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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Italian Conference on Big Data and Data Science, September</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Machine Learning Based Access Control</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Mohammad Nur Nobi</string-name>
          <email>mohammadnur.nobi@my.utsa.edu</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ram Krishnan</string-name>
          <email>ram.krishnan@utsa.edu</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ravi Sandhu</string-name>
          <email>ravi.sandhu@utsa.edu</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science</institution>
          ,
          <addr-line>UTSA, Texas, USA 78249</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Electrical and Computer Engineering</institution>
          ,
          <addr-line>UTSA, Texas, USA 78249</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute for Cyber Security (ICS)</institution>
          ,
          <addr-line>UTSA, Texas, USA 78249</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>NSF Center for Security and Privacy Enhanced Cloud Computing (C-SPECC)</institution>
          ,
          <addr-line>UTSA, Texas, USA 78249</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>The University of Texas at San Antonio (UTSA)</institution>
          ,
          <addr-line>Texas, USA 78249</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>2</volume>
      <fpage>0</fpage>
      <lpage>21</lpage>
      <abstract>
        <p>While machine learning-based access control systems demonstrated their potential in large-scale and complex applications context for accurate and generalized access decisions, the security of such systems is equally important due to the vulnerability of a machine learning (ML) model to adversarial attacks. A small modification to the input could lead the ML model to make a completely inaccurate access decision. This paper explores ML-based access control's adversarial attack problem, focusing on manipulating information of users and resources to gain unauthorized access. We experiment with this problem in two simulated systems where a ResNet model decides access. We demonstrate that it is possible to design adversarial attacks for ML models deployed for access decisions. Also, there is potential to reduce adversarial attacks to some extent by utilizing access control-specific constraints.</p>
      </abstract>
      <kwd-group>
        <kwd>authorization</kwd>
        <kwd>access control</kwd>
        <kwd>machine learning</kwd>
        <kwd>adversarial attack</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        LGOBE
(R. Sandhu)
such as RBAC [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], ABAC [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], ReBAC [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], etc., have demonstrated their efectiveness in the
access control arena for a long time. However, with the increased complexity of computing
systems, their generality, flexibility, and usability come at a higher cost and are somewhat
inadequate [
        <xref ref-type="bibr" rid="ref4 ref5 ref6">4, 5, 6</xref>
        ]. To deal with such large-scale access control systems, the use of Machine
Learning (ML) is becoming common in diferent areas such as policy mining [
        <xref ref-type="bibr" rid="ref7 ref8 ref9">7, 8, 9</xref>
        ], attribute
engineering [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], role mining [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ], etc. Contemporary researches also manifest the advantages
of using an ML model for more accurate access control decision-making [
        <xref ref-type="bibr" rid="ref12 ref13 ref14 ref15 ref4 ref6">4, 6, 12, 13, 14, 15</xref>
        ].
These systems decide accesses based on a trained ML model instead of a written access control
policy [16]. We refer to such systems as machine learning based access control (MLBAC). In
      </p>
      <p>MLBAC, the access control decisions (grant or deny) are made using user and resource metadata
and attributes. Metadata and attributes are the user/resource features that an ML model learns
for subsequent access decisions in MLBAC. For simplicity, we refer to both metadata and
attributes as ‘metadata’. These metadata could be expressed in categorical (e.g., ‘security_level,’
‘designation’) and continuous (e.g., ‘age,’ ‘salary’) data.</p>
      <p>
        Among diferent ML models, neural networks are prevalent for obtaining a generalized and
accurate MLBAC system due to their ability to capture features from complex input [
        <xref ref-type="bibr" rid="ref14 ref4 ref6">4, 6, 14</xref>
        ].
Such quality of the neural networks poses some security concerns as they are highly sensitive
to the minor changes in the input— that is, a slight manipulation or introduction of additional
information to the input may result in an unintended output [17]. In ML, this issue is known
as an adversarial attack, and the manipulated data is an adversarial example. For instance, in
MLBAC, an attacker could perturb the user/resource metadata to gain access to a resource
forcibly. Figure 1 demonstrates the adversarial attack problem in MLBAC. An MLBAC is
deployed in a system where a user requests to access a resource at time ‘t1’, which the system
denies. At time ‘t2’, the user by itself or a third-party adversary purposefully manipulates
the respective user and resource metadata to gain access. As illustrated in the figure, system
administrators (sysadmin) may store metadata in the databases with diferent levels of security
restrictions, e.g., Tier 1, Tier 2, etc. Therefore, the adversary may or may not equally access
and modify each metadata. For example, an adversary may not have access to the ‘job_role’
metadata as a more restricted database could store them. On the contrary, the adversary may
manipulate (e.g., ‘expertise’ metadata) or influence (e.g., login_frequency) some metadata to
which the user may have direct or indirect access. As shown in the figure, after the manipulation,
the user requests the same access at the time ‘t3’, which is eventually granted by the MLBAC
system.
