p}$
---|---|---|---
$\delta_{2l}^{1}$ | 0 | 0 | 1
$\delta_{3l}^{1}$ | 0 | 0 | 0
$\delta_{3l}^{2}$ | 1 | 0 | 0
$\delta_{1l}^{2}$ | 1 | 1 | 1
$\delta_{1l}^{3}$ | 0 | 0 | -
$\delta_{2l}^{3}$ | 1 | 1 | -

Assume that in this case initially the path under consideration is path
$p_{2}$. To check whether the rest of the connections can provide security for
the connection using path $p_{2}$,the following procedure is followed: path
$p_{2}$ has two common nodes with path $p_{1}$ (nodes $2$ and $4$) and since
these nodes are the source and destination nodes of $p_{2}$, then connection
$p_{1}$ could be used to provide security for all links that belong to
$p_{2}$. Hence, the values of $\delta_{11}^{2}$, $\delta_{12}^{2}$, and
$\delta_{13}^{2}$ are equal to $1$ for the first, second, and third link of
path $p_{2}$, respectively. It is important to note that on the other hand,
connection $p_{2}$ can only provide security for the third link (link $2-4$)
of connection $p_{1}$, resulting in $\delta_{23}^{1}$ = $1$. Thus, clearly,
$\delta_{1l}^{2}\neq\delta_{2l}^{1}$. Similarly, the first link of $p_{2}$ can
be secured by $p_{3}$, since nodes $2$ and $5$ are common between these paths
and therefore $\delta_{21}^{3}$ = $1$. Also, in this case, $p_{2}$ can be used
to provide security for all links in $p_{3}$, since $2$ and $5$ are the source
and destination nodes of $p_{3}$, respectively. Therefore, $\delta_{31}^{2}$ =
$\delta_{32}^{2}=1$. Table 4.1 presents the $\delta$ coefficients for all path
combinations in this example.

It is noted that the order of the nodes in the path and the direction of the
path itself are taken into consideration in the determination of the $\delta$
coefficient. For example, $p_{3}$ has two common nodes with $p_{1}$ (nodes $2$
and $3$), but it cannot provide any security for that connection, since in
path $p_{3}$, node $2$ is traversed before node $3$, whereas the opposite is
the case with path $p_{1}$. Algorithm 1 below is used to calculate the
$\delta$ coefficients. Specifically, to calculate the $\delta$ coefficients,
the algorithm takes as input the set of all the pre-calculated candidate paths
$P$. Then, for each pair of candidate paths $p$ and $p^{\prime}$, their common
nodes are found and they are stored in set $CN$. Next, if the size of set $CN$
is greater than $1$ (i.e., there are at least two common nodes between paths
$p$ and $p^{\prime}$), then starting from the source node, for each node $i$
in path $p$, if that node is included in $CN$ (i.e., $i$ is a common node for
both $p$ and $p^{\prime}$), the order of the node $p(i)$ in $p^{\prime}$ is
stored in $S_{node}$. Subsequently, starting from the destination node of $p$,
for each node $j$ that is traversed after node $i$ in $p$, if the node is
included in $CN$, the order of the node $p(j)$ in $p^{\prime}$ is found and is
stored in $E_{node}$. If $E_{node}$ is greater than $S_{node}$ (i.e., node
$p(j)$ is traversed after node $p(i)$ in both $p$ and $p^{\prime}$), then all
the links between nodes $p(i)$ and $p(j)$ in $p$ can be secured by path
$p^{\prime}$. Thus, the $\delta_{p^{\prime}}^{p}$ coefficient is equal to $1$
for all these links.

Algorithm 1 Calculation of $\delta$ coefficients

Input: Set of candidate paths P
Output: $\delta$ coefficients

1:for each candidate path $p\in P$ do

2: $Z$: number of nodes $\in p$

3: for each candidate path $p^{\prime}\in P^{\prime}$ do

4: Initialize empty set $CN$,

5: Find common nodes between paths $p$ and $p^{\prime}$ and store them in $CN$

6: if $|CN|>1$ then

7: for i = 1: $Z$ do

8: if $p(i)\in CN$ then

9: $S_{node}$ = order of node $p(i)$ in $p^{\prime}$

10: for j = $Z$: i+1 do

11: if $p(j)\in CN$ then

12: $E_{node}$ = order of node $p(j)$ in $p^{\prime}$

13: if $E_{node}>S_{node}$ then

14: $L^{\prime}$: set of links between nodes $p(i)$ and $p(j)$ in path $p$

15: $\delta_{p^{\prime}l}^{p}=1$ $\forall l\in L^{\prime}$

16: Go to next candidate path $p^{\prime}$ (line 3)

