Microsoft Word - Kaaniche-WEEDS-DSN06-final.doc
Empirical Analysis and Statistical Modeling  
of Attack Processes based on Honeypots  
M. Kaâniche1, E. Alata1, V. Nicomette1, Y. Deswarte1, M. Dacier2  
1LAAS-CNRS, Université de Toulouse 
7 Avenue du Colonel Roche, 31077 Toulouse Cedex 4, France 
{kaaniche, ealata, deswarte, nicomett}@laas.fr 
2Eurécom  
2229 Route des Crêtes, BP 193, 06904 Sophia Antipolis Cedex, France 
dacier@eurecom.fr 
Abstract 
Honeypots are more and more used to collect data on 
malicious activities on the Internet and to better 
understand the strategies and techniques used by 
attackers to compromise target systems. Analysis and 
modeling methodologies are needed to support the 
characterization of attack processes based on the data 
collected from the honeypots. This paper presents some 
empirical analyses based on the data collected from the 
Leurré.com honeypot platforms deployed on the Internet 
and presents some preliminary modeling studies aimed 
at fulfilling such objectives.  
1. Introduction 
Several initiatives have been developed during the 
last decade to monitor malicious threats and activities on 
the Internet, including viruses, worms, denial of service 
attacks, etc. Among them, we can mention the Internet 
Motion Sensor project [1], CAIDA [2], DShield [3], and 
CADHo [4]. These projects provide valuable 
information on security threats and the potential damage 
that they might cause to Internet users. Analysis and 
modeling methodologies are necessary to extract the 
most relevant information from the large set of data 
collected from such monitoring activities that can be 
useful for system security administrators and designers 
to support decision making. The designers are mainly 
interested in having representative and realistic 
assumptions about the kind of threats and vulnerabilities 
that their system will have to cope with once it is used in 
operation. Knowing who are the enemies and how they 
proceed to defeat the security of target systems is an 
important step to be able to build systems that can be 
resilient with respect to the corresponding threats. From 
the system security administrators’ perspective, the 
collected data should be used to support the 
development of efficient early warning and intrusion 
detection systems that will enable them to better react to 
the attacks targeting their systems. 
As of today, there is still a lack of methodologies and 
significant results to fulfill the objectives described 
above, although some progress has been achieved 
recently in this field. The CADHo project “Collection 
and Analysis  of Data from Honeypots” [4], an ongoing 
research action started in September 2004, is aimed at 
contributing to filling such a gap by carrying out the 
following activities:   
1)  deploying a distributed platform of honeypots [5] 
that gathers data suitable to analyze the attack 
processes targeting a large number of machines 
connected to the Internet;  
2)  developing analysis methodologies and modeling 
approaches to validate the usefulness of this 
platform by carrying out various analyses, based on 
the collected data, to characterize the observed 
attacks and model their impact on security. 
A honeypot is a machine connected to a network but 
that no one is supposed to use. In theory, no connection 
to or from that machine should be observed. If a 
connection occurs, it must be, at best an accidental error 
or, more likely, an attempt to attack the machine.  
The Leurré.com data collection environment  [5], set 
up in the context of the CADHo project, has deployed, 
as of to date, thirty five honeypot platforms at various 
locations from academia and industry, in twenty five 
countries over the five continents. Several analyses 
carried out based on the data collected so far from these 
honeypots have revealed that very interesting 
observations and conclusions can be derived with 
respect to the attack activities observed on the Internet 
[4, 6-9]. In addition, several automatic data analyses and 
clustering techniques have been developed to facilitate 
the extraction of relevant information from the collected 
data. A list of papers detailing the methodologies used 
and the results of these analyses is available in [6]. 
This paper focuses on modeling-related activities 
based on the data collected from the honeypots. We first 
discuss the objectives of such activities and the 
challenges that need to be addressed. Then we present 
some examples of models obtained from the data. 
The paper is organized as follows. Section 2 presents 
the data collection environment. Section 3 focuses on 
the modeling of attacks based on the data collected from 
the honeypots deployed. Modeling examples are 
presented in Section 4. Finally, Section 5 discusses 
future work. 
2.  The data collection environment  
The data collection environment (called Leurré.com 
[5]) deployed in the context of the CADHo project is 
based on low-interaction honeypots using the freely 
available software called honeyd [10]. Since September 
2004, 35 honeypot platforms have been progressively 
deployed on the Internet at various geographical 
locations. Each platform emulates three computers 
running Linux RedHat, Windows 98 and Windows NT, 
respectively, and various services such as ftp, web, etc. 
A firewall ensures that connections cannot be initiated 
from the computers, only replies to external solicitations 
are allowed. All the honeypot platforms are centrally 
managed to ensure that they have exactly the same 
configuration. The data gathered by each platform are 
securely uploaded to a centralized database with the 
complete content, including payload of all packets sent 
to or from these honeypots, and additional information 
to facilitate its analysis, such as the IP geographical 
localization of packets’ source addresses, the OS of the 
attacking machine, the local time of the source, etc. 
3. Modeling objectives 
Modeling involves three main steps: 
1) The definition of the objectives of the modeling 
activities and the quantitative measures to be 
evaluated. 
2) The development of one (or several) models that are 
suitable to achieve the specified objectives. 
3) The processing of the models and the analysis of the 
results to support system design or operation 
activities.  