      </p>
      <p>This area is studied carefully and comprehensively in the domains where inputs are generally
images [18, 19], e.g., computer vision. However, this problem is equally important in the access
control domain, especially for MLBAC, where the input data is non-image. As discussed, in
MLBAC, the input is the user/resource’s metadata which is tabular data expressed in terms of a
set of categorical and continuous values. Also, as shown in Figure 1, metadata may have diferent
levels of restrictions. Therefore, the adversarial attack needs to be investigated concerning the
access control domain. This paper investigates adversarial attacks in MLBAC. In particular,
we consider an MLBAC where the ML model is a deep neural network. To the best of our
knowledge, this is the first work of its kind in the access control domain. We summarize our
contributions as follows.
• We define adversarial attack problems in the MLBAC context. We also propose customized
objective functions for imposing additional constraints in the same context.
• We simulate the adversarial attack cases in the deep neural network-based MLBAC with two
complex and large-scale systems. Also, we consider underlying user/resource metadata in
both systems contain a mix of categorical and continuous data.
• We evaluate the performance of our experimentation and demonstrate that applying
accessibility constraints makes it harder for the adversarial attack generation.</p>
      <p>The rest of the paper is organized as follows. Section 2 discusses related work. Section 3
defines the adversarial attack problem in the context of MLBAC. Later, we discuss overall
experimentation methodologies in Section 4. We present evaluation metrics and results in
Section 5. Finally, Section 6 concludes the paper.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <sec id="sec-2-1">
        <title>2.1. Machine Learning Based Access Control (MLBAC)</title>
        <p>In MLBAC, an ML model decides accesses based user and resource’s metadata and attributes.
We briefly discuss them below.</p>
        <p>
          Cappelletti et al. [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] experiment with multiple ML techniques, including Decision Tree [20],
Random Forest (RF) [21], Support Vector Machines (SVM) [22], and Multi-Layer Perceptron
(MLP) [23], for making access control decisions. The authors train the ML models using access
history. The authors suggest using neural networks for complex systems. Chang et al. [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ]
present an SVM-based time-constraint access control approach associated with the time (e.g., a
user may only have access to a resource during ofice hours). When an access request is made,
the trained SVM grants security access based on the user’s information and given time. Liu
et al. [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] propose a technique utilizing an RF algorithm. The authors build RF based on the
access logs of an existing access control system.
        </p>
        <p>
          A more advanced ML algorithm is also becoming common to tackle situations where access
control requirements are complex. For example, Karimi et al. [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] establish a framework using
a reinforcement learning (RL) algorithm that maps access requests to the access decisions.
An RL agent learns access control policies through feedback (rewards for the right decision,
otherwise penalties) from the users/administrators and subsequently makes access decisions.
Srivastava et al. [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ] developed risk adaptive access control (RAdAC) using a neural network
and an RF algorithm for dynamic access decisions. Before deciding on accesses, the RAdAC
assesses the genuineness of the user and the risk of the access based on metadata such as access
time, location, user history, resource sensitivity, etc. Recently, Nobi et al. [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ] proposed a Deep
Learning Based Access Control (DLBAC) using deep neural networks, including ResNet [24],
DenseNet [25], etc. The DLBAC train ML models using authorization tuples that represent
the existing access control state. The evaluation results suggest that DLBAC can make more
generalized and accurate access decisions than an ABAC system and other ML methods. The
authors also provide two strategies for understanding DLBAC decisions by exploiting deep
learning interpretation techniques.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Adversarial Attack for Tabular Data</title>
        <p>As discussed, the input data in the access control domain is in tabular format—this section
reviews existing adversarial attacks in the tabular data context.</p>
        <p>There are tremendous research eforts for the adversarial attacks and defenses in the diferent
domains, such as image, graph, text, etc. [18, 19, 26]. However, we do not see similar eforts for
the tabular data domain. Ballet et al. [17] propose an imperceptible adversarial attack for the
tabular data domain. The authors manipulate less important features to a greater extent, adding
a minimal perturbation to the more important features to ensure imperceptibility. Cartella
et al. [27] present an adversarial attack for imbalanced tabular data for fraud detection. The
proposed method obtains adversarial examples that are less perceptible when analyzed by
humans. Kumar et al. [28] propose an adversarial attack for a payment system, focusing on
generating adversarial examples on the tabular dataset with limited resources (the least number
of queries used). The authors experiment with a gradient-free approach in black-box settings.
