An Indistinguishability Model for Evaluating Diverse Classes of Phishing Attacks and Quantifying Attack Efficacy

Narasimha Shashidhar & Lei Chen
International Journal of Security (IJS), Volume (9) : Issue (2) : 2015 15
An Indistinguishability Model for Evaluating Diverse Classes of
Phishing Attacks and Quantifying Attack Efficacy
Narasimha Shashidhar karpoor@shsu.edu
Department of Computer Science
Sam Houston State University
Huntsville, TX 77384, USA
Lei Chen lchen@georgiasouthern.edu
Department of Information Technology
Georgia Southern University
Statesboro, GA 30458, USA
Abstract
Phishing is a growing threat to Internet users and causes billions of dollars in damage every year.
While there are a number of research articles that study the tactics, techniques and procedures
employed by phishers in the literature, in this paper, we present a theoretical yet practical model
to study this menacing threat in a formal manner. While it is common folklore knowledge that a
successful phishing attack entails creating messages that are indistinguishable from the natural,
expected messages by the intended victim, this concept has not been formalized. Our model
attempts to capture a phishing attack in terms of this indistinguishability between the natural and
phishing message probability distributions. We view the actions performed by a phisher as an
attempt to create messages that are indistinguishable to the victim from that of “normal”
messages. To the best of our knowledge, this is the first study that places phishing on a concrete
theoretical framework and offers a new perspective to analyze this threat. We propose metrics to
analyze the success probability of a phishing attack taking into account the input used by a
phisher and the work involved in creating deceptive email messages. Finally, we study and apply
our model to a new class of phishing attacks called collaborative spear phishing that is gaining
momentum. Recent examples include Operation Woolen-Goldfish in 2015, Rocket Kitten in 2014
and Epsilon email breach in 2011. We point out fundamental flaws in the current email-based
marketing business model which enables such targeted spear phishing collaborative attacks. In
this sense, our study is very timely and presents new and emerging trends in phishing.
Keywords: Phishing, Email Fraud, Data Hiding, Identity Linking, Social Engineering.
1. INTRODUCTION
Phishing is a sophisticated and rapidly growing social engineering threat aimed at gleaning
sensitive information such as user names, passwords and financial information from
unsuspecting victims. In this context, victims comprise not only of people, but also corporations
and even nation states and leads to billions of dollars in damage each year [1]. The attack
campaigns typically involve sending an innocuous looking message to victims in an attempt to
deliver malware, glean personally identifiable information or to further a shift in power control,
either political or economic [20]. Attacks are typically carried out via standard communication
channels such as email or instant messaging by masquerading as legitimate and trustworthy
entities. Being a social engineering attack, most studies of this threat have focused on
understanding the techniques used by phishers, devising clever strategies to thwart these attacks
and the human factors associated with phishing. As of 2015, phishing has become a major vector
for cyberattacks employed by several threat groups [14]. As an example, Rocket Kitten is a cyber-
threat group that actively undermines European and Israeli companies via phishing. In a recent
white-paper published by Trend Micro in March 2015 [14], the authors dissect the modus-

operandi of these phishers and conclude that the methods used by these groups are extremely
sophisticated in comparison to those in the past. Furthermore, these cyber-attacks are
conjectured to be state-sponsored and the academic and industry groups are still exploring the
inner workings of these schemes. To address the sophistication and the devious nature of these
latest phishing attacks, in this paper, we deviate from the older empirical approach and propose a
theoretical yet practical model that captures the interstitial dynamics of this threat. A novel feature
of our security model is that it captures the inherent human factor and consequently complements
the existing empirical study of phishing.