The data collected from the honeypots can be 
processed in various ways to characterize the attack 
processes and perform predictive analyses. In particular, 
modeling activities can be used to: 
• Identify the probability distributions that best 
characterize the occurrence of attacks and their 
propagation through the Internet.  
• Analyze whether the data collected from different 
platforms exhibit similar or different malicious 
attack activities. 
• Model the time relationships that may exist between 
attacks coming from different sources (or to different 
destinations). 
• Predict the occurrence of new waves of attacks on a 
given platform based on the history of attacks 
observed on this platform as well as on the other 
platforms. 
For the sake of illustration, we present in the 
following sections simple preliminary models based on 
the data collected from our honeypots that are aimed at 
fulfilling such objectives. 
4. Examples 
The examples presented in the following address:  
1) The analysis of the time evolution of the number of 
attacks taking into account the geographic location 
of the attacking machine. 
2) The characterization and statistical modeling of the 
times between attacks. 
3) The analysis of the propagation of attacks throughout 
the honeypot platforms. 
The data considered for the examples has been 
collected from January 1st, 2004 to April 17, 2005, 
corresponding to a data collection period of 320 days.  
We take into account the attacks observed on 14 
honeypot platforms among those deployed so far. The 
selected honeypots correspond to those that have been 
active for almost the whole considered period. The total 
number of attacks observed on these honeypots is 
816476. These attacks are not uniformly distributed 
among the platforms. In particular, the data collected 
from three platforms represent more than fifty percent of 
the total attack activity. 
4.1 Attack occurrence and geographic distribution 
The preliminary models presented in this sub-section 
address: i) the time-evolution modeling of the number of 
attacks observed on different honeypot platforms, and ii) 
the analysis of potential correlations for the attack 
processes observed on the different platforms taking into 
account the geographic location of the attacking 
machines and the proportion of attacks observed on each 
platform, wrt. to the global attack activity. 
Let us denote by: 
− Y(t) the function describing the evolution of the 
number of attacks per unit of time observed on all 
the honeypots during the observation period,  
− Xj(t) the function describing the evolution of the 
number of attacks per unit of time observed on all 
the honeypots during the observation period for 
which the IP address of the attacking machine is 
located in country j . 
In a first stage, we have plotted, for various time 
periods, Y(t) and the curves Xj(t) corresponding to 
different countries j. Visual inspection showed 
surprising similarities between Y(t) and some Xj(t). To 
confirm such empirical observations, we have then 
decided to rigorously analyze this phenomenon using 
mathematical linear regression models.  
Considering a linear regression model, we have 
investigated if Y(t) can be estimated from the 
combination of the attacks described by Xj(t), taking into 
account a  limited number of countries j. Let us denote 
by Y*(t) the estimated model. 
Formally, Y*(t) is defined as follows: 
Y*(t) = Σαj Xj(t) + β         j= 1, 2, .. k (1) 
Constants αj and β  correspond to the parameters of 
the linear model that provide the best fit with the 
observed data, and k is the number of countries 
considered in the regression.  
The quality of fit of the model is measured by the 
statistics R2 defined by: 
R2 = Σ(Y*(i) – Yav)
 2/ Σ(Y (i) – Yav) 2 (2) 
Y (i) and Y*(i) correspond to the observed and estimated 
number of attacks for unit of time i, respectively. Yav is 
the average number of attacks per unit of time, taking 
into account the whole observation period.  
Indeed, R is the correlation factor between the 
estimated model and the observed values. The closer the 
R2 value is to 1, the better the estimated model fits the 
collected data.  
We have applied this model considering linear 
regressions involving one, two or more countries. 
Surprisingly, the results reveal that a good fit can be 
obtained by considering the attacks from one country 
only. For example, the models providing the best fit 
taking into account the total number of attacks from all 
the platforms are obtained by considering the attacks 
issued from either UK, USA, Russia or Germany only. 
The corresponding R2 values are of the same order of 
magnitude (0.944 for UK, 0.939 for USA, 0.930 for 
Russia and 0.920 for Germany), denoting a very good fit 
of the estimated models to the collected data. For 
example, the estimated model obtained when 
considering the attacks from Russia only is defined by 
equation (3): 
Y*(t) = 44.568 X1(t) + 1555.67 (3) 
X1(t) represents the evolution of the number of attacks 
from Russia. Figure 1 plots the evolution of the 
observed and estimated number of attacks per unit  of 
time during the data collection period considered in this 
example. The unit of time corresponds to 4 days. It is 
noteworthy that, similar conclusions are obtained if we 
consider another granularity for the unit of time, for 
example one day, or one week. 
These results are even more surprising that the 
attacks from Russia and UK represent only a small 
proportion of the total number of attacks (1.9% and 
3.7% respectively). Concerning the USA, although the 
proportion is higher (about 18%), it is not sufficient to 
explain the linear model. 
Figure 1- Evolution of the number of attacks per unit of time 
observed on all the platforms and estimated model considering 
attacks from Russia only 
We have applied similar analyses by respectively 
considering each honeypot platform in order to 
investigate if similar conclusions can be derived by 
comparing their attack activities per source country to 
their global attack activities. The results are summarized 
in Table 1. The second column identifies the source 
country that provides the best fit. The corresponding R2 
value is given in the third column. Finally, the last three 
columns give the R2 values obtained when considering 
UK, USA, or Russia in the regression model.  