17: end if

18: end if

19: end for

20: end if

21: end for

22: end if

23: end for

24:end for

It is important to note that, using this process, it is ensured that node
$p(i)$ is traversed prior to node $p(j)$, which is also the case for path
$p^{\prime}$, in order for path $p^{\prime}$ to provide security for path $p$.
Further, if more than $2$ common nodes are found, the links secured may vary
depending on which two common nodes are selected. However, following this
process, the set of common nodes that result in $p^{\prime}$ securing the
largest number of links of path $p$ is selected. This is a direct consequence
of the way the common nodes are selected (i.e., the first common node is found
while searching from the source node to the destination and the second common
node is found by starting from the destination node).

###  4.2 Routing

For the routing sub-problem, the pre-calculated $k$-shortest candidate paths
that are able to satisfy a requested connection are considered. These
$k$-shortest paths can be sorted based on different metrics (e.g., number of
hops, modulation format, most/least used nodes/links, etc.). In this work,
each node ($n$) and link ($l$) are characterized by the number of established
connections that use them (denoted as $U_{n}$ and $U_{l}$, respectively).
Further, each path takes the value of the node/link with the highest value of
$U_{n}$/$U_{l}$ among all the nodes/links it traverses ($U_{p,n},U_{p,l}$).
The paths of the non-confidential connections can then be sorted based on the
following criteria, which provide the best results in terms of spectrum
utilization and level of security, as presented in Savva19 :

  * •

Most used nodes/links (MUN/MUL): The candidate paths for each $s$-$d$ pair are
sorted in descending order based on the value $U_{p,n}$/$U_{p,l}$ of each
path. By selecting the path which comprises of the most used nodes/links, the
number of XOR operations for a confidential connection will potentially
increase.

  * •

Maximum spectrum efficiency (MSE): The candidate paths are sorted in
descending order based on the number of hops and the modulation format used
(hybrid metric defined in ICC_Giannis ). Thus, connections are established
having as an aim to maximize the spectrum efficiency of the network, rather
than maximizing the number of XOR operations.

After sorting the paths, the non-confidential connections are established
using the first path that has available spectrum resources, based on one of
the aforementioned sorting strategies.

For the confidential connections, the candidate path that produces the most
XOR operations is used, which also depends on the spectrum slots selected. To
achieve this, an XOR spectrum slot metric (XOR-SSMp) is used, that counts the
number of XOR operations performed for a specific path $p$ and group of
frequency slots. In addition, the XOR-SSMp metric can be further
differentiated as follows:

  * •

Minimum XOR spectrum slot metric (MXOR-SSMp): The MXOR-SSMp metric counts the
minimum number of XOR operations over all links of candidate path $p$. This is
the metric that was first introduced and used in Savva19 . By using this
metric the aim is to maximize the level of security provided for the “weakest
link” of the candidate path (the link with the least number of XOR operations
performed).

  * •

Average XOR spectrum slot metric (AXOR-SSMp): The AXOR-SSMp metric calculates
the average number of XOR operations per link that are provided for candidate
path $p$. By using this metric the aim is to maximize the average number of
XOR operations performed on each link of the candidate path (provided that the
minimum threshold is met, as explained below).

###  4.3 Spectrum Allocation

For the spectrum allocation sub-problem, available spectrum resources must be
allocated for a requested connection satisfying the slot continuity,
contiguity, and non-overlapping constraints RSA . To calculate the number of
frequency slots $f_{dp}$ required for a given connection $d$ if candidate path
$p$ is selected, we use $f_{dp}=\frac{B_{d}}{B_{rate}\cdot MF_{p}}$, where
$B_{d}$ is the bit-rate requested by connection $d$, $B_{rate}$ is the baud
rate of each spectrum slot in the network, and $MF_{p}$ is the modulation
format (expressed in bits/symbol) that can be used for candidate path $p$,
which is based on the overall distance of path $p$.

For the non-confidential connections, the spectrum allocation is performed in
a first-fit manner, where the first group of frequency slots from the sorted
candidate paths that is able to establish the connection is allocated. For the
confidential connections, the process of allocating spectrum resources is
based on maximizing the number of XOR operations that can be performed for the
selected path and group of frequency slots, utilizing one of the two
aforementioned XOR-SSM metrics. Algorithm 2 below describes the NC-RSA
approach for a given confidential demand. Also, an example in Fig. 4 is used
to better explain the proposed algorithm when using either metric.

