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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Adversarial Deep Learning Against Intrusion Detection Classifiers</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Maria Rigaki</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ahmed Elragal</string-name>
          <email>ahmed.elragal@ltu.se</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Luleå University of Technology</string-name>
        </contrib>
      </contrib-group>
      <abstract>
        <p>Traditional approaches in network intrusion detection follow a signature-based approach, however the use of anomaly detection approaches and machine learning techniques have been studied heavily for the past twenty years. The continuous change in the way attacks are appearing, the volume of attacks, as well as the improvements in the big data analytics space, make machine learning approaches more alluring than ever. The intention of this paper is to show that using machine learning in the intrusion detection domain should be accompanied with an evaluation of its robustness against adversaries. Several adversarial techniques have emerged lately from the deep learning research, largely in the area of image classification. These techniques are based on the idea of introducing small changes in the original input data in order to make a machine learning model to misclassify it. This paper follows a big data analytics methodology and explores adversarial machine learning techniques that have emerged from the deep learning domain, against machine learning classifiers used for network intrusion detection. We look at several well-known classifiers and study their performance under attack over several metrics, such as accuracy, F1-score and receiver operating characteristic. The approach used assumes no knowledge of the original classifier and examines both general and targeted misclassification. The results show that using relatively simple methods for generating adversarial samples it is possible to lower the detection accuracy of intrusion detection classifiers as much as 27%. Performance degradation is achieved using a methodology that is simpler than previous approaches and it requires only 6.14% change between the original and the adversarial sample, making it a candidate for a practical adversarial approach.</p>
      </abstract>
      <kwd-group>
        <kwd>Adversarial machine learning</kwd>
        <kwd>intrusion detection</kwd>
        <kwd>big data analytics</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>Despite the security measures deployed in enterprise networks, security breaches are still a
source of major concern. Intrusion detection is dealing with unwanted access to systems and
information by any type of user or software. There are two major categories of IDS: Network IDS
(NIDS), which monitor network segments and analyze network traffic at different layers in order
to detect intruders and Host based IDS (HIDS), which are installed in host machines and they try
to determine malicious activities based on different indicators such as processes, log files,
unexpected changes in the host and so on. The focus in this paper is on NIDS.
In large enterprise networks the amount of network traffic that is generated on a daily basis,
requires consideration about gathering, storing and processing of said traffic. While one
approach is to discard parts of the data or log less information, the emergence of Big Data
Analytics (BDA) as well as the improvement in computing power, memory and the decrease in
storage costs, transforms the situation into a big data problem.  
Traditional approaches in the area of intrusion detection mainly revolve around signature /
misuse approaches which have the limitation that they work only with known attack patterns
and that they require extensive domain knowledge. Anomaly detection techniques based on
statistical or machine learning approaches promise more flexibility and less dependency in
domain knowledge and are more scalable when it comes to big data. Using BDA methods seems
like a very likely approach as the amount and speed of data generated is expected to increase
further in the future. However, one has to question not only the performance of the BDA
methods proposed, but also their stability and robustness against adversaries that will most
certainly try to attack them.</p>
      <p>In this paper, we utilize adversarial machine learning methods against machine learning
classifiers that are used for NIDS. The methods were previously introduced in image based
datasets and we examine their suitability in the NIDS domain in terms of ability to degrade
machine learning classifier performance and in terms of practical value. We also present some
initial results regarding classifier robustness against the most promising methods and under the
specified threat model, as well as a potential feature selection method that can be used by
attackers in order to masquerade their traffic as normal.</p>
    </sec>
    <sec id="sec-2">
      <title>2 Related Work</title>
      <p>Despite the numerous research activities around machine learning and intrusion detection, there
has been substantially less focus on adversarial machine learning, i.e. the robustness of the
machine learning methods in the face of adversaries. A qualitative taxonomy for the threat
models against machine learning systems was introduced by Barreno et al. (2006). It placed the
attacks in three axes: Influence (causative or exploratory), security violations (integrity,
confidentiality) and specificity (indiscriminate or targeted). The same taxonomy was used by
Huang et al. (2011) and was extended further to include privacy as a security violation when the
adversary is able to extract information from the classifier.</p>
      <p>Another taxonomy was introduced by Papernot et al. (2016a) and focuses on two axes:
Complexity which ranges from simple confidence reduction to complete source / target
misclassification and knowledge which ranges from knowledge about architecture, training tools
and data to just knowledge of a few samples. If the attacker knows anything regarding the
architecture, the training data or the features used, the attack is considered a white-box attack.