Contributions: Our first contribution in this paper is the development of a theoretical framework
for phishing. Our model is also very practical and designed to study a large class of phishing
attacks including the non-traditional, but emerging threats such as the Android Market fake
banking apps [19]. It is well known that a successful phishing attack entails creating messages
that are indistinguishable from the natural, expected messages by the intended victim. Firstly, we
formalize this notion in the broadest sense possible to encompass a wide range of attacks. This is
important because the rate of growth of phishing attack sophistication does not lend itself to
traditional empirical analysis or study. Our model captures the dynamics of phishing in terms of
indistinguishability between the natural and phishing message distributions. From the perspective
of a phisher, one can view the creation of a phishing message as an attempt to embed a
deceptive message within an innocent looking email or instant message. To this end, we treat the
problem to be “spiritually” similar to the problem of Steganography. Our motivation stems from the
observation that while the goal in Steganography is to create an innocent looking message with a
hidden payload without arousing the suspicion of any eavesdropper, a phisher tries to create an
“innocent” looking message with a hidden (malicious) payload (such as the GHOLE Malware
used by the cyber-threat group Rocket Kitten [14]) without arousing suspicion even from the
recipient. We note that our work brings out an elegant, hidden connection between the disparate
fields of Steganography and Phishing and we hope that this connection will lead to new and
diverse perspectives on phishing detection research.
Secondly, we propose metrics to measure the success probability of a phishing detection
algorithm and consequently the success probability of a phishing attempt. We also define the
notion of overhead as the ratio of the amount of work done by a phisher to the payoff that s/he
receives upon concluding the phishing campaign. This notion of overhead will be useful when we
analyze the impact of the Epsilon email breach [16] and the associated payoff for the phishers.
Finally, we describe a new class of phishing attacks, called collaborative spear phishing, an
advanced class of spear phishing attacks that may stem from the latest threat posed by the
Epsilon email breach [16], Rocket Kitten [14], and Operation Woolen-Goldfish [14] in the recent
past. A server breach at the Internet marketing company Epsilon, a unit of Alliance Data Systems
Corporation, exposed the names and email addresses of millions of people [22] across different
organizations. This breach is being described as the worst of its kind by the media [15],
particularly since the breach apparently lasted for months despite warnings of targeted attacks
against email service providers. Rocket Kitten is a cyber-threat group (presumed to be state
sponsored), that launches targeted spear phishing attacks (Operation Woolen-Goldfish) against
Israeli and European companies. Their primary approach is to deliver a malware payload,
typically the GHOLE virus onto unsuspecting corporate employees’ machines, the latest event
occurring in February 2015 [14]. Once the payload has been delivered, and the victim’s machines
successfully compromised, additional payloads including keyloggers are injected into the infected
machine. In this paper, we also point out some of the fundamental flaws in the current email-
based marketing business model, which is a by-product of service industrialization. This is an
important discussion due to the spate of cyber-attacks and breaches against major businesses
such as Home Depot, Target etc. currently. Thus, our study is very timely and presents emerging
trends in phishing using new tools and analysis techniques to detect and instrument these events.

2. PRIOR WORK
Phishing is primarily a social engineering attack and has attracted a lot of research interest in this
context. Most studies of phishing have focused on understanding the techniques used by
phishers, devising clever strategies to thwart these attacks and the human factors associated with
this threat.
Dhamija et al. [4] and Downs et al. [6] studied the factors affecting the success of different
malicious strategies used by phishers in an effort to build systems better capable of thwarting
phishing attempts. The impact of social networking websites on phishing was studied by Jagatic
et al. [10] who found that Internet users may be over four times as likely to become victims if they
are solicited by someone appearing to be a known acquaintance. A personality-bias based
analysis on the susceptibility of individuals to fall prey to phishing attacks was conducted by Ding
et al. [5] and demonstrated that a dictionary based semantic similarity approach to analyzing
personality models showed promising results. Some of the strategies devised to thwart phishing
attacks mentioned in the literature include: Dynamic Security Skins [3] that allows a remote web
server to prove its identity in a way that is easy for a human user to verify and hard for an attacker
to spoof; Visual Cryptography and Iris Detection based techniques [17, 12]; Natural language
techniques [21]; Detecting phishing emails and websites using machine learning techniques [8];
Web Wallet [24], a browser sidebar which users can use to submit their sensitive information
online; password management and website-login innovations [25] and Cantina, a novel, content-
based approach to detecting phishing web sites, based on information retrieval and text mining
algorithms [27]. Another line of research [26, 23] focuses on the evaluation of anti-phishing tools
and their effectiveness.