Mathov et al. [29] propose a framework for adversarial examples in heterogeneous tabular data,
including discrete, real-number values, categorical, etc. The proposed framework defines a
distribution-aware constraint and then incorporates them by embedding the heterogeneous
input into a continuous latent space.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Adversarial Attack in MLBAC</title>
      <sec id="sec-3-1">
        <title>3.1. Adversarial Attack Problem</title>
        <p>This section discusses the MLBAC adversarial attack problem. For any access request to the
MLBAC, the input to the model is both user and resource metadata, and the MLBAC decides
whether the user has access or not. Given the ground truth of an access decision of a request and
respective user/resource metadata, we can express them as a tuple of user metadata, resource
metadata, and an access decision. We refer to such tuple as an authorization tuple. For example,
an authorization tuple ⟨u1, r1, {grant}⟩ indicates that a user u1 has access to the resource r1.
The u1 and r1 also represent the set of their respective metadata and metadata values.</p>
        <p>We consider  represents a set of authorization tuples where user and resource metadata
are denoted by   with  ∈ [ 1… ] and associated with a binary access decision   representing
either grant (1) or deny (0). Also,   is defined by a ‘vector’ of user and resource metadata values
and expressed as:   = ⟨  1 ∶  1 ,  2 ∶  2 , …,   ∶   ,  1 ∶  1 ,  2 ∶  2 , …,   ∶   ⟩. The pair
  ∶   indicates   is the value of  ℎ user metadata   . Similarly, the pair   ∶   indicates   is
the value of  ℎ resource metadata   .</p>
        <p>Also, we consider  ∶  ⟶ { 0, 1 } , a binary classifier mapping to access decisions where the
grant is represented by ‘1’ and deny as ‘0’, which is obtained from comparing the probability of
access at the output of the classifier with a threshold.</p>
        <p>For a given user-resource metadata values  , the access decision  =  () , and target access
decision  ≠  , we aim to generate an optimal perturbation   such that
 () =  ≠  ( + 
 ) =</p>
        <p>Our goal is to generate an adversarial example such that we can minimize the amount of
perturbation (  ) and gain the desired access  . To accomplish that, we define our objective
function as the accumulation of access change constraint and minimization of   :
(  ) = L( +   , ) +  ‖   ‖</p>
        <p>Where L(, ) is the value of loss of the binary classifier  calculated for the input  and
target access decision  . Also, ‖   ‖ measures the   norm of perturbation and  &gt; 0 is the weight
associated to the amount of perturbation.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Accessibility Constraint</title>
        <p>The objective function we discussed above considers that the attacker has the flexibility to modify
any user/resource metadata to obtain their desired access. In MLBAC, there are metadata with
diferent levels of restrictions, as discussed in Section 1 and illustrated in Figure 1. Therefore,
an adversary can not access and modify every metadata equally. A sysadmin could explicitly
impose such restrictions, and the adversary could not directly access and modify some of the
metadata. For example, a user’s ‘job_role’ information comes from the system, which is dificult,
if not impossible, to modify and will take more efort. On the other hand, the adversary could
influence some metadata, such as ‘expertise’, and maybe modify it with less efort. Without
loss of generality, we refer to such notion of restrictions and the ability to access them as the
accessibility constraint.</p>
        <p>To impose the accessibility constraint while generating perturbation (  ), we extend our
objective function as below:</p>
        <p>(  ) = L( +   , ) +  ‖   ∘ ‖
Where  is the accessibility constraint expressing the magnitude of restrictions with respect to
each metadata, ∘ is the element-wise product operator, and  &gt; 0 is the weight for the penalty of
perturbing metadata with higher accessibility constraint. We hypothesize that exploiting
accessibility constraint with the proposed objective function will make the perturbation generation
harder.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Adversarial Attack Approach</title>
        <p>After formulating objective functions, we aim to develop an approach to optimize the objective
function minimization problem and generate perturbed examples. Researchers have proposed
numerous approaches, such as the Fast Gradient Sign Method (FGSM) [30], Projected Gradient
Descent (PGD) [31], Carlini &amp; Wagner Attacks [32], etc., to generate adversarial attacks that can
deceive a trained deep neural network with higher accuracy. However, most of the algorithms
have been proposed for the image domain. Due to the data characteristics in the access control
domain, these algorithms may not readily mislead the ML model in MLBAC. A few works