If the adversary’s knowledge is limited to Oracle attacks or she has only access to limited number
of samples, the attack is considered a black-box attack.</p>
      <p>
        Viewing the problem from the attacker perspective, attacks can also be categorized as poisoning
or evasion ones. Different poisoning attacks have been described in Biggio et al. (2012) and
        <xref ref-type="bibr" rid="ref8">Xiao
et al. (2015)</xref>
        . Both studies try to poison the training data in different ways.
        <xref ref-type="bibr" rid="ref8">Xiao et al. (2015)</xref>
        devised attacks against linear classifiers such as Lasso and Ridge by maximizing the classification
error with regards to the training points, while Biggio et al. (2012) attacked Support Vector
Machines (SVM) by injecting samples to the training set in order to find the attack point that will
maximize the classification error.
      </p>
      <p>Evasion attacks have been studied by Ateniese et al., (2015), Biggio et al. (2010) and Biggio et al
(2013). The latter proposed a methodology which requires the generation of multiple training
sets and subsequently the creation of several classifiers which are combined to create a
metaclassifier. This meta-classifier is used in order to extract statistical properties from the data but
not the features themselves, which makes it an attack against privacy.</p>
      <p>
        Deep Learning (DL) methods have been wildly successful in recent years especially in areas such
as computer vision and speech recognition. As part of this development, Adversarial Deep
Learning (ADL) have also surfaced, mostly centered around the computer vision domain.
        <xref ref-type="bibr" rid="ref6">Szegedy
et al. (2013)</xref>
        showed that making very small variations in an image, one could fool a Deep Learning
model to misclassify it. The variations can be small enough that can be imperceptible to humans.
Several methods of producing adversarial samples have been proposed so far which trade on
complexity, speed of production and performance:

      </p>
      <p>
        Evolutionary algorithms were proposed by
        <xref ref-type="bibr" rid="ref2">Nguyen et al. (2015)</xref>
        but the method is
relatively slow compared to the two other alternatives.
 Fast Gradient Sign Method (FGSM) proposed by Goodfellow et al., (2014).
 Jacobian-based Saliency Map Attack (JSMA)
        <xref ref-type="bibr" rid="ref3 ref5">(Papernot et al., 2016a)</xref>
        is more
computationally expensive than the fast gradient sign method but it has the ability to
create adversarial samples with less degree of distortion.
      </p>
      <p>It is not only Deep Learning models that are vulnerable to adversarial samples produced by the
above methods. Shallow linear models are also plagued by the same problem and so are model
ensembles. The only models that have shown some resistance to adversarial samples are Radial
Basis Function (RBF) networks, however, they cannot generalize very well (Goodfellow et al.,
2014). The concept of transferability was thoroughly tested by Papernot et al. (2016b). The
authors tested several classifiers both as source for adversarial sample generation as well as
target models. However, the testing was confined to image classifiers.</p>
      <p>
        When it comes to ADL, the domain of the different attacks and adversarial sample generation
has mainly revolved around the area of image classification and computer vision. Recent work
has shown that it is also possible to create adversarial samples against neural network malware
classifiers (Grosse et al., 2016). Other applications of general AML in security involve spam
classifiers
        <xref ref-type="bibr" rid="ref1 ref9">(Nelson et al., 2008; Zhou et al., 2012; Huang et al., 2011)</xref>
        , malware analysis (Biggio et
al., 2014; Grosse et al., 2016), biometrics (Biggio et al., 2010) and network traffic identification
(Ateniese et al., 2015). There are also two studies related to Intrusion detection (Biggio et al.,
2010; Huang et al., 2011) and they both assume a causative influence model.
      </p>
      <p>This paper follows a different approach than most of the previous work in the adversarial
machine learning field which was either addressing poisoning attacks or was focused on evasion
attacks against specific target classifiers. Although we approach the problem as a white-box
attack (we have knowledge of the features), we do not require knowledge of the target classifier.