It can be noticed that the quality of the regressions 
measured when considering attacks from Russia only is 
generally low for all platforms (R2 less than 0.80). This 
indicates that the property observed at the global level is 
not visible when looking at the local activities observed 
on each platform. However, for the majority of the 
platforms, the best regression models often involve one 
of the three following countries: USA, Germany or UK, 
which also provide the best regressions when analyzing 
the global attack activity considering all the platforms 
together. Two exceptions are found with P6 and P8 for 
which the observed attack activities exhibit different 
characteristics with respect to the origin of the attacks 
(Taiwan, China), compared to the other platforms.  
The trends discussed above have been also observed 
when considering a different granularity for the unit of 
time (e.g., 1 day or 1 week) as well as different data 
observation periods.  
Platform Country 
providing 
the best 
model 
Best 
model 
Russia 
P1 Germany 0.895 0.873 0.858 0.687 
P2 USA 0.733 0.464 0.733 0.260 
P4 Germany 0.722 0.197 0.373 0.161 
P5 Germany 0.874 0.869 0.872 0.608 
P6 UK 0.861 0.861 0.699 0.656 
P8 Taiwan 0.796 0.249 0.425 0.212 
P9 Germany 0.754 0.630 0.624 0.631 
P11 China 0.746 0.303 0.664 0.097 
P13 Germany 0.738 0.574 0.412 0.389 
P14 Germany 0.708 0.510 0.546 0.087 
P20 USA 0.912 0.787 0.912 0.774 
P21 SPAIN 0.791 0.620 0.727 0.720 
P22 USA 0.870 0.176 0.870 0.111 
P23 USA 0.874 0.659 0.874 0.517 
Global UK 0.944 0.944 0.939 0.930 
Table 1 – Estimated models for each platform: correlation 
factors for the countries providing the best fit and for UK, USA 
and Russia 
To summarize, two main findings can be derived 
from the results presented above:  
1) Some trends exhibited at the global level considering 
the attack processes on all the platforms together are 
not observed when analyzing each platform 
individually (this is the case, for example, of attacks 
from Russia). On the other hand, we have observed 
the other situation where the trends observed 
globally are also visible locally on the majority of 
the platforms (this is the case, for example, of attacks 
from USA, UK and Germany). 
2) The attack processes observed on each platform are 
very often highly correlated with the attack processes 
originating from a particular country. The country 
providing the best regressions locally, does not 
necessary exhibit high correlations when considering 
other platforms or at the global level. These trends 
seem to result from specific factors that govern the 
attack processes observed on each platform. 
4.2 Distribution of times between attacks 
In this example, we focus on the analysis and the 
modeling of the times between attacks observed on 
different honeypot platforms.  
Let us denote by ti, the time separating the 
occurrence of attack i and attack (i-1). Each attack is 
associated to an IP address, and its occurrence time is 
defined by the time when the first packet is received 
from the corresponding address at one of the three 
virtual machines of the honeypot platform. All the 
packets received from the same IP address within 24 
hours are supposed to belong to the same attack session.  
We have analyzed the distribution of the times 
between attacks observed on each honeypot platform. 
Our objective was to find analytical models that 
faithfully reflect the empirical data collected from each 
platform. In the following, we summarize the results 
obtained considering 5 platforms for which we have 
observed the highest attack activity.  
4 .2.1 Empirical analyses 
Table 2 gives the number of intervals of times 
between attacks observed at each platform considered in 
the analysis as well as the corresponding number of IP 
addresses. As illustrated by Figure 2, most of these 
addresses have been observed only once at a given 
platform. Nevertheless, some IP addresses have been 
observed several times, the maximum number of visits 
per IP address for the five platforms was 57, 96, 148, 
183, and 83 (respectively). Indeed, the curves plotting 
the number of IP addresses as a function of the number 
of attacks for each address follow a heavy-tailed power 
law distribution. It is noteworthy that such distributions 
have been observed in many performance and 
dependability related studies in the context of the 
Internet, e.g., transfer and interarrival times, burst sizes, 
sizes of files transferred over the web, error rates in web 
servers, etc. 
 P5 P6 P9 P20  P23 
Number of ti 85890 148942 46268 224917 51580 
Number of IP 
addresses 
79549 90620 42230 162156 47859 
Table 2 - Numbers of intervals of times between attacks  (ti) and 
of different IP addresses observed at each platform  
Figure 2- Number of IP addresses versus the number of attacks 
per IP address observed at each platform  (log-log scale) 
4 .2.2 Modeling 
Finding tractable analytical models that faithfully 
reflect the observed times between attacks is useful to 
characterize the observed attack processes and to find 
appropriate indicators that can be used for prediction 
purposes. We have investigated several candidate 
distributions, including Weibull, Lognormal, Pareto, and 
the Exponential distribution, which are traditionally 
used in reliability related studies. The best fit for each 
platform has been obtained using a mixture model 
combining a Pareto and an exponential distribution.  
Let us denote by T the random variable 
corresponding to the time between the occurrence of two 
consecutive attacks at a given platform, and t a 
realization of T. Assuming that the probability density 
function pdf(t) associated to T is characterized by a 
mixture distribution combining a Pareto distribution and 
an exponential distribution, then f(t) is defined as 
follows. 
pdf (t) = P
(t +1)
+ (1" P
k is the index parameter of the Pareto distribution, λ is 
the rate associated to the exponential distribution and Pa 
is a probability. 