consider the non-image tabular data domain [17, 27, 33]. These works have demonstrated their
potential in generating adversarial attacks for ML models applied in multiple use-cases such as
ifnancial services [ 17], fraud detection [27], etc.</p>
        <p>Ballet et al. [17] propose the LowProFool algorithm to solve the optimization problem for
the continuous tabular data using a gradient descent approach. As MLBAC input is tabular
data containing both categorical and continuous metadata, and we have a similar optimization
problem, we adopt their algorithm for minimizing our objective function  . We customize the
algorithm and adjust the parameters such that we can optimize our objective function and
supports continuous and categorical data. We further discuss this in Section 4.5.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Methodology</title>
      <sec id="sec-4-1">
        <title>4.1. Determining Accessibility Constraint</title>
        <p>
          In MLBAC system, the access decisions are made based on user/resource metadata. In practice,
this metadata could come from diferent sources, where some sources are more secured than
others. For example, a highly restricted database may store a user’s sensitive information, such
as ‘job_role.’ In contrast, a less secured database may store less sensitive data such as ‘expertise.’
Also, not every metadata/attributes equally influences the access decisions [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. Therefore, the
sysadmin may restrict influential and sensitive metadata/attributes with more security. We
utilize the notion of accessibility constraint (as discussed in Section 3.2) to simulate such security
restriction levels for each of the metadata.
        </p>
        <p>
          Instead of randomly determining some metadata as more restricted and others as less
restricted, we measure the correlation for each user and resource metadata for a decision. More
concretely, we calculate the absolute value of Pearson’s [34] correlation coeficient of each
metadata with respect to the access decision. For this purpose, we could utilize other methods
crafted specifically for the access control domain, such as the global interpretation-based method
developed by Nobi et al. [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ], where they determine the influence of each metadata for a specific
decision for an ML model. However, we rely on Pearson’s correlation as it can better simulate
human intuition through a linear correlation based on the data [17]. For our proposed objective
function, we generate accessibility constraint values in the range of 0 to 1 for each metadata. A
higher constraint value of metadata indicates the respective metadata is more secured, thereby
less accessible by the adversary while generating perturbation.
        </p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Dataset for MLBAC Adversarial Attack Experimentation</title>
        <p>
          MLBAC makes access control decisions based on user and resource metadata and attributes
values. Before that, MLBAC needs training with available ground truth to decide on subsequent
access control requests. Generally, the ground truth could be access history, existing
authorization information, etc., communicated through authorization tuples [
          <xref ref-type="bibr" rid="ref13 ref14 ref6">6, 13, 14</xref>
          ]. (We discussed
the authorization tuple in Section 3.1.) We call such a collection of authorization tuples a dataset
that represents the current access control state of a system.
        </p>
        <p>
          Each dataset represents the metadata information of users and resources and their access
control state. However, metadata values could be a mix of continuous (e.g., ‘age,’ ‘salary’) and
categorical (e.g., ‘security_level,’ ‘designation’) data. We are unaware of any publicly available
access control dataset representing mixed metadata values. There are two access control datasets
from Amazon [35, 36]. Both of these datasets contain only categorical metadata/attributes values.
As a result, for this work, we experiment with two simulated datasets1, named 5 - 5 -ℎ12
and 5 - 5 -ℎ19 , developed by Nobi et al. [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. The authors create these datasets using the
data generation method proposed in [37] and introduce diferent complexities to simulate some
real-world scenario. Each dataset has around five thousand users, five thousand resources, and
four diferent operations. The 5 - 5 -ℎ12 dataset, we refer to as System-1, has around
12K authorization tuples. Each user has eight user metadata (0, 1, … , 7 ), and
each resource has eight resource metadata ( 0,  1, … ,  7 ). On the other hand, the
5 - 5 -ℎ19 dataset has around 19K authorization tuples, whereas a user has ten metadata
(0, 1, … , 9 ) and a resource has ten metadata ( 0,  1, … ,  9 ). We
refer to this dataset as System-2.