Algorithm 2 NC-RSA for a given confidential demand

Input: $G(V,E),$ Set of candidate paths P, Paths currently established
$P_{e}$, Confidential demand D ($s,d,B,1$), XOR threshold $T$, Spectrum slot
metric $\mathcal{S}$
Output: Confidential Connection Establishment

1:for each candidate path $p\in P_{s,d}$ do

2: Find a set of paths $P_{used}\in P_{e}$ that are used by the established
connections, such that $\sum_{l=1}^{|V|}\delta_{p^{\prime}l}^{p}>0$, for each
$p^{\prime}\in P_{used}$

3: Create temporary matrix $t$ = $L\times F$, where $L$ = number of links in
path $p$ and $F$ = overall number of frequency slots.

4: Initialize all entries of $t$ to $0$.

5: for each path $p_{u}\in P_{used}$ do

6: Using $\delta_{p_{u}}^{p}$ coefficient, increase by one the values for each
link $l$ where $\delta_{p_{u}l}^{p}=1$ and spectrum slots that are covered by
$p_{u}$ within $t$.

7: end for

8: Initialize XOR-SSM${}_{p}=0$

9: if $\mathcal{S}==0$ then $\triangleright$ MXOR-SSM is utilized

10: for each group $(a-b)$ of available frequency slots (FS) in $p$ that can
be allocated to $D$ do

11: $c^{a-b}_{z}$= $\sum_{n=a}^{b}t_{z,n}$, for $z=1$ to $L$

12: $\mathcal{C}^{a-b}=min(c^{a-b}_{1},...,c^{a-b}_{L})$

13: XOR-SSM${}_{p}=max($XOR-SSM${}_{p},\mathcal{C}^{a-b})$

14: end for

15: else$\triangleright$ AXOR-SSM is utilized

16: for each group $(a-b)$ of available FS in $p$ that can be allocated to $D$
do

17: $c^{a-b}_{z}$= $\sum_{n=a}^{b}t_{z,n}$, for $z=1$ to $L$

18: if $min(c^{a-b}_{1},...,c^{a-b}_{L})\geq T$ then

19: $\mathcal{C}^{a-b}=(\sum_{z=1}^{L}c^{a-b}_{z})/L$

20: XOR-SSM${}_{p}=max($XOR-SSM${}_{p},\mathcal{C}^{a-b})$

21: end if

22: end for

23: end if

24:end for

25:Select candidate path $p$ with the highest value of the XOR-SSM metric.

26:if XOR-SSM${}_{p}\geq T$ then

27: Connection is established using path $p$ and group of frequency slots
($a-b$).

28:else

29: Connection is rejected.

30:end if

Specifically, in Algorithm 2, for a given confidential connection, the XOR-
SSMp metric is calculated for each candidate path $p$. To do this, a temporary
matrix (denoted as $t$ in the algorithm) is used, with size $L\times F$, where
$L$ denotes the number of links of the candidate path and $F$ denotes the
overall number of frequency slots of each link in the network. Next, the set
of the already established paths with a non-zero vector coefficient
$\delta_{p_{u}}^{p}$ for path $p$ under investigation is found (denoted as
$P_{used}$ in the algorithm, $p_{u}\in P_{used}$). This set of paths can be
used to satisfy the ET constraint. Subsequently, for each path $p_{u}$, the
values for the links and spectrum slots that are covered by $p_{u}$ within $t$
are increased by $1$. Next, for each available group of frequency slots
$(a-b)$, the number of XOR operations performed on each link $z$ of path $p$
are calculated using the following equation: $c^{a-b}_{z}$ =
$\sum_{n=a}^{b}t_{z,n}$, where $a$ and $b$ are the starting and ending slots
selected. In the case that MXOR-SSM is selected, the minimum
$\mathcal{C}^{a-b}=min(c^{a-b}_{1},...,c^{a-b}_{L})$ value is selected (i.e.,
the weakest link in terms of the number of XOR operations performed in path
$p$ is considered). On the other hand, in the case that AXOR-SSM is selected,
then if the minimum number of XOR operations on each link is greater than or
equal to the given acceptable threshold [$min(c^{a-b}_{1},...,c^{a-b}_{L})\geq
T$], the average number of XOR operations per link in the candidate path $p$
and group of frequency slots ($a-b$) is calculated via
$\mathcal{C}^{a-b}=(\sum_{z=1}^{L}c^{a-b}_{z})/L$. This procedure (for MXOR-
SSM or AXOR-SSM) is repeated for all groups of frequency slots, and the group
of frequency slots with the maximum value of $\mathcal{C}$ is selected. In
addition, this procedure is repeated for all candidate paths that can
establish connection $s$-$d$, and the maximum value of $\mathcal{C}$ amongst
all candidate paths is selected and is considered as the value of the XOR
metric for path $p$ (using either the MXOR-SSM or the AXOR-SSM metric). If the
XOR metric found has a value greater than or equal to threshold $T$, then the
connection is established in that group of frequency slots. Otherwise, it is
rejected.