We have used the R statistical package [11] to estimate 
the parameters that provide the best fit to the collected 
data. The quality of fit is assessed by applying the 
Kolmogorov-Smirnov statistical test. The results are 
presented in Figure 3. It can be noticed that for all the 
platforms, the mixed distribution provides a good fit to 
the observed data whereas the exponential distribution is 
not suitable to describe the observed attack processes. 
Thus, the traditional assumption considered in hardware 
reliability evaluation studies assuming that failures 
occur according to a Poisson process does not seem to 
be satisfactory when considering the data observed form 
our honeypots. These results have been also confirmed 
when considering the data collected during other 
observation periods.  
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Pa = 0.0051
k = 0.173
! = 0.121/sec.
p-value = 0.90
Data Mixture (Pareto, Exp.)
Exponential
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0115
k = 0.1183
! = 0.1364/sec.
p-value = 0.999
 a) P5 b) P6 
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0019
k = 0.1668
! = 0.276/sec.
p-value = 0.99
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0144
k = 0.0183
! = 0.0136/sec.
p-value = 0.90
 c) P9 d) P20 
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0031
k = 0.1240
! = 0.275/sec.
p-value = 0.985
e) P23 
Figure 3- Observed and estimated times between attacks probability density functions. 
4.3 Propagation of attacks 
Besides analyzing the attack activities observed at 
each platform in isolation, it is useful to identify 
phenomena that reflect propagation of attacks through 
different platforms. In this section, we analyze simple 
scenarios where a propagation between two platforms is 
assumed to occur when the IP address of an attacking 
machine observed at a given platform is also observed at 
another platform. Such a situation might occur for 
example as a result of a scanning activity or might be 
resulting from the propagation of worms.  
For the sake of illustration, we restrict the analysis to 
the five platforms considered in the previous example. 
For each attacking IP address in the data collected from 
the five platforms during the period of the study, we 
identified: 1) all the occurrences with the same source 
address, 2) the times of each occurrence and 3) the 
platform on which each occurrence has been reported. A 
propagation is said to occur for this IP address from 
platform Pi to platform Pj when the next occurrence of 
this address is observed on Pj after visiting Pi.  
Based on this information we build a propagation 
graph where each node identifies a platform and a 
transition between two nodes identifies a propagation 
between the nodes. A probability is associated to each 
transition to characterize its likelihood of occurrence.  
Figure 4 presents the propagation graph obtained for 
the five platforms included in the analysis. Considering 
platforms P6 and P20, it can be seen that only a few IP 
addresses that attacked these platforms have been 
observed on the other platforms. The situation is 
different when considering platforms P5, P9, and P23.  
In particular, it can be noticed that propagation between 
P5 and P9 is highly probable. This is related in 
particular to the fact that the addresses of the 
corresponding platforms belong to the same /8 network 
domain. More thorough and detailed analyses are 
currently carried out based on the propagation graph in 
order to take into account timing information for the 
corresponding transitions and also the types of attacks 
observed, in order to better explain the propagation 
phenomena illustrated by the graph. 
Figure 4- Propagation graph 
5. Conclusion 
This paper presented simple examples and 
preliminary models illustrating various types of 
empirical analysis and modeling activities that can be 
carried out based on the data collected from honeypots 
in order to characterize attack processes. The honeypot 
platforms deployed so far in our project belong to the 
family of so-called “low interaction honeypots”. Thus, 
hackers can only scan ports and send requests to fake 
servers without ever succeeding in taking control over 
them. In our project, we are also interested in running 
experiments with “high interaction” honeypots where 
attackers can really compromise the targets. Such 
honeypots are suitable to collect data that would enable 
us to study the behaviors of attackers once they have 
managed to get access to a target and try to progress in 
the intrusion process to get additional privileges. Future 
work will be focused on the deployment of such 
honeypots and the exploitation of the collected data to 
better characterize attack scenarios and analyze their 
impact on the security of the target systems. The 
ultimate objective would be to build representative 
stochastic models that will enable us to evaluate the 
ability of computing systems to resist to attacks and to 
validate them based on real attack data. 
Acknowledgement. This work has been carried out in the 
context of the CADHo project, an ongoing research action 
funded by the French ACI “Securité & Informatique” 
(www.cadho.org). It is partially supported by the ReSIST 
European Network of Excellence (www .resist-noe.org). 
References 
[1] M. Bailey, E. Cooke, F. Jahanian, J. Nazario, and D. 
Watson, "The Internet Motion Sensor: A Distributed 
Blackhole Monitoring System," Proc. 12th Annual 
Network and Distributed System Security Symposium 
(NDSS), San Diego, CA, Feb. 2005. 
[2] Home Page of the CAIDA Project, http://www.caida.org/ 
[3] DShield Distributed Detection System homepage, 
http://www.honeynet.org/ 
[4] E. Alata, M. Dacier, Y. Deswarte, M. Kaâniche, K. 
Kortchinsky, V. Nicomette, V.H. Pham, F. Pouget,  
Collection and Analysis of Attack data based on 
honeypots deployed on the Internet”, 1st Workshop on 
Quality of Protection, Milano, Italy, September 2005.  