        </p>
        <p>However, both datasets contain categorical metadata values, as integers, of which each value
represents a category. In practice, one could anticipate a mix of continuous and categorical
data [29]. To simulate the notion of mixed data, we consider metadata values of both datasets
as mixed data. In particular, we assume that the first half of the user and resource metadata
are continuous and consider an integer a real value. We also consider the rest of the metadata
as nominal categorical data, where each integer represents a category, and the order of the
category does not matter. As the metadata contains mixed data, they need to be processed
eficiently such that the underlying ML model can properly consume the training data [ 38]. The
following section discusses their preprocessing.</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Data Preprocessing</title>
        <p>This section explains the processing of the System-1, which is equally applicable to System-2.
⟨1011|2021|30 49 5 26 63 129 3 42 | 43 49 5 16 63 108 3 3 |⟨1 1 0 1⟩⟩ is a sample authorization
tuple of the System-1 dataset where 1011 and 2021 are the user and resource’s unique numbers.
The next eight elements indicate the metadata values of a user, the following eight elements
represent the resource’s metadata values, and the final four binary digits (1 for grant, 0 for deny)
signify four diferent operation’s access to the resource.</p>
        <p>For our experiment, we consider the first four user metadata ( 0 to 3 ) and the first
four resource metadata ( 0 to  3 ) to be continuous, and the rest of the metadata are
1https://github.com/dlbac/DlbacAlpha/tree/main/dataset/synthetic
categorical. Also, we utilize only one operation (out of four operations) that indicates whether
the user has access to the respective resource or not (grant/deny). Figure 2 illustrates the data
preprocessing of System-1 dataset. We normalize continuous data using the MinMaxScaler
approach [39] and apply one-hot encoding [38] for the categorical portion of the metadata. As
shown in the figure, we merge continuous normalized data, a vector, with the one-hot encoded
categorical data matrix. The merged matrix, holding values between 0 and 1, acts as the ML
model’s input.</p>
      </sec>
      <sec id="sec-4-4">
        <title>4.4. Candidate ML Model for MLBAC</title>
        <p>
          A deep neural network has significant benefits for controlling access in dynamic, complex, and
large-scale systems [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. Considering the scale of our datasets and data characteristics, we utilize
a deep neural network for MLBAC. In particular, we consider ResNet [24] as our candidate
ML model. We note that one could use other deep neural networks, including Xception [40],
DenseNet [25], etc., although we do not anticipate any significant changes in our results.
        </p>
        <p>
          For System-1 and System-2 datasets, we exploit the ResNet ML models with 8 and 50 residual
layers, respectively, as suggested in [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. There is a convolution, a batch normalization
operation [41], and a ReLU [42] activation function in each layer. The final activation layer’s output
is flattened and fed into a dense layer with a sigmoid activation function as the MLBAC needs
to make a binary access decision (grant or deny).