The value of the metric (e.g., $x$) selected signifies that either at least
$x$ XOR operations are used to secure the confidential connection in each link
(using MXOR-SSM) or an average number of $x$ XOR operations are used to
provide security for each link of that connection, given that the threshold
requirement $T$ is satisfied at each link of the path (using AXOR-SSM). Both
processes also imply that the ET and FSM constraints are satisfied for that
confidential connection. On the other hand, if $x<T$, there is at least one
link in the path where the threshold requirement is not satisfied, and the
connection is not considered secure.

To clearly demonstrate this procedure, in Fig. 4, assume a network with $F$ =
$5$ and a candidate path $p_{1}$ ($1-2-6$) that requires $3$ frequency slots.
Also, the set $P_{e}$ of connections currently established in the network
consists of paths {$p_{2}$, $p_{3}$, $p_{4}$, $p_{5}$, $p_{6}$, $p_{7}$,
$p_{8}$}. Table 4 provides information on each path (route along with the
spectrum slots that each connection utilizes). Also, the $\delta$ coefficient
is shown for each path in $P_{e}$ and path $p_{1}$.

Figure 4: Example of NC-RSA algorithm for a given confidential connection. Table 4: Information for connections currently established in the network. | Connection
---
Id
| Path
---
Selected
| Spectrum
---
Slots allocated
$\delta_{p^{\prime}1}^{p_{1}}$ | $\delta_{p^{\prime}2}^{p_{1}}$
$p_{2}$ | $2-4-6-3$ | $4-5$ | $0$ | $1$
$p_{3}$ | $1-4-5-6$ | $3-4$ | $1$ | $1$
$p_{4}$ | $2-3$ | $1-2$ | $0$ | $0$
$p_{5}$ | $1-2$ | $1$ | $1$ | $0$
$p_{6}$ | $6-2$ | $1-3$ | $0$ | $0$
$p_{7}$ | $2-3-6$ | $4-5$ | $0$ | $1$
$p_{8}$ | $1-4-2$ | $1-2$ | $1$ | $0$

As discussed in the previous sections, a path must have at least two common
nodes with the confidential one to provide security for that connection. Thus,
$p_{4}$ is not able to provide any security for connection $p_{1}$. Also,
since the direction of the path and the common nodes plays a key role in
providing security for the confidential connection, path $p_{6}$ is also not
able to provide any security for the given demand. As a result, $P_{used}$
consists of paths {$p_{2}$, $p_{3}$, $p_{5}$, $p_{7}$, $p_{8}$}. For example,
connection $p_{2}$ contributes to cells $t_{(2,4)}$ and $t_{(2,5)}$, since it
can cover spectrum slots $4$ and $5$ in the second link of $p_{1}$. On the
other hand, connection $p_{5}$ could provide security to the confidential
connection, but since it uses the same link as $p_{1}$, the spectrum slots
allocated to $p_{5}$ (i.e., slot $1$) are excluded from the available group of
frequency slots to satisfy the non-overlapping constraint. This value is
designated as ‘$-$’. The resulting $t$ matrix using all paths in $P_{used}$ is
shown in Table 6.

Table 5: Number of XOR operations per slot ($t$ matrix). | Spectrum Slot id
---|---
1 | 2 | 3 | 4 | 5
Link id | 1 (1-2) | $-$ | $1$ | $1$ | $1$ | $0$
2 (2-6) | $-$ | $0$ | $1$ | $3$ | $2$

Table 6: Number of XOR operations per link and group of available frequency slots. | $c_{z}^{2-4}$ | $c_{z}^{3-5}$
---|---|---
Link id (z) | 1 | $3$ | $2$
2 | $4$ | $6$

Next, the number of XOR operations must be calculated for each group of
frequency slots that could be used to establish the confidential demand. To
calculate the number of XOR operations on link $1$ and frequency slots $2-4$,
$c^{2-4}_{1}$ = $t_{(1,2)}$ \+ $t_{(1,3)}$ \+ $t_{(1,4)}$ = $1$ \+ $1$ \+ $1$
= $3$. The same process is performed for all links that belong to the
candidate path and the selected group of frequency slots $3-5$. It is noted
that this process is not performed for spectrum slots $1-3$, since they are
not available for the confidential demand. The result for each group of
frequency slots and the links of the candidate path is shown in Table 6.