[5]  F. Pouget, M. Dacier, V. H. Pham, “Leurré.com: On the 
Advantages of Deploying a Large Scale Distributed 
Honeypot Platform”, Proc. E-Crime and Computer 
Evidence Conference (ECCE 2005), Monaco, Mars 2005. 
[6] L. Spitzner, Honeypots: Tracking Hackers, Addison-
Wesley, ISBN from-321-10895-7, 2002 
[7] Project Leurré.com. Publications web page, 
http://www.leurrecom.org/paper.htm  
[8] M. Dacier, F. Pouget, H. Debar, “Honeypots: Practical 
Means to Validate Malicious Fault Assumptions on the 
Internet”, Proc. 10th IEEE International Symposium 
Pacific Rim  Dependable Computing (PRDC10), Tahiti, 
March 2004, pages 383-388. 
[9] M. Dacier, F. Pouget, H. Debar, “Attack Processes found 
on the Internet”, Proc. OTAN Symp. on Adaptive Defense 
in Unclassified Networks, Toulouse, France, April 2004. 
[10] Honeyd Home page, 
http://www.citi.umich.edu/u/provos/honeyd/ 
[11] R statistical package Home page, http://www.r-project.org

  Honeypots are more and more used to collect data on malicious activities on
the Internet and to better understand the strategies and techniques used by
attackers to compromise target systems. Analysis and modeling methodologies are
needed to support the characterization of attack processes based on the data
collected from the honeypots. This paper presents some empirical analyses based
on the data collected from the Leurr{\'e}.com honeypot platforms deployed on
the Internet and presents some preliminary modeling studies aimed at fulfilling
such objectives.

Introduction 
Several initiatives have been developed during the 
last decade to monitor malicious threats and activities on 
the Internet, including viruses, worms, denial of service 
attacks, etc. Among them, we can mention the Internet 
Motion Sensor project [1], CAIDA [2], DShield [3], and 
CADHo [4]. These projects provide valuable 
information on security threats and the potential damage 
that they might cause to Internet users. Analysis and 
modeling methodologies are necessary to extract the 
most relevant information from the large set of data 
collected from such monitoring activities that can be 
useful for system security administrators and designers 
to support decision making. The designers are mainly 
interested in having representative and realistic 
assumptions about the kind of threats and vulnerabilities 
that their system will have to cope with once it is used in 
operation. Knowing who are the enemies and how they 
proceed to defeat the security of target systems is an 
important step to be able to build systems that can be 
resilient with respect to the corresponding threats. From 
the system security administrators’ perspective, the 
collected data should be used to support the 
development of efficient early warning and intrusion 
detection systems that will enable them to better react to 
the attacks targeting their systems. 
As of today, there is still a lack of methodologies and 
significant results to fulfill the objectives described 
above, although some progress has been achieved 
recently in this field. The CADHo project “Collection 
and Analysis  of Data from Honeypots” [4], an ongoing 
research action started in September 2004, is aimed at 
contributing to filling such a gap by carrying out the 
following activities:   
1)  deploying a distributed platform of honeypots [5] 
that gathers data suitable to analyze the attack 
processes targeting a large number of machines 
connected to the Internet;  
2)  developing analysis methodologies and modeling 
approaches to validate the usefulness of this 
platform by carrying out various analyses, based on 
the collected data, to characterize the observed 
attacks and model their impact on security. 
A honeypot is a machine connected to a network but 
that no one is supposed to use. In theory, no connection 
to or from that machine should be observed. If a 
connection occurs, it must be, at best an accidental error 
or, more likely, an attempt to attack the machine.  
The Leurré.com data collection environment  [5], set 
up in the context of the CADHo project, has deployed, 
as of to date, thirty five honeypot platforms at various 
locations from academia and industry, in twenty five 
countries over the five continents. Several analyses 
carried out based on the data collected so far from these 
honeypots have revealed that very interesting 
observations and conclusions can be derived with 
respect to the attack activities observed on the Internet 
[4, 6-9]. In addition, several automatic data analyses and 
clustering techniques have been developed to facilitate 
the extraction of relevant information from the collected 
data. A list of papers detailing the methodologies used 
and the results of these analyses is available in [6]. 
This paper focuses on modeling-related activities 
based on the data collected from the honeypots. We first 
discuss the objectives of such activities and the 
challenges that need to be addressed. Then we present 
some examples of models obtained from the data. 
The paper is organized as follows. Section 2 presents 
the data collection environment. Section 3 focuses on 
the modeling of attacks based on the data collected from 
the honeypots deployed. Modeling examples are 
presented in Section 4. Finally, Section 5 discusses 
future work. 
2.  The data collection environment  
The data collection environment (called Leurré.com 
[5]) deployed in the context of the CADHo project is 
based on low-interaction honeypots using the freely 
available software called honeyd [10]. Since September 
2004, 35 honeypot platforms have been progressively 
deployed on the Internet at various geographical 
locations. Each platform emulates three computers 
running Linux RedHat, Windows 98 and Windows NT, 
respectively, and various services such as ftp, web, etc. 