A graph-theoretic model to analyze the effort expended by a phisher to launch an attack was
studied by Jakobsson [11]. A phishing attack was modeled using a graph in which nodes
correspond to knowledge and edges captured traversal from one node to another. Edges were
associated with costs to reflect the effort of the phisher. This paper also defined a new attack
approach called the context aware phishing attack using a method called identity linking -
determining the correspondence between identities and email addresses of a victim.
Our model is designed to capture the dynamics of every facet of the phishing threat and not
isolated to measuring the effort expended by the phisher. Furthermore, we describe attacks such
as collaborative spear phishing that are far more complex than the context aware attack and thus
subsumes the earlier attack put forth by Jakobsson [11].
2.1 Notations and Definitions
For a probability distribution P with support X, we use the notation P[x] to denote the probability
that P assigns to ‫ݔ‬ ∈ ܺ. A random variable X is a function over a sample space Ω, X ∶ Ω → S, for
some set S and we say that the random variable X takes values in the set S. The probability
distribution on S described by the random variable X is denoted by ܲ௑.
2.2 Statistical Distance
We use statistical distance as the measure of distance between two random variables and the
probability distributions described by these random variables. The statistical distance is the
largest possible difference between the probabilities that two probability distributions can assign
to the same event. There are several other metrics one could use to measure the distance
between two distributions. However, statistical distance is the most widely used and well defined
metric as described in the literature. We would like to note that our model does not preclude use
of other metrics in this context. Shoup [18] presents a detailed treatment of statistical distance
and its properties.
Definition: Let X and Y be random variables which both take values in a finite set S with
probability distributions ܲ௑ and ܲ௒. The statistical distance between X and Y is defined as

International Journal of Security (IJ
So, two random variables (and the corresponding probability distributions)
߳-close to each-other if Δ|ܺ, ܻ| ൏
about the two distributions – natural
other, thereby capturing the notion of indistinguishability.
3. THE PHISHING MODEL
In this section, we describe our phishing model as depicted by Figure 1
our phishing indistinguishability model
the seminal steganography model presented by Cachin
communication channel to capture email, instant and other means of communication. For the
purpose of our discussion here, let us use the example of email communication. Let us consider
an individual’s email inbox. The phishing problem specifies two message distributions
corresponding to the two sources of messages that can find their way to that individual’s email
inbox: The Natural (N) and the Phishing (
are shown on the left as two black boxes. Typically, we are unaware of the exact probability
distributions associated with these input sources and will treat them as such in our description.
The individual’s inbox normally receives mess
0) corresponding to the phisher being inactive. The natural distribution is meant to capture the
distribution of messages that a person expects to see. When the phisher is active (switch is set to
1) s/he receives phishing messages. The algorithm used by the phisher operates on some input
stream to create the deceptive messages. The Distinguisher algorithm
to distinguish between the messages from these two distributions and ess
from being phished. Often, the receiver of the email plays the role of the distinguisher
Figure 1 depicts the distinguisher algorithm
receiver along with the softwar
collectively form the Distinguisher algorithm
algorithm D and the receiver is meant to signify this relationship between these entities. The
arrow out of the receiver pointing to output/action symbolizes the act of clicking on a link or acting
upon the instructions in the received message, whether natural or phishing.
3.1 Evaluating the Success of a Phishing
The success of a phishing attempt is measured by the intended victim’s ability to distinguish
between “natural” and “phishing” messages over the communication channel. To characterize
(IJS), Volume (9) : Issue (2) : 2015
ΔሾX, Yሿ ൌ
1
2
෍หܲ௑ሺ௦ሻ െ ܲ௒ሺ௦ሻห

௦∈ௌ
.
So, two random variables (and the corresponding probability distributions) X and Y
൏ ߳. This notion of ߳-closeness will be useful to us when we talk
natural messages and phishing messages – being close to each
capturing the notion of indistinguishability.