Finally, to calculate the XOR-SSM metric, $\mathcal{C}$ must be calculated for
each group of available frequency slots. In case the MXOR-SSM metric is used,
$\mathcal{C}^{2-4}$ = $min(c^{2-4}_{1},c^{2-4}_{2})$ = $min(3,4)$= $3$, and
$\mathcal{C}^{3-5}$ = $min(c^{3-5}_{1},c^{3-5}_{2})$ = $min(2,6)$ = $2$
respectively, as shown in Table 8 for the group of frequency slots $2-4$ and
$3-5$. Now, XOR-SSM${}_{p_{1}}$ = $max(\mathcal{C}^{2-4}$,
$\mathcal{C}^{3-5})$ = $max(3,2)=3$, using frequency slots $2-4$. On the other
hand, if the AXOR-SSM metric is used, $\mathcal{C}^{2-4}$ =
$(c^{2-4}_{1}+c^{2-4}_{2})/2$ = $(3+4)/2$ = $3.5$, and $\mathcal{C}^{3-5}$ =
$(c^{3-5}_{1}+c^{3-5}_{2})/2$ = $(2+6)/2$ = $4$ (Table 8). Hence, XOR-SSMp =
$max(3.5,4)$ = $4$ using frequency slots $3-5$. It is noted that, for example,
in the case $T$ = $3$, then this would not be an acceptable solution (i.e.,
$min(2,6)$ = $2<T$) and therefore, frequency slots $2-4$ would be selected.

Table 7: Calculation of $\mathcal{C}$ for each group of frequency slots using MXOR-SSM. |  | Group of
---
frequency
slots (x - y)
2 - 4 | 3 - 5
$\mathcal{C}^{x-y}$ | $3$ | $2$

Table 8: Calculation of $\mathcal{C}$ for each group of frequency slots using AXOR-SSM. |  | Group of
---
frequency
slots (x - y)
2 - 4 | 3 - 5
$\mathcal{C}^{x-y}$ | $3.5$ | $4$

Following either approach to solve the NC-RSA problem for the confidential
demands will, in many cases, result in a high blocking probability, since
confidential connections that do not meet the required threshold $T$ are
immediately blocked. To overcome this problem, the algorithms illustrated in
the flowchart of Fig. 5 is proposed.

Figure 5: Flowchart of proposed algorithm to minimize blocking (eliminate
blocking due to the level of security requirements)

As shown in the flowchart, the candidate paths are first pre-calculated and
the $\delta$ coefficient is calculated for each pair of paths. Then, a typical
RSA is implemented for the non-confidential demands with one of the routing
strategies proposed, while the NC-RSA algorithm is used for the confidential
demands with either the MXOR-SSM or AXOR-SSM metrics utilized. After all
demands are allocated in the network, the confidential connections that are
not secured (i.e., less XOR operations than the threshold $T$ are performed in
at least one link of their selected path), and were previously rejected are
re-entered in the network and the NC-RSA is again solved for these connections
(utilizing now existing connections that were not available the first time the
NC-RSA heuristic was implemented). Also, the new number of XOR operations is
calculated for the already established demands. Finally, any confidential
connection that was not previously established is the network, as it was not
meeting the level of security requirements, is now established, regardless of
the level of security provided (these connections are later on in the
performance section identified as unsecured confidential connections (e.g.,
Fig. 10 illustrates the percentage of secured confidential demands)).
Nevertheless blocking still exists due to lack of network resources for both
non-confidential as well as confidential connections. It is noted that
additional (dummy) lightpaths can be added with the sole purpose to ensure
security for the confidential connections that do not reach the required
threshold $T$. However, this is not within the focus of this work and will be
considered as future work.