A firewall ensures that connections cannot be initiated 
from the computers, only replies to external solicitations 
are allowed. All the honeypot platforms are centrally 
managed to ensure that they have exactly the same 
configuration. The data gathered by each platform are 
securely uploaded to a centralized database with the 
complete content, including payload of all packets sent 
to or from these honeypots, and additional information 
to facilitate its analysis, such as the IP geographical 
localization of packets’ source addresses, the OS of the 
attacking machine, the local time of the source, etc. 
3. Modeling objectives 
Modeling involves three main steps: 
1) The definition of the objectives of the modeling 
activities and the quantitative measures to be 
evaluated. 
2) The development of one (or several) models that are 
suitable to achieve the specified objectives. 
3) The processing of the models and the analysis of the 
results to support system design or operation 
activities.  
The data collected from the honeypots can be 
processed in various ways to characterize the attack 
processes and perform predictive analyses. In particular, 
modeling activities can be used to: 
• Identify the probability distributions that best 
characterize the occurrence of attacks and their 
propagation through the Internet.  
• Analyze whether the data collected from different 
platforms exhibit similar or different malicious 
attack activities. 
• Model the time relationships that may exist between 
attacks coming from different sources (or to different 
destinations). 
• Predict the occurrence of new waves of attacks on a 
given platform based on the history of attacks 
observed on this platform as well as on the other 
platforms. 
For the sake of illustration, we present in the 
following sections simple preliminary models based on 
the data collected from our honeypots that are aimed at 
fulfilling such objectives. 
4. Examples 
The examples presented in the following address:  
1) The analysis of the time evolution of the number of 
attacks taking into account the geographic location 
of the attacking machine. 
2) The characterization and statistical modeling of the 
times between attacks. 
3) The analysis of the propagation of attacks throughout 
the honeypot platforms. 
The data considered for the examples has been 
collected from January 1st, 2004 to April 17, 2005, 
corresponding to a data collection period of 320 days.  
We take into account the attacks observed on 14 
honeypot platforms among those deployed so far. The 
selected honeypots correspond to those that have been 
active for almost the whole considered period. The total 
number of attacks observed on these honeypots is 
816476. These attacks are not uniformly distributed 
among the platforms. In particular, the data collected 
from three platforms represent more than fifty percent of 
the total attack activity. 
4.1 Attack occurrence and geographic distribution 
The preliminary models presented in this sub-section 
address: i) the time-evolution modeling of the number of 
attacks observed on different honeypot platforms, and ii) 
the analysis of potential correlations for the attack 
processes observed on the different platforms taking into 
account the geographic location of the attacking 
machines and the proportion of attacks observed on each 
platform, wrt. to the global attack activity. 
Let us denote by: 
− Y(t) the function describing the evolution of the 
number of attacks per unit of time observed on all 
the honeypots during the observation period,  
− Xj(t) the function describing the evolution of the 
number of attacks per unit of time observed on all 
the honeypots during the observation period for 
which the IP address of the attacking machine is 
located in country j . 
In a first stage, we have plotted, for various time 
periods, Y(t) and the curves Xj(t) corresponding to 
different countries j. Visual inspection showed 
surprising similarities between Y(t) and some Xj(t). To 
confirm such empirical observations, we have then 
decided to rigorously analyze this phenomenon using 
mathematical linear regression models.  
Considering a linear regression model, we have 
investigated if Y(t) can be estimated from the 
combination of the attacks described by Xj(t), taking into 
account a  limited number of countries j. Let us denote 
by Y*(t) the estimated model. 
Formally, Y*(t) is defined as follows: 
Y*(t) = Σαj Xj(t) + β         j= 1, 2, .. k (1) 
Constants αj and β  correspond to the parameters of 
the linear model that provide the best fit with the 
observed data, and k is the number of countries 
considered in the regression.  
The quality of fit of the model is measured by the 
statistics R2 defined by: 
R2 = Σ(Y*(i) – Yav)
 2/ Σ(Y (i) – Yav) 2 (2) 
Y (i) and Y*(i) correspond to the observed and estimated 
number of attacks for unit of time i, respectively. Yav is 
the average number of attacks per unit of time, taking 
into account the whole observation period.  
Indeed, R is the correlation factor between the 
estimated model and the observed values. The closer the 
R2 value is to 1, the better the estimated model fits the 
collected data.  
We have applied this model considering linear 
regressions involving one, two or more countries. 
Surprisingly, the results reveal that a good fit can be 
obtained by considering the attacks from one country 
only. For example, the models providing the best fit 
taking into account the total number of attacks from all 
the platforms are obtained by considering the attacks 
issued from either UK, USA, Russia or Germany only. 
The corresponding R2 values are of the same order of 
magnitude (0.944 for UK, 0.939 for USA, 0.930 for 
Russia and 0.920 for Germany), denoting a very good fit 
of the estimated models to the collected data. For 
example, the estimated model obtained when 
considering the attacks from Russia only is defined by 
equation (3): 
Y*(t) = 44.568 X1(t) + 1555.67 (3) 
X1(t) represents the evolution of the number of attacks 
from Russia. Figure 1 plots the evolution of the 
observed and estimated number of attacks per unit  of 
time during the data collection period considered in this 
example. The unit of time corresponds to 4 days. It is 
noteworthy that, similar conclusions are obtained if we 
consider another granularity for the unit of time, for 
example one day, or one week. 