Secondly, the latest approaches that use deep neural networks as an attack source, have been
used mostly with image classification and in that respect, we differ significantly because we
target the NIDS domain which has its own very specific constraints that need to be taken into
account.</p>
    </sec>
    <sec id="sec-3">
      <title>3 Methodology</title>
      <p>From a methodological perspective, the paper followed a BDA methodology and adhered to
several of the guidelines proposed by Müller et al. (2016). The research was conducted in a series
of steps and as expected from a BDA type of research and several of these steps were conducted
in an iterative manner. Step 1 included the analysis of related work and identification of gaps in
existing research. It also contained the definition of the objectives for the paper. The first defined
objective was the analysis of the different methods using in adversarial sample creation (JSMA
and FSGM) and their suitability to the NIDS domain. The second objective was the analysis of
several classical machine learning classifiers in terms of metrics such as overall classification
accuracy, F1-score and Area Under the Curve (AUC). In a multi-class classification setting there
are multiple ways to calculate the chosen metrics. In this paper, we are using a micro-average of
all classes for Accuracy and F1 and present the AUC only for the normal class. This way Accuracy
and F1-score can give an indication of the overall robustness of the classifiers, while the AUC can
give us insight on how well the targeted misclassification attack worked against the ”normal”
class. Step 2 was the stage of data collection, analysis and preprocessing. This is detailed further
in section 3.1.</p>
      <p>Step 3 was the data modelling step where the main activities were the selection and training of
the baseline classifiers as well as the adversarial test set generation. The classifiers selected were
a Decision Tree based on the CART algorithm, a Support Vector Machine (SVM) with a linear
kernel, a Random Forest classifier and a Majority Voting ensemble method that combined the
previous three classifiers. The reason for selecting the first three was that they are very popular
and very different approaches and the selection of Voting ensemble method was done in order
to examine the robustness of classifier ensembles. The classification problem was a 5-class
problem and it required the usage of the ”One-vs-the-rest (OvR) multiclass/multilabel strategy”
for some of the classifiers which do not support multi-class problems out of the box.
A Multi-Layer Perceptron (MLP) was used as the source for the adversarial test set generation
using both the FGSM and JSMA methods. The MLP was trained initially using the original training
dataset. More details about the adversarial sample generation process are provided in section
3.2.</p>
      <p>Step 4 was mainly about the evaluation of the results. The study evaluated the two methods used
for adversarial test set generation (JSMA and FGSM) mainly in terms of their suitability for usage
in a NIDS environment. It is well known that in terms of speed FGSM is faster, but the results
produced by this method cannot be used for intrusion detection problems. The next activity
during evaluation was to test the robustness of the baselined classifiers. Since JSMA was deemed
the more suitable of the two methods, only the test set generated by JSMA was considered for
the evaluation of the classifiers. The third part of the evaluation was to look into the differences
between the adversarial data and the original test data. During this activity, the main purpose
was to examine the nature of the features that are frequently altered and identify the ones that
are altered more frequently.</p>
      <sec id="sec-3-1">
        <title>3.1 Data Selection and Pre-processing</title>
        <p>Despite the numerous studies which have been conducted in the NIDS domain, the lack of
representative datasets which include a variety of attacks is one of the recurring themes. The
majority of the studies still use the KDD’99 dataset (KDD Cup 1999 Data, 1999) or its derivation,
the NSL-KDD (NSL-KDD dataset, 2009). Although these datasets are severely outdated, they have
been chosen as a basis for this study mainly due to lack of better alternatives and secondly
because the purpose of the study is the robustness of classifiers and not making claims about
prediction capabilities and generalization.</p>
        <p>
          The NSL-KDD dataset improved a number of shortcomings in the KDD’99 while keeping the
number of features unchanged. The changes introduced by
          <xref ref-type="bibr" rid="ref7">Tavallaee et al. (2009)</xref>
          were related
to the removal of redundant records in the training and test sets and also in adjusting the level
of difficulty of classification for certain attacks. In this study, we used NSL-KDD as our main
dataset. The data pre-processing phase included the following steps:


        </p>
        <p>All categorical (symbolic) variables were transformed to numerical using One-hot
encoding.  