##  5 Performance Evaluation

To evaluate the proposed heuristic algorithm, an EON is implemented using
bandwidth variable transponders that operate using the following modulation
formats: BPSK, QPSK, $8$-QAM, and $16$-QAM. The transmission reach for each
modulation format is given by $9300$, $4600$, $1700$, and $800$ km
respectively. The network topology utilized in the simulations is shown in
Fig. 7, consisting of $14$ nodes and $42$ directed links. For this network, a
flexible grid is implemented, with a channel spacing of $12.5$ GHz which
results in a total of $320$ spectrum slots with a baud rate of $10.7$ Gbauds
for each link in the network. The requested demands are randomly generated
using a uniform distribution for all $s$-$d$ pairs, where each demand size
varies from $20$ to $100$ Gbps, while the number of candidate paths used for
the first set of simulations is set to $5$ ($k$=$5$). Each presented result is
the average of $10$ experiments performed with different generated sets of
demands, where for all simulations $30\%$ of the overall number of demands are
designated as confidential. Finally, a PC with an i7-3930K CPU and $24$ GB RAM
is used for all simulations.

Figure 6: Network topology used in the simulations, consisting of $14$ nodes
and $42$ directed links.

Figure 7: Average number of minimum XOR operations over all confidential
demands.

When using network coding, the level of security provided for a confidential
connection can by quantified by the minimum and average number of XOR
operations performed on each link of its established path. In this work, the
threshold for the number of XOR operations that a connection must have on each
link of its path in order to be considered as secure is set to $1$ ($T=1$).
This means that the number of XOR operations ($N$) that must be performed at
each link of the path used by a given confidential connection must be $N\geq
1$, in order to consider the specific connection as secure.

By increasing the minimum number of XOR operations that occur at the links of
the established path for the confidential connection, then even if an
eavesdropper taps the weakest link of this confidential connection (i.e., the
link with the smallest number of XOR operations performed), all connections
used in these XOR operations will have to be compromised before the
eavesdropper can make sense of the confidential information. The average
number of minimum XOR operations over all confidential demands is presented in
Fig. 7, when the three routing strategies are utilized for both the AXOR-SSM
and MXOR-SSM metrics.

Using the MXOR-SSM-MUL or MXOR-SSM-MUN routing strategies provides the highest
minimum number of XOR operations performed for each demand, on average,
compared to the rest of the cases examined. This is to be expected, since the
MXOR-SSM metric has as an aim to select the candidate path and group of
frequency slots that maximize the minimum number of XOR operations for the
confidential demand. Further, it is shown that by using the AXOR-SSM metric
and either the MUL or MUN routing algorithms provides results close to the
MXOR-SSM algorithm. This is due to the fact that in this case a relatively
small number of candidate paths is utilized. Thus, in order to satisfy the
required XOR threshold for each link, while also maximizing the average number
of XOR operations, a solution where the minimum number of XOR operations is
close to the MXOR-SSM case is selected. Indeed, as shown in Table 9 below, the
difference between AXOR-SSM and MXOR-SSM, in terms of the minimum number of
XOR operations per demand, increases with the number of candidate paths.
Finally, the MSE routing strategy provides the least number of XOR operations
per confidential connection which is to be expected, since it has as an aim to
add non-confidential connections in a spectrum efficient manner, rather than
to provide more XOR operations for the confidential ones. Nevertheless, in all
cases, the results indicate that on the average the minimum number of XOR
operations that take place per link per demand is between $2$-$3$, higher than
the predefined XOR threshold ($T=1$).

Figure 8: Average number of XOR operations per link per confidential
connection.

Figure 9: Blocking probability for different routing strategies and XOR
spectrum slot metrics.

As discussed in the previous sections, the number of XOR operations performed
on each link is a key point for the level of security provided to a
confidential demand. Accounting for the average number of XOR operations per
link per demand is another useful metric that could describe the average
amount of connections that have to be compromised to make the confidential
demand vulnerable. Thus, Figure 9 presents the average number of XOR
operations per link per confidential connection in the network, when using
different slot allocation metrics and routing techniques for the candidate
paths.

The AXOR-SSM metric provides the best results in terms of the average number
of XOR operations performed, which is to be expected, since it has as an aim
to maximize the total number of XOR operations for a connection, as long as
the XOR threshold is satisfied for all links. On the other hand, using the
MXOR-SSM metric, which aims to maximize the minimum number of XOR operations
over all links of the demand, does not always provide the best results in
terms of the total number of XOR operations performed for the confidential
connections. Further, the MUL routing strategy results in a larger number of
XOR operations compared to both the MSE and MUN routing strategies when either
spectrum allocation metric is used. This is due to the fact that since the
direction of the paths in the XOR process is taken into consideration, a
confidential path that can use other existing connections traversing a highly
utilized link (i.e., traverses the nodes in the same order through a link-
disjoint path) will potentially increase the XOR operations performed in its
path. Thus, utilizing the MUL sorting technique maximizes the utilization of
specific links in the network, which subsequently results in providing a
higher level of security for the confidential demands (contrary to results in
Savva19 , where the direction of the paths was not considered).