These results are even more surprising that the 
attacks from Russia and UK represent only a small 
proportion of the total number of attacks (1.9% and 
3.7% respectively). Concerning the USA, although the 
proportion is higher (about 18%), it is not sufficient to 
explain the linear model. 
Figure 1- Evolution of the number of attacks per unit of time 
observed on all the platforms and estimated model considering 
attacks from Russia only 
We have applied similar analyses by respectively 
considering each honeypot platform in order to 
investigate if similar conclusions can be derived by 
comparing their attack activities per source country to 
their global attack activities. The results are summarized 
in Table 1. The second column identifies the source 
country that provides the best fit. The corresponding R2 
value is given in the third column. Finally, the last three 
columns give the R2 values obtained when considering 
UK, USA, or Russia in the regression model.  
It can be noticed that the quality of the regressions 
measured when considering attacks from Russia only is 
generally low for all platforms (R2 less than 0.80). This 
indicates that the property observed at the global level is 
not visible when looking at the local activities observed 
on each platform. However, for the majority of the 
platforms, the best regression models often involve one 
of the three following countries: USA, Germany or UK, 
which also provide the best regressions when analyzing 
the global attack activity considering all the platforms 
together. Two exceptions are found with P6 and P8 for 
which the observed attack activities exhibit different 
characteristics with respect to the origin of the attacks 
(Taiwan, China), compared to the other platforms.  
The trends discussed above have been also observed 
when considering a different granularity for the unit of 
time (e.g., 1 day or 1 week) as well as different data 
observation periods.  
Platform Country 
providing 
the best 
model 
Best 
model 
Russia 
P1 Germany 0.895 0.873 0.858 0.687 
P2 USA 0.733 0.464 0.733 0.260 
P4 Germany 0.722 0.197 0.373 0.161 
P5 Germany 0.874 0.869 0.872 0.608 
P6 UK 0.861 0.861 0.699 0.656 
P8 Taiwan 0.796 0.249 0.425 0.212 
P9 Germany 0.754 0.630 0.624 0.631 
P11 China 0.746 0.303 0.664 0.097 
P13 Germany 0.738 0.574 0.412 0.389 
P14 Germany 0.708 0.510 0.546 0.087 
P20 USA 0.912 0.787 0.912 0.774 
P21 SPAIN 0.791 0.620 0.727 0.720 
P22 USA 0.870 0.176 0.870 0.111 
P23 USA 0.874 0.659 0.874 0.517 
Global UK 0.944 0.944 0.939 0.930 
Table 1 – Estimated models for each platform: correlation 
factors for the countries providing the best fit and for UK, USA 
and Russia 
To summarize, two main findings can be derived 
from the results presented above:  
1) Some trends exhibited at the global level considering 
the attack processes on all the platforms together are 
not observed when analyzing each platform 
individually (this is the case, for example, of attacks 
from Russia). On the other hand, we have observed 
the other situation where the trends observed 
globally are also visible locally on the majority of 
the platforms (this is the case, for example, of attacks 
from USA, UK and Germany). 
2) The attack processes observed on each platform are 
very often highly correlated with the attack processes 
originating from a particular country. The country 
providing the best regressions locally, does not 
necessary exhibit high correlations when considering 
other platforms or at the global level. These trends 
seem to result from specific factors that govern the 
attack processes observed on each platform. 
4.2 Distribution of times between attacks 
In this example, we focus on the analysis and the 
modeling of the times between attacks observed on 
different honeypot platforms.  
Let us denote by ti, the time separating the 
occurrence of attack i and attack (i-1). Each attack is 
associated to an IP address, and its occurrence time is 
defined by the time when the first packet is received 
from the corresponding address at one of the three 
virtual machines of the honeypot platform. All the 
packets received from the same IP address within 24 
hours are supposed to belong to the same attack session.  
We have analyzed the distribution of the times 
between attacks observed on each honeypot platform. 
Our objective was to find analytical models that 
faithfully reflect the empirical data collected from each 
platform. In the following, we summarize the results 
obtained considering 5 platforms for which we have 
observed the highest attack activity.  
4 .2.1 Empirical analyses 
Table 2 gives the number of intervals of times 
between attacks observed at each platform considered in 
the analysis as well as the corresponding number of IP 
addresses. As illustrated by Figure 2, most of these 
addresses have been observed only once at a given 
platform. Nevertheless, some IP addresses have been 
observed several times, the maximum number of visits 
per IP address for the five platforms was 57, 96, 148, 
183, and 83 (respectively). Indeed, the curves plotting 
the number of IP addresses as a function of the number 
of attacks for each address follow a heavy-tailed power 
law distribution. It is noteworthy that such distributions 
have been observed in many performance and 
dependability related studies in the context of the 
Internet, e.g., transfer and interarrival times, burst sizes, 
sizes of files transferred over the web, error rates in web 
servers, etc. 
 P5 P6 P9 P20  P23 
Number of ti 85890 148942 46268 224917 51580 
Number of IP 
addresses 
79549 90620 42230 162156 47859 
Table 2 - Numbers of intervals of times between attacks  (ti) and 
of different IP addresses observed at each platform  
Figure 2- Number of IP addresses versus the number of attacks 
per IP address observed at each platform  (log-log scale) 
4 .2.2 Modeling 
Finding tractable analytical models that faithfully 
reflect the observed times between attacks is useful to 
characterize the observed attack processes and to find 
appropriate indicators that can be used for prediction 
purposes. We have investigated several candidate 
distributions, including Weibull, Lognormal, Pareto, and 
the Exponential distribution, which are traditionally 
used in reliability related studies. The best fit for each 
platform has been obtained using a mixture model 
combining a Pareto and an exponential distribution.  