THE PHISHING MODEL
this section, we describe our phishing model as depicted by Figure 1. As noted earlier, we build
our phishing indistinguishability model on the Steganography security model. In particular, we use
the seminal steganography model presented by Cachin [2]. We use the notion of a
individual’s email inbox. The phishing problem specifies two message distributions
) and the Phishing (P) message distributions. The two source distributions
The individual’s inbox normally receives messages from the Natural distribution (switch is set to
) corresponding to the phisher being inactive. The natural distribution is meant to capture the
e receives phishing messages. The algorithm used by the phisher operates on some input
stream to create the deceptive messages. The Distinguisher algorithm D is tasked with being able
to distinguish between the messages from these two distributions and essentially protect the user
from being phished. Often, the receiver of the email plays the role of the distinguisher
Figure 1 depicts the distinguisher algorithm D to be distinct from the receiver. In real life, the
receiver along with the software tools, browser toolbar extensions, and spam/phisher filters
collectively form the Distinguisher algorithm D. The bidirectional arrow between the Distinguisher
and the receiver is meant to signify this relationship between these entities. The
upon the instructions in the received message, whether natural or phishing.
FIGURE 1: The Phishing Model.
Evaluating the Success of a Phishing Attempt
18
Y are said to be
closeness will be useful to us when we talk
being close to each
. As noted earlier, we build
urity model. In particular, we use
. We use the notion of a
individual’s email inbox. The phishing problem specifies two message distributions
ource distributions
ages from the Natural distribution (switch is set to
) corresponding to the phisher being inactive. The natural distribution is meant to capture the
e receives phishing messages. The algorithm used by the phisher operates on some input
is tasked with being able
entially protect the user
from being phished. Often, the receiver of the email plays the role of the distinguisher D although
to be distinct from the receiver. In real life, the
e tools, browser toolbar extensions, and spam/phisher filters
. The bidirectional arrow between the Distinguisher
and the receiver is meant to signify this relationship between these entities. The

natural communication we need to define and formalize the communication channel. We follow
the standard terminology used in the literature to define communication channels [9]. We let
‫ܧ‬ ൌ ݁ଵ, ݁ଶ, … , ݁௦ denote an alphabet and treat the communication channel as a family of random
variables ‫ܫ‬ ൌ {‫ܫ‬௛}௛∈ா∗. These channel distributions model a history-dependent notion of channel
data that captures the notion of real-life communication. As an example, if E were to represent
the set of the “email alphabet” and ℎ ∈ ‫ܧ‬∗
, the history of emails received by a person thus far,
then ‫ܫ‬௛ represents the random variable that captures the probability distribution of the person’s
email inbox at that point in time. In our model, we have captured the history dependence of
communication and an individual’s expectance to “see” a message in his inbox.
In evaluating the success of a phishing attempt, we need to take into consideration the amount of
randomness present in a person’s email inbox. We use min-entropy as the measure of this
randomness. The min-entropy of a random variable X, taking values in a set V, is the quantity
‫ܪ‬ஶሺܺሻ ≜ ݉݅݊୴∈୚ ሺെ log Prሾܺ ൌ ‫ݒ‬ሿሻ.
We say that a communication channel (such as an email inbox) has min-entropy ߜ if for all ℎ ∈ ‫ܧ‬∗
,
‫ܪ‬ஶሺ‫ܫ‬௛ሻ > ߜ. We would like an individual’s inbox, for all histories, to have some non-zero
randomness, i.e, ߜ > 0. This randomness parameter is designed to capture the diversity of the
messages present in a person’s inbox. As an example, if someone were to receive only one
particular kind of email, then there is no randomness present in this communication scheme. The
study of phishing on such a communication channel is not as interesting since the success
probability of a phishing attempt in this situation is very small. Observe that the metric min-
entropy is designed to capture the worst-case entropy inherent in a distribution. Naturally, other
measures of entropy can also be applied to our model as well.
Let us now discuss the success probability of the Distinguisher algorithm D in being able to detect
a phishing message. Let us overload the notation and let P denote the phishing algorithm as well
as the distribution of the phishing messages produced by it. We now define the advantage of the
Distinguisher D over the phishing algorithm P as:
‫ݒ݀ܣ‬஽
௉ሺ݉ሻ ൌ ฬPrሾ‫ܦ‬ሺ݉ሻ ൌ ‫ݏݏ݁ܿܿݑݏ‬ሿ െ
1
2
ฬ , ሺ1ሻ
where m is the message to be distinguished and D(m) = success is the event that the
Distinguisher D was successful in identifying a phishing message. Observe that any Distinguisher
algorithm has an advantage of ½ in being able to detect a phishing message by merely flipping a
fair coin. Hence, we need to look at the absolute value of the difference between the success
probability of D from ½.