Normalization of all features using Min-Max Scaler was performed in order to avoid
having features with very large values dominating the dataset, which could be
problematic in some classifiers such as the linear SVM and the MLP.  
</p>
        <p>The problem was transformed to a 5-class classification one by changing the attack label
from 39 distinct attack categories to four (”DoS”, ”U2R”, ”R2L”, ”Probe”) and ”normal”.
After preprocessing was the training and test datasets had 122 features. The number of data
points in the training set was 125973 and in the test set 22544.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2 Adversarial Samples Generation</title>
        <p>The methods used for adversarial sample generation in this paper are the Fast Gradient Sign
Method (FSGM) and the Jacobian-based Saliency Map Attack (JSMA). Both of them rely on the
idea that when generating a small perturbation  of the original sample  , the resulting sample
 ∗ can exhibit adversarial characteristics:
In FSGM, the perturbation  is generated by computing the gradient of the cost function  in
respect to the input  :</p>
        <p>∗ =  + 
 =</p>
        <p>(∇  ( ,  ,  ))
where  are model parameters,  is the input to the model, y the labels associated with  ,  a
very small value and  ( ,  ,  ) is the cost function used when training the neural network. The
gradient component can be computed from the neural network using backpropagation, which is
what makes this method very fast. The perturbation is then added to the initial sample and the
final result produces a misclassification.</p>
        <p>In JSMA, the process is slightly more elaborate and it requires three steps. In the first step the
Jacobian of the overall neural network function  in respect to the input  :
  =
 ( )

The Jacobian is used in calculating a Saliency map, which in essence gives an indication of which
features will have more effect on the misclassification if they are perturbed. The third part of the
process is to iteratively select the feature that will have the highest impact and use it to perturb
the initial sample. If the new sample leads to misclassification the process stops, if not, the next
feature is selected and added to the perturbed sample. The process usually has a parameter
which defines the maximum number of iterations which is a direct measure of the allowed
sample distortion.</p>
        <p>Both of the above methods have initially been design for image classification but they can be
applied to other problem domains as we will see in the following sections.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4 Results</title>
      <sec id="sec-4-1">
        <title>4.1 Baseline models</title>
        <p>A number of different classifiers were trained and tested using the NSL-KDD train and test sets
respectively, in order to be used as a baseline. The results on the test set are presented in Table
1. All models have an overall accuracy and F1-score around 75%. The major differences are
observed in the AUC score where the Decision Tree and the Random Forest classifier outperform
the SVM and the Majority Voting ensemble. This essentially means that the first two methods
are performing slightly better in classifying the ”normal” test samples exhibiting a lower FPR. This
can also be observed in Figure 1 to 4.</p>
        <sec id="sec-4-1-1">
          <title>Accuracy</title>
        </sec>
        <sec id="sec-4-1-2">
          <title>F1-score</title>
        </sec>
        <sec id="sec-4-1-3">
          <title>AUC (normal class)</title>
        </sec>
        <sec id="sec-4-1-4">
          <title>Method</title>
        </sec>
        <sec id="sec-4-1-5">
          <title>Decision Tree</title>
        </sec>
        <sec id="sec-4-1-6">
          <title>Random Forest</title>
        </sec>
        <sec id="sec-4-1-7">
          <title>Linear SVM 0.73</title>
        </sec>
        <sec id="sec-4-1-8">
          <title>Voting ensemble 0.75</title>
          <p>MLP 0.75
Table 1 Test set results for 5-class classification
0.73
0.74
0.76
0.76</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>4.2 Adversarial Test Set Generation</title>
        <p>Both the FSGM and JSMA methods were used in order to generate adversarial test sets from the
original test set. A pre-trained MLP was used as the underlying model for the generation. Table