Next, the blocking probability of the network is presented (Fig. 9) when
different metrics and routing techniques are utilized. In this figure, the
case where all connections are designated as non-confidential, allocated using
the MSE routing strategy, is also presented as a benchmark (designated as “0%
MSE”). It is clearly demonstrated that the MUL routing strategy results in a
much higher blocking probability compared to the MSE case, since the paths
chosen, utilizing the former strategy, aim to increase the level of security
of the confidential connection (by being utilized at the most used links or
nodes), rather than to maximize the efficient use of spectrum resources, which
is precisely the aim of the latter strategy. In fact, the MSE approach,
satisfies the appropriate threshold of XOR operations per link in the network,
while also providing a very low blocking probability, similar to the
performance of the benchmark case.

Clearly, the number of candidate paths for each $s$-$d$ pair that a
confidential connection can use will also have a great impact on the network
performance in terms of the level of security, blocking probability, and
spectrum utilization, as shown in Table 9. Note that only results for the
MXOR-SSM-MUL, AXOR-SSM-MUL and AXOR-SSM-MSE policies are shown, as these
policies provide the best results (as previously shown in Figs. 7-9). Again,
the results for the 0%-MSE case are provided as benchmark.

Table 9: Impact of $k$ on level of security, blocking probability, and spectrum utilization. Result | Technique | k
---|---|---
5 | 10 | 20
Average number of minimum XOR operations | MXOR-SSM-MUL | 2.45 | 2.83 | 3.09
AXOR-SSM-MUL | 2.38 | 2.75 | 2.99
AXOR-SSM-MSE | 2.02 | 2.19 | 2.50
0% - MSE | - | - | -
Average number of XOR operations per link per demand | MXOR-SSM-MUL | 2.66 | 3.17 | 3.60
AXOR-SSM-MUL | 2.95 | 3.76 | 4.28
AXOR-SSM-MSE | 2.36 | 2.87 | 3.57
0% - MSE | - | - | -
Blocking probability | MXOR-SSM-MUL | 0.04 | 0.11 | 0.17
AXOR-SSM-MUL | 0.04 | 0.13 | 0.20
AXOR-SSM-MSE | 0 | 0 | 0
0% - MSE | 0 | 0 | 0
Number of spectrum slots utilized | MXOR-SSM-MUL | 7561 | 8429 | 9219
AXOR-SSM-MUL | 7734 | 8723 | 9456
AXOR-SSM-MSE | 5243 | 5754 | 6538
0% - MSE | 4232 | 4257 | 4322

From Table 9, it is evident that the larger the number of candidate paths for
each $s$-$d$ pair, the larger the number of XOR operations that can be
performed for each confidential demand. Thus, both the average and minimum
number of XOR operations increase as $k$ increases, for all NC-RSA strategies.
It should be noted though, that as $k$ increases, the number of additional
spectrum slots utilized, as well as the blocking probability will also
increase, since now both confidential and non-confidential demands will use
paths that are not efficient in terms of spectrum utilization, as they instead
select a solution which maximizes the number of XOR operations performed by
the confidential demands. Thus, the choice of $k$ should be one that provides
a balanced solution between the efficiency of the network and the level of
security provided for the confidential demands.

From the results presented, for any choice of $k$ (and as discussed
previously), the AXOR-SSM-MUL approach provides the highest number of XOR
operations on average for each confidential demand, while also satisfying the
minimum threshold for each link for all confidential connections. On the other
hand, the AXOR-SSM-MSE approach provides a much lower blocking probability,
while achieving a slightly smaller number of XOR operations. Thus, for the
rest of the simulations, the AXOR-SSM-MUL approach, which provides the best
results in terms of the level of security provided for the confidential
demands and the AXOR-SSM-MSE approach, which provides the most efficient usage
of the spectrum while providing an acceptable level of security for the
confidential connections will be utilized. In conjunction, a set of $10$
candidate paths for each $s$-$d$ pair will be used, in order to provide a
balanced solution in terms of level of security and spectrum efficiency. Also,
$1500$ connections are now established in the network to better illustrate how
each approach performs as the number of demands increases considerably.