An alternative definition for the advantage of the Distinguisher D over the phishing algorithm P is
obtained from the observation that the total variation distance between two probability measures
N and P is the largest possible difference between the probabilities that these two probability
distributions can assign to the same event, in particular to the event D(m) = success.
‫ݒ݀ܣ‬஽
௉ሺ݉ሻ ൌ
1
2
෍ |ܰሺ݉ሻ െ ܲሺ݉ሻ|
௠ ∈ ெ
, ሺ2ሻ
where N and P are the natural and the phishing message distributions respectively and
represents the messages in the message set M (the user’s inbox). Our model captures phishing
in terms of this indistinguishability between the natural and phishing message distributions.
We can now define the capacity C of an individual to shield him/her from a phishing attack as:
‫ܥ‬ ൌ max
஽
{‫ݒ݀ܣ‬஽
௉ሺ݉ሻ} , ሺ3ሻ

this maximum taken over all Distinguisher algorithms D available at the individual’s disposal. This
definition is meant to capture the different software tools such as browser toolbars, add-ons and
other installed tools using any techniques that one might use to defend against phishing.
We now derive the measure for evaluating the success probability SP of a phishing attempt P as:
ܵ௣ ൌ 1 െ ‫ .ܥ‬ሺ4ሻ
We say that a user is ሺ߳, ߜሻ െ ‫݁ݎݑܿ݁ݏ‬ from a phishing attack if for all his email-inboxes with min-
entropy ߜ, we have ܵ௉ ൏ ߳. The overhead of a phisher is judged by the relation between the
amount of work done by a phisher and the corresponding payoff. We adopt the ratio o = w/p as a
measure for overhead. Obviously, if the payoff is high and the work done is low, then the
overhead is low. This measure is useful in comparing the damage caused by different phishing
attacks.
In this paragraph, we discuss the different parameters that contribute towards the work done by a
phisher. Drake et al., present an anatomy of a phishing email where they enumerate the different
tricks used by phishers in an attempt to create deceptive messages that are indistinguishable
from the original messages [7]. The most important (and expensive to acquire) of these
parameters are the personally identifiable information (PII) such as name, email address, the final
four digits of an account number, year of expiration etc. The other costs associated with work are
technical in nature, i.e., creating similar sounding domain names such as tax-revenue.com,
ebaybuyerprotection.com, creating emails that appear to come from legitimate “From:” email
address, designing the structure and content of the email, creating a plausible premise, using
JavaScript event handlers, redirection, etc. We define work to comprise essentially of two main
parts – work done in collecting personally identifiable information, PII and the technical work, i.e,
‫ݓ‬ ൌ ‫ݓ‬௉ூூ + ‫ݓ‬௧.
4. COLLABORATIVE SPEAR PHISHING
In this section, we discuss an emerging, new class of phishing attacks, that we call collaborative
spear phishing. We wish to shed light on this new class of phishing attacks that may become
popular as a result of the latest server breach at the email marketing giant Epsilon [16] and other
breaches on major U.S. retailers. This attack is an advanced class of spear phishing that a
phisher may develop using collaborative filtering techniques described below. In April 2011, a
server breach at the Internet marketing company Epsilon, a unit of Alliance Data Systems
Corporation, exposed the names and email addresses of millions of people [16]. While a
complete list of all the companies affected by the breach is not yet known, roughly 50 companies
are said to be on that list, including Best Buy, Citibank, Disney, JPMorgan Chase, The Home
Shopping Network, Hilton, Marriott and the College Board. This breach is being described as the
worst of its kind by the media [15]. Such attacks have already started becoming prevalent as was
observed recently in the attack campaigns launched by Rocket Kitten in 2014 and 2015 [14].
Collaborative filtering is the process of filtering for information or patterns using techniques
involving collaboration among multiple data sources. Commonly used to infer purchase statistics
by implementing recommendation algorithms for item recommendation by Amazon and other
online retailers, this technique can now be used to launch highly advanced phishing attacks.