2 below, shows the difference between the two methods in terms of changed features on
average as well as the unique features changed for all data points in the test set.</p>
        <sec id="sec-4-2-1">
          <title>Method</title>
        </sec>
        <sec id="sec-4-2-2">
          <title>FGSM</title>
        </sec>
        <sec id="sec-4-2-3">
          <title>JSMA</title>
          <p>Table 2 Adversarial feature statistics</p>
        </sec>
        <sec id="sec-4-2-4">
          <title>Number of unique</title>
          <p>altered features
122
66</p>
        </sec>
        <sec id="sec-4-2-5">
          <title>Avg. altered features per data point</title>
          <p>122
7.5</p>
        </sec>
        <sec id="sec-4-2-6">
          <title>Percentage of</title>
          <p>altered features
100
6.14
As it was expected the FSGM method changes each feature very little while JSMA searches
through the features of each data point and changes one at each iteration in order to produce
an adversarial sample. This means that FSGM is not suitable for a domain such as NIDS since the
features are generated from network traffic and it would not be possible for an adversary to
control them in such a fine-grained manner. In contrast, JSMA only changes a few features at a
time and while it is iterative and takes more time to generate the adversarial test set, the low
number of features that need to be changed on average might mean there is a basis for a practical
attack. The above is totally in line with the observations by Huang et al. (2011) where the
importance of domain applicability is highlighted as a potential problem for an attacker.</p>
        </sec>
      </sec>
      <sec id="sec-4-3">
        <title>4.3 Model Evaluation on Adversarial Data</title>
        <p>The results of the baseline models using the adversarial test set generated by the JSMA method
in terms of Accuracy, F1-score and AUC are presented in Table 5. In terms of overall classification
accuracy all classifiers were affected. The most severely affected is the Linear SVM with a drop
of 27% and the Decision Tree whose accuracy dropped by 18%. When it comes to F1-score, the
Linear SVM was affected the most and its score was reduced by 27%. The Random Forest showed
the highest robustness by dropping only 6%.</p>
        <p>The AUC over the normal class is an indicator of how robust were the classifiers against targeted
misclassification towards the normal class. It provides a measure on how many attacks were
misclassified as normal traffic. The best performing classifier was again the Random Forest, while
the Decision Tree performed reasonably well. Both the Linear SVM and the Voting classifier were
severely affected, losing 23 percentage points each.</p>
        <sec id="sec-4-3-1">
          <title>Method</title>
        </sec>
        <sec id="sec-4-3-2">
          <title>Accuracy</title>
        </sec>
        <sec id="sec-4-3-3">
          <title>F1-score</title>
        </sec>
        <sec id="sec-4-3-4">
          <title>Decision Tree 0.55 0.60</title>
        </sec>
        <sec id="sec-4-3-5">
          <title>Random Forest 0.64 0.70</title>
          <p>Linear SVM 0.46 0.48</p>
        </sec>
        <sec id="sec-4-3-6">
          <title>Voting ensemble 0.63 0.63</title>
          <p>MLP 0.43
Table 5 Adversarial test set results for 5-class classification</p>
          <p>AUC
(normal
class)
0.75
0.81
0.54
0.47
Based on the results, it seems that the only method that was robust across all metrics was the
Random Forest. The Decision Tree was also quite robust especially in terms of AUC, which does
not coincide with the results by Papernot et al. (2016b). In the latter study, Decision Tree was
one of the worst performing methods. This is also an indication that robustness of classifiers
against adversarial methods is affected by the different datasets and potentially the application
domain.</p>
          <p>The worst performing classifier was the Linear SVM, which is not surprising as linearity was one
of the reasons given by Goodfellow et al. (2014) as a potential explanation of the phenomenon.
Another interesting result by Papernot et al. (2016b) was that a Linear model when used as a
source of adversarial sample generation was actually one of the most successful ones, which is a
finding worth exploring in the NIDS domain as well.