The percentage of the established confidential connections that are properly
secured (i.e., satisfying the ET and FSM constraints) is subsequently
presented in Fig. 10. As shown in this figure, different routing techniques
can have a significant effect on the number of secure confidential
connections. Clearly, from the results presented, the MUL technique performs
better compared to the MSE routing strategy, since connections are forced to
traverse the same links, and therefore, more connections can be found that can
be XOR-ed with the confidential connection. However, it is noted that when
using the MSE routing strategy, the percentage of secure connections increases
with the number of demands that are established in the network. On the other
hand, the percentage of confidential connections that are securely established
in the network utilizing the MUL strategy decreases as the number of demands
increases, since the resources of the candidate paths that could provide
security for the confidential demands are saturated, leading to the usage of
less secure candidate paths. In order to secure all confidential demands, it
is again noted that additional dummy lightpaths can be utilized in the XOR
process in order to provide security for any unsecured confidential
connections established in the network.

Figure 10: Percentage of secured confidential connections established in the
network ($k=10$).

Next, the blocking probability is presented in Fig. 12 when more connections
($1500$) are established in the network and more candidate paths ($k=10$) are
considered for each connection. From the results obtained, again the MUL
sorting strategy is shown to provide a much higher blocking probability
compared to the MSE strategy. In fact, the MSE strategy provides a much lower
blocking probability, close to the benchmark case, for a large percentage of
connections (more than $90\%$ for more than $1000$ demands), while also
satisfying the appropriate threshold of XOR operations per link in the network
(Fig. 10).

Selecting different routing and spectrum allocation strategies for each
confidential connection will, on the one hand, secure the confidential
connections against an eavesdropping attack, but, on the other hand, could
force the algorithm to deviate from an efficient spectrum utilization
solution. Figure 12 presents the number of utilized spectrum slots when using
the MUL and MSE routing strategies versus the benchmark case (all connections
are designated as non-confidential and the candidate paths are routed based on
the MSE technique). In this case, there is no blocking in the network (enough
network resources are available), in order to obtain the exact number of
spectrum resources utilized for each set of demands. As shown in the figure,
the MUL routing strategy (which provides the largest number of XOR operations,
on average, for the confidential connections) requires much more spectrum
resources to establish all connections, compared to MSE. On the other hand,
using the MSE approach to provide security for confidential connections
results in an acceptable (i.e., above designated threshold) number of XOR
operations on average for the confidential demands, while at the same time it
requires much fewer resources compared to the MUL case. In fact, using MSE,
the number of additional resources allocated to the network is slightly
increased compared to the case where all connections are not confidential
(“0%-MSE” - benchmark case). This is the case, since all non-confidential
connections are assigned using the best path available (in terms of hops and
modulation format).

Figure 11: Blocking probability using
different routing techniques ($k=10$).

Figure 12: Number of spectrum slots utilized to establish all connections in
the network.

##  6 Conclusions

In this work, a novel heuristic approach is proposed, that utilizes the
concept of network coding in EONs to provide security for confidential
connections against eavesdropping attacks. Using the proposed approach, the
physical layer security is increased, since connections established at link-
disjoint paths combine their datastreams to encrypt the confidential data,
thus an eavesdropper must now compromise several connections traversing
different parts of the network in order to make sense of any accessed
confidential data.

Performance results indicate that using the average XOR spectrum slot metric
(AXOR-SSM) to evaluate each candidate path and group of spectrum slots
required for the confidential demands results in a higher number of XOR
operations performed on each link of the confidential path, and thus it
provides an increased level of security against an adversary that attempts to
compromise confidential data. Also, the combination of the AXOR-SSM metric
with the most used links (MUL) routing strategy, provides the highest number
of XOR operations for each confidential demand at the expense of a significant
increase in the spectrum resources utilized, while the maximum spectrum
efficiency (MSE) routing strategy provides a similar number of XOR operations
at the expense of a small percentage of additional spectrum slots. Therefore,
using the AXOR-SSM-MSE approach, the required level of security of the
confidential connections is achieved, while spectrum utilization and blocking
probability are similar to the ones for the benchmark case, where all
connections are considered as non-confidential.

Ongoing work includes the development of integer linear programming (ILP)
formulations to provide an optimal solution to the NC-RSA problem, as well as
the consideration of additional physical layer constraints that are imposed by
the utilization of network coding via XOR operations.

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