        </p>
      </sec>
      <sec id="sec-4-5">
        <title>4.5. Customization of LowProFool Algorithm</title>
        <p>As discussed in Section 3.3, we exploit the LowProFool [17] algorithm for generating adversarial
examples for the MLBAC. We modify the algorithm and parameters to support continuous and
categorical data and help minimize our proposed objective functions discussed in Section 3.1
and 3.2. We replace the objective function with our proposed one and take accessibility constraint
( ) as input. We define the loss function L as the binary cross-entropy function. Also, we guide
the perturbation to the positive of the gradient if our target access is a ‘grant (1)’. Otherwise,
we guide to the negative of the gradient. As discussed, our experiment’s preprocessed input
holds values between 0 and 1. Therefore, we modify the  () function to control the value of
each metadata such that it does not cross the range. We floor the value to 1 if it exceeds one,
and we ceil it to zero if the value becomes negative.</p>
        <p>In addition, the algorithm controls the growth of the perturbation using the scaling factor
parameter  . Also, we need to provide a weight parameter  that helps to minimize perturbing
the metadata with higher accessibility constraints. For the System-1, we choose the parameters
 and  as 0.2 and 6, respectively. These values are 0.7 and 5.7 for the System-2. We follow a
trial-and-error process for choosing them. We have created a GitHub repository consisting of
our experimentation’s source code and datasets2.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Evaluation</title>
      <sec id="sec-5-1">
        <title>5.1. Evaluation Metrics</title>
        <p>The eficiency of an adversarial attack is measured as the ratio of successfully crafted adversarial
examples, and the total number of samples attempted to prepare the adversarial example. This
ratio is known as the Success Rate [17]. Let us consider  as the number of samples attempted
for the adversarial example creation. We also consider  containing every tuple (,   ) such
that  ∈  and   a successfully crafted adversarial examples from  with  () ≠  (  ). We define
the Success Rate as follows:
   =
||
||</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Evaluation Methodology</title>
        <p>We propose two diferent objective functions for the MLBAC system, as discussed in Section 3.1
and 3.2. In one case, we consider that adversary has equal access to every metadata and, thereby,
could change any metadata at any level. In another case, we consider a scenario where each
metadata may have been stored in places with diferent levels of restrictions (accessibility
constraint). As a result, an adversary could not access and modify every metadata equally. In
such a case, the adversarial example generation would be harder, and we anticipate a lower
Success Rate. We evaluate both cases and refer to the first as the ‘Without Accessibility
Constraint’ and the latter as the ‘With Accessibility Constraint.’</p>
        <p>As discussed, we experiment with two datasets System-1 and System-2, having a diferent
number of samples and data characteristics. We evaluate the performance of both of the datasets.
Also, we create a diferent subset of samples measured by sample count and eventually determine
the average performance for the respective dataset.
2https://github.com/dlbac/MLBAC-AdversarialAttack
(a) Performance Evaluation of System-1.
(b) Performance Evaluation of System-2.</p>
      </sec>
      <sec id="sec-5-3">
        <title>5.3. Results</title>
        <p>Figure 3 illustrates the overall performance of MLBAC adversarial attack simulation. Figure 3a
demonstrates the performance of System-1. As shown in the figure, the success rate of
adversarial attacks without imposing any additional constraint is above 95%. However, when we
restrict the system considering accessibility constraint, the success rate reduces to an average
of 75%. We observe a similar result in the System-2 case, as demonstrated in Figure 3b. In this
case, without any constraint, the success rate is above 98%. We observe an identical trend for
the scenario when we apply the constraint. The average success rate goes down to 79%. In both
cases, we observe that the proposed adversarial method could successfully design adversarial
examples at a higher success rate. However, by restricting the flexibility of the adversary by
limiting their access to diferent metadata at a diferent level, we see a dramatic reduction in
the performance, justifying our hypothesis made in Section 3.2.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusion and Future Work</title>
      <p>This paper defines the adversarial attack problem in the MLBAC context where a trained ML
model decides access. We customize objective functions by imposing additional accessibility
constraint to reflect the access control context. We experiment with adversarial attack cases in the
deep neural network-based MLBAC with two complex, large-scale systems. Also, we consider
systems where underlying user/resource metadata contains both categorical and continuous
data. We thoroughly evaluate the performance of MLBAC adversarial attack experimentation
and demonstrate that it is possible to restrict an adversarial attack to some extent by introducing
a security constraint.</p>
      <p>In this work, we measure accessibility constraint using the correlation method. Exploring
other methods to simulate such restrictions and accessibility would be interesting. Also, the
adversarial attack and the proposed objective functions have dependencies on multiple
parameters. The performance of the attack method has a strong connection with these parameter
values, which we determine using a trial-and-error approach. A further investigation is needed
to minimize dependencies and find their values more systematically. Besides, we consider
the white-box attack scenario, where we assume the adversary has access to the ML model in
MLBAC. It would be interesting to explore a black-box scenario where the adversary cannot
access the MLBAC model. Also, the proposed accessibility constraint exhibits its prospect of
safeguarding against adversarial attacks, which may not be suficient in some cases. A thorough
investigation is needed to determine defense techniques in the access control context.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <p>We would like to thank the CREST Center For Security And Privacy Enhanced Cloud Computing
(C-SPECC) through the National Science Foundation (NSF) (Grant Award #1736209) and the NSF
Division of Computer and Network Systems (CNS) (Grant Award #1553696) for their support
and contributions to this research.
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