After generating the adversarial test set using JSMA, the features were ranked in terms of
frequency with which they appear in the adversarial test set as changed. This was calculated by
subtracting the original test set from the adversarial test set</p>
          <p>=  ∗ −  
where  ∗ is the adversarial test set and</p>
          <p>is the original test set. In order to find which features
were altered for each data point  ( ) we need to find the feature indexes  where feature  ( ) ≠

0.</p>
          <p>Feature
dst_host_same_srv_rate
dst_host_srv_count
same_srv_rate
count
srv_count
dst_host_count
flag_SF
src_bytes
dst_bytes
logged_in</p>
          <p>Description
destination host
% of connections to the same service and
number of connections to the same
service and destination host as the current
connection in the past 100 connections
% of connections to the same service
number of connections to the same host
as the cur- rent connection in the past 100
connections
number of connections to the same
service as the current connection in the
past 100 connections
number of connections to the same
destination host as the current connection
in the past 100 connections
TCP connection flag
number of data bytes from source to
destination
source
number of data bytes from destination to
1 if successfully logged in; 0 otherwise
Looking at the top ten features presented in Table 6, one can get an idea of which ones contribute
most during the generation of adversarial samples. The top two are about the rate and the count
of the connections to the same host and port. This feature is particularly telling and one way an
attacker could get around it would be to lessen the number of requests they generate. This is
especially relevant to traffic generated by bots that generate connections to external command
and control servers and can hide their traffic under normal traffic that a user creates. A similar
type of thinking can be applied to other count and rate types of features. This type of discussion
is also relevant to DoS type of attacks and while this dataset is quite old, we have seen attacks
historically that followed the ”low and slow” approach in order to appear as close to legitimate
traffic as possible.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5 Conclusion</title>
      <p>The main contribution of this paper is that we showed that adversarial techniques which were
introduced in the image classification domain can be transferred to the intrusion detection
domain with varying degrees of success in lowering classification accuracy (10%-27%). Most
importantly, the degradation of classification accuracy occurred using methods which do not
require knowledge of the target classifier. We also evaluated the practicality of the different
methodologies and found that the methodology proposed by Papernot et al. (2016a) has the
potential to be used in practical attacks, since it requires very few modifications of the original
samples.</p>
      <p>The above contributions indicate that when machine learning is used, it should be accompanied
with relevant adversarial testing and strengthening where possible. This is increasingly important
as machine learning is becoming ubiquitous and its robustness is relevant to both the security
and the safety of people.</p>
      <p>However, it should be noted that a practical attack would require some idea on how the raw
network data are processed and the types of features that are generated. In our case, we had a
pre-processed dataset and not raw data which made it easier to attack. In other words, one does
not need access to the exact model or to the training dataset but some knowledge about the how
the data is preprocessed and how features are generated, is required. Nonetheless, knowledge
about feature generation should not be considered untenable as it could come from reverse
engineering techniques. Even if we know the features used, it would still require work to adjust
the traffic profiles of the specific attack. Contrary to the image classification problem, where each
bit in the image can be considered a feature which can be easily altered, not all traffic related
characteristics can be changed even if an adversary has the ability to craft specific network
packets and payloads. Application related considerations are a potential hindrance for
adversaries in NIDS classification based systems, but this would require from NIDS classifiers to
use features that are not easily manipulated by an attacker.</p>
    </sec>
    <sec id="sec-6">
      <title>6 Future Work</title>
      <p>This paper presents a first attempt in transferring adversarial methods from the deep learning
image classification domain to the NIDS domain. While several studies have proposed defenses
against these methods, these defenses do not generalize quite well. A future study would be to
examine some of these defenses and establish whether they improve the situation or not.
Another extension of this study would be to try out different models as source for the adversarial
sample generation instead of using neural networks.</p>
      <p>The problem of the existence of reliable data in the NIDS domain is well known and it was the
driving factor for the selection of the specific dataset used in the paper. Future work would
benefit from evaluating other data and potentially the implementation of a proof of concept in
an environment with live traffic, or a better traffic mix that is more representative of modern
large-scale networks.</p>
      <p>Finally, the examination of the effects of the adversarial methods in different attack classes would
potentially yield a better overview of which features are more important for each attack type
when it comes to adversarial sample generation. This might eventually be used as a way for an
adversary to select a strategy that would allow them to hide their malicious traffic depending on
the chosen attack.
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with smarter ones: How to extract meaningful data from machine learning classifiers. International
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Proceedings of the 2006 ACM Symposium on Information, Computer and Communications Security.
ACM, pp. 16–25.</p>
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attacks against machine learning at test time, in: Joint European Conference on Machine Learning and
Knowledge Discovery in Databases. Springer, pp. 387–402.</p>
      <p>Biggio, B., Fumera, G., Roli, F., 2010. Multiple classifier systems for robust classifier design in adversarial
environments. International Journal of Machine Learning and Cybernetics 1, 27–41.</p>
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