1 Modeling and Detection of Camouflaging Worm

Wei Yu, Xun Wang, Prasad Calyam, Dong Xuan, and Wei Zhao

Abstract—Active worms pose major security threats to the Internet. This is due to the ability of active worms to propagate in an automated fashion as they continuously compromise computers on the Internet. Active worms evolve during their propagation and thus pose great challenges to defend against them. In this paper, we investigate a new class of active worms, referred to as Camouflaging Worm (C-Worm in short). The C-Worm is different from traditional worms because of its ability to intelligently manipulate its scan traffic volume over time. Thereby, the C-Worm camouflages its propagation from existing worm detection systems based on analyzing the propagation traffic generated by worms. We analyze characteristics of the C-Worm and conduct a comprehensive comparison between its traffic and non-worm traffic (background traffic). We observe that these two types of traffic are barely distinguishable in the time domain. However, their distinction is clear in the frequency domain, due to the recurring manipulative nature of the C-Worm. Motivated by our observations, we design a novel spectrum-based scheme to detect the C-Worm. Our scheme uses the Power Spectral Density (PSD) distribution of the scan traffic volume and its corresponding Spectral Flatness Measure (SFM) to distinguish the C-Worm traffic from background traffic. Using a comprehensive set of detection metrics and real-world traces as background traffic, we conduct extensive performance evaluations on our proposed spectrum-based detection scheme. The performance data clearly demonstrates that our scheme can effectively detect the C-Worm propagation. Furthermore, we show the generality of our spectrum-based scheme in effectively detecting not only the C-Worm, but traditional worms as well.

Index Terms—Worm, Camouflage, Anomaly Detection. !