Let us denote by T the random variable 
corresponding to the time between the occurrence of two 
consecutive attacks at a given platform, and t a 
realization of T. Assuming that the probability density 
function pdf(t) associated to T is characterized by a 
mixture distribution combining a Pareto distribution and 
an exponential distribution, then f(t) is defined as 
follows. 
pdf (t) = P
(t +1)
+ (1" P
k is the index parameter of the Pareto distribution, λ is 
the rate associated to the exponential distribution and Pa 
is a probability. 
We have used the R statistical package [11] to estimate 
the parameters that provide the best fit to the collected 
data. The quality of fit is assessed by applying the 
Kolmogorov-Smirnov statistical test. The results are 
presented in Figure 3. It can be noticed that for all the 
platforms, the mixed distribution provides a good fit to 
the observed data whereas the exponential distribution is 
not suitable to describe the observed attack processes. 
Thus, the traditional assumption considered in hardware 
reliability evaluation studies assuming that failures 
occur according to a Poisson process does not seem to 
be satisfactory when considering the data observed form 
our honeypots. These results have been also confirmed 
when considering the data collected during other 
observation periods.  
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Pa = 0.0051
k = 0.173
! = 0.121/sec.
p-value = 0.90
Data Mixture (Pareto, Exp.)
Exponential
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0115
k = 0.1183
! = 0.1364/sec.
p-value = 0.999
 a) P5 b) P6 
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0019
k = 0.1668
! = 0.276/sec.
p-value = 0.99
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0144
k = 0.0183
! = 0.0136/sec.
p-value = 0.90
 c) P9 d) P20 
1 31 61 91 121 151 181 211 241 271
Time between attacks (seconds)
Mixture (Pareto, Exp.)
Exponential
Pa = 0.0031
k = 0.1240
! = 0.275/sec.
p-value = 0.985
e) P23 
Figure 3- Observed and estimated times between attacks probability density functions. 
4.3 Propagation of attacks 
Besides analyzing the attack activities observed at 
each platform in isolation, it is useful to identify 
phenomena that reflect propagation of attacks through 
different platforms. In this section, we analyze simple 
scenarios where a propagation between two platforms is 
assumed to occur when the IP address of an attacking 
machine observed at a given platform is also observed at 
another platform. Such a situation might occur for 
example as a result of a scanning activity or might be 
resulting from the propagation of worms.  
For the sake of illustration, we restrict the analysis to 
the five platforms considered in the previous example. 
For each attacking IP address in the data collected from 
the five platforms during the period of the study, we 
identified: 1) all the occurrences with the same source 
address, 2) the times of each occurrence and 3) the 
platform on which each occurrence has been reported. A 
propagation is said to occur for this IP address from 
platform Pi to platform Pj when the next occurrence of 
this address is observed on Pj after visiting Pi.  
Based on this information we build a propagation 
graph where each node identifies a platform and a 
transition between two nodes identifies a propagation 
between the nodes. A probability is associated to each 
transition to characterize its likelihood of occurrence.  
Figure 4 presents the propagation graph obtained for 
the five platforms included in the analysis. Considering 
platforms P6 and P20, it can be seen that only a few IP 
addresses that attacked these platforms have been 
observed on the other platforms. The situation is 
different when considering platforms P5, P9, and P23.  
In particular, it can be noticed that propagation between 
P5 and P9 is highly probable. This is related in 
particular to the fact that the addresses of the 
corresponding platforms belong to the same /8 network 
domain. More thorough and detailed analyses are 
currently carried out based on the propagation graph in 
order to take into account timing information for the 
corresponding transitions and also the types of attacks 
observed, in order to better explain the propagation 
phenomena illustrated by the graph. 
Figure 4- Propagation graph 
5. Conclusion 
This paper presented simple examples and 
preliminary models illustrating various types of 
empirical analysis and modeling activities that can be 
carried out based on the data collected from honeypots 
in order to characterize attack processes. The honeypot 
platforms deployed so far in our project belong to the 
family of so-called “low interaction honeypots”. Thus, 
hackers can only scan ports and send requests to fake 
servers without ever succeeding in taking control over 
them. In our project, we are also interested in running 
experiments with “high interaction” honeypots where 
attackers can really compromise the targets. Such 
honeypots are suitable to collect data that would enable 
us to study the behaviors of attackers once they have 
managed to get access to a target and try to progress in 
the intrusion process to get additional privileges. Future 
work will be focused on the deployment of such 
honeypots and the exploitation of the collected data to 
better characterize attack scenarios and analyze their 
impact on the security of the target systems. The 
ultimate objective would be to build representative 
stochastic models that will enable us to evaluate the 
ability of computing systems to resist to attacks and to 
validate them based on real attack data. 
Acknowledgement. This work has been carried out in the 
context of the CADHo project, an ongoing research action 
funded by the French ACI “Securité & Informatique” 
(www.cadho.org). It is partially supported by the ReSIST 
European Network of Excellence (www .resist-noe.org). 
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