While any breach that leaks personally identifiable information is a blessing to phishers, this
particular breach at Epsilon is much more so. In the context of this breach, a phisher might now
try to infer potential accounts that an individual may have with organizations using information
that he already possesses. Furthermore, it gives a plausible premise that a phisher may use to
hide his tracks. Observe that the breach at Epsilon leaked much more information than just
personally identifiable information – It leaked the relationships that an individual has with different
organizations. The phisher is able to observe that a particular account is affiliated with a number
of organizations and hence is able to filter for more information than s/he could otherwise.

As a quick example, we use a very simple Item-to-Item recommendation algorithm to illustrate
this attack. The table below captures Alice, Bob and Emily’s relationship with three organizations.
A Yes in the table below corresponds to the affirmative knowledge that a phisher has obtained
(Using the Epsilon database, Retailer breaches or otherwise) about an individual’s relationship
with that organization and No (no knowledge) corresponds to the lack of this knowledge.
Name Best Citibank JPMorgan
Buy Chase
Alice Yes No Yes
Bob No Yes Yes
Emily No Yes No
TABLE 1: Collaborative Phishing.
The cosine between Best Buy and Citibank is obtained by:
ሺ1, 0, 0ሻ ⋅ ሺ0, 1, 1ሻ
‖ሺ1, 0, 0ሻ‖‖ሺ0, 1, 1ሻ‖
ൌ 0 .
The cosine between Best Buy and JPMorgan Chase is obtained by:
ሺ1, 0, 0ሻ ⋅ ሺ1, 1, 0ሻ
‖ሺ1, 0, 0ሻ‖‖ሺ1, 1, 0ሻ‖
ൌ
1
√2
మ .
The cosine between Citibank and JPMorgan Chase is obtained by:

ሺ0, 1, 1ሻ ⋅ ሺ1, 1, 0ሻ
‖ሺ0, 1, 1ሻ‖‖ሺ1, 1, 0ሻ‖
ൌ
1
2
.
Hence, a phisher armed with the knowledge that a particular individual who has an account with
Best Buy can make an educated guess that h/she may possibly have an account with JPMorgan
Chase as well. This makes good sense because many Best Buy Credit accounts are indeed
handled by JPMorgan Chase. While we have used a very elementary algorithm for the sake of
exposition, a motivated phisher could use an elaborate collaborative filtering algorithm such as
Slope One [13] to improve the success of this attack. While the context-aware attack proposed by
Jakobsson [11] uses the concept of identity-linking to launch phishing attacks, our proposed
attack is not only context-aware but also is capable of extrapolating for information that the
phishers don’t yet have.
In this paragraph, we point out some of the fundamental flaws in the current email-based
marketing business model, which we believe is a by-product of service industrialization - treating
services as an industrial process. By placing the personally identifiable information of millions of
customers under the control of one organization, such as Epsilon, the overhead for the phisher is
dramatically reduced – The work is diminished and the payoff is maximized. Furthermore, the
phishers can now send targeted emails to their victims thereby making sure that these emails are
out of the hands of the phishing research community. They can also ensure guaranteed delivery
of their phishing emails by spoofing the correct “From” email addresses that most people have
saved in their address books. Gary Warner [22] has an elaborate discussion of such targeted
phishing attacks and we have already started seeing such sophisticated attacks [14].

5. CONCLUSION
Our primary goal in this paper was to present a treatment of phishing in a formal theoretical
framework. Our model captures the dynamics of phishing in terms of indistinguishability between
the natural and phishing message distributions. We propose metrics to analyze the success
probability of a phishing attack which takes into account the input parameters used by a phisher
and the associated work involved to create deceptive email messages. Finally, we present a new
class of phishing attacks, called collaborative spear phishing which is an advanced class of spear
phishing that may stem from the latest threat posed by the Epsilon email breach and other retailer
breaches in the recent past. We also point out some of the fundamental flaws in the current
email-based marketing business model, which is a by-product of service industrialization. In this
sense, our study is very timely and presents new and emerging trends in phishing. We hope that
our model will help shed some more light on the threats posed by phishing.
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