1 INTRODUCTION attacks of unprecedented scale [10]. For an adversary, super- An active worm refers to a malicious software program that botnets would also be extremely versatile and resistant to propagates itself on the Internet to infect other computers. The countermeasures. propagation of the worm is based on exploiting vulnerabilities Due to the substantial damage caused by worms in the of computers on the Internet. Many real-world worms have past years, there have been significant efforts on developing caused notable damage on the Internet. These worms include detection and defense mechanisms against worms. A network- “Code-Red” worm in 2001 [1], “Slammer” worm in 2003 [2], based worm detection system plays a major role by moni- and “Witty”/“Sasser” worms in 2004 [3]. Many active worms toring, collecting, and analyzing the scan traffic (messages to are used to infect a large number of computers and recruit identify vulnerable computers) generated during worm attacks. them as bots or zombies, which are networked together to form In this system, the detection is commonly based on the self- botnets [4]. These botnets can be used to: (a) launch massive propagating behavior of worms that can be described as Distributed Denial-of-Service (DDoS) attacks that disrupt the follows: after a worm-infected computer identifies and infects Internet utilities [5], (b) access confidential information that a vulnerable computer on the Internet, this newly infected 1 can be misused [6] through large scale traffic sniffing, key computer will automatically and continuously scan several IP logging, identity theft etc, (c) destroy data that has a high addresses to identify and infect other vulnerable computers. As monetary value [7], and (d) distribute large-scale unsolicited such, numerous existing detection schemes are based on a tacit advertisement emails (as spam) or software (as malware). assumption that each worm-infected computer keeps scanning There is evidence showing that infected computers are being the Internet and propagates itself at the highest possible speed. rented out as “Botnets” for creating an entire black-market Furthermore, it has been shown that the worm scan traffic industry for renting, trading, and managing “owned” com- volume and the number of worm-infected computers exhibit puters, leading to economic incentives for attackers [4], [8], exponentially increasing patterns [2], [11], [12], [13], [14]. [9]. Researchers also showed possibility of “super-botnets,” Nevertheless, the attackers are crafting attack strategies that networks of independent botnets that can be coordinated for intend to defeat existing worm detection systems. In particular, ‘stealth’ is one attack strategy used by a recently-discovered • Wei Yu is with the Department of Computer and Information Sciences, active worm called “Atak” worm [15] and the “self-stopping” Towson University, Towson, MD 21252. E-mail: [email protected]. worm [16] circumvent detection by hibernating (i.e., stop • Xun Wang is with Cisco Systems Inc, San Jose, CA 95134. propagating) with a pre-determined period. Worm might also Email: [email protected] • Prasad Calyam is with OARnet, The Ohio State University, Columbus, OH use the evasive scan [17] and traffic morphing technique to 43210. Email: [email protected]. hide the detection [18]. • Dong Xuan is with the Dept. of Computer Science and Engineering, This worm attempts to remain hidden by sleeping (suspend- The Ohio State University, Columbus, OH 43210. Email: [email protected] state.edu. ing scans) when it suspects it is under detection. Worms that • Wei Zhao is with Department of Computer and Information Science, University of Macau, Macau, China. E-mail: [email protected]. 1. In this paper, we interchangeably use the terms - worm-infected computer and worm instance. 2 adopt such smart attack strategies could exhibit overall scan Furthermore, we demonstrate the effectiveness of our traffic patterns different from those of traditional worms. Since spectrum-based detection scheme in comparison with existing the existing worm detection schemes will not be able to detect worm detection schemes. We define several new metrics. such scan traffic patterns, it is very important to understand Maximal Infection Ratio (MIR) is the one to quantify the such smart-worms and develop new countermeasures to defend infection damage caused by a worm before being detected. against them. Other metrics include Detection Time (DT) and Detection In this paper, we conduct a systematic study on a new Rate (DR). Our evaluation data clearly demonstrate that our class of such smart-worms denoted as Camouflaging Worm (C- spectrum-based detection scheme achieves much better detec- Worm in short). The C-Worm has a self-propagating behavior tion performance against the C-Worm propagation compared similar to traditional worms, i.e., it intends to rapidly infect with existing detection schemes. Our evaluation also shows as many vulnerable computers as possible. However, the C- that our spectrum-based detection scheme is general enough Worm is quite different from traditional worms in which it to be used for effective detection of traditional worms as well. camouflages any noticeable trends in the number of infected The remainder of the paper is organized as follows. In computers over time. The camouflage is achieved by manip- Section 2, we introduce the background and review the related ulating the scan traffic volume of worm-infected computers. work. In Section 3, we introduce the propagation model of Such a manipulation of the scan traffic volume prevents exhibi- the C-Worm. We present our spectrum-based detection scheme tion of any exponentially increasing trends or even crossing of against the C-Worm in Section 4. The performance evaluation thresholds that are tracked by existing detection schemes [19], results of our spectrum-based detection scheme is provided in [20], [21]. We note that the propagation controlling nature Section 5. We conclude this paper in Section 6. of the C-Worm (and similar smart-worms, such as “Atak”) cause a slow down in the propagation speed. However, by carefully controlling its scan rate, the C-Worm can: (a) still 2 BACKGROUNDAND RELATED WORK achieve its ultimate goal of infecting as many computers as 2.1 Active Worms possible before being detected, and (b) position itself to launch subsequent attacks [4], [5], [6], [7]. Active worms are similar to biological viruses in terms of their We comprehensively analyze the propagation model of the infectous and self-propagating nature. They identify vulnerable C-Worm and corresponding scan traffic in both time and computers, infect them and the worm-infected computers frequency domains. We observe that although the C-Worm propagate the infection further to other vulnerable computers. scan traffic shows no noticeable trends in the time domain, In order to understand worm behavior, we first need to model it demonstrates a distinct pattern in the frequency domain. it. With this understanding, effective detection and defense Specifically, there is an obvious concentration within a narrow schemes could be developed to mitigate the impact of the range of frequencies. This concentration within a narrow worms. For this reason, tremendous research effort has focused range of frequencies is inevitable since the C-Worm adapts on this area [12], [24], [14], [25], [16]. to the dynamics of the Internet in a recurring manner for Active worms use various scan mechanisms to propagate manipulating and controlling its overall scan traffic volume. themselves efficiently. The basic form of active worms can be The above recurring manipulations involve steady increase, categorized as having the Pure Random Scan (PRS) nature. In followed by a decrease in the scan traffic volume, such that the PRS form, a worm-infected computer continuously scans the changes do not manifest as any trends in the time domain a set of random Internet IP addresses to find new vulnerable or such that the scan traffic volume does not cross thresholds computers. Other worms propagate themselves more effec- that could reveal the C-Worm propagation. tively than PRS worms using various methods, e.g., network Based on the above observation, we adopt frequency domain port scanning, email, file sharing, Peer-to-Peer (P2P) networks, analysis techniques and develop a detection scheme against and Instant Messaging (IM) [26], [27]. In addition, worms use wide-spreading of the C-Worm. Particularly, we develop a different scan strategies during different stages of propagation. novel spectrum-based detection scheme that uses the Power In order to increase propagation efficiency, they use a local Spectral Density (PSD) distribution of scan traffic volume in network or hitlist to infect previously identified vulnerable the frequency domain and its corresponding Spectral Flatness computers at the initial stage of propagation [12], [28]. They Measure (SFM) to distinguish the C-Worm traffic from non- may also use DNS, network topology and routing information worm traffic (background traffic). Our frequency domain anal- to identify active computers instead of randomly scanning IP ysis studies use the real-world Internet traffic traces (Shield addresses [11], [21], [27], [29]. They split the target IP address logs dataset) provided by SANs Internet Storm Center (ISC) space during propagation in order to avoid duplicate scans [22], [23]2. Our results reveal that non-worm traffic (e.g., [21]. Li et al. [30] studied a divide-conquer scanning technique port-scan traffic for port 80, 135 and 8080) has relatively that could potentially spread faster and stealthier than a larger SFM values for their PSD distributions. Whereas, the traditional random-scanning worm. Ha et al. [31] formulated C-Worm traffic shows comparatively smaller SFM value for the problem of finding a fast and resilient propagation topology its respective PSD distribution. and propagation schedule for Flash worms. Yang et al. [32] studied the worm propagation over the sensor networks. 2. ISC monitors and collects port-scan traffic data from around 1 million IP addresses spanning several thousands of organizations in different geograph- Different from the above worms, which attempt to accelerate ical regions. the propagation with new scan schemes, the Camouflaging 3

Worm (C-Worm) studied in this paper aims to elude the de- rules for detecting the worm propagation. For example, tection by the worm defense system during worm propagation. Venkataraman et al. and Wu et al. in [20], [21] proposed Closely related, but orthogonal to our work, are the evolved schemes to examine statistics of scan traffic volume, Zou et active worms that are polymorphic [33], [34] in nature. Poly- al. presented a trend-based detection scheme to examine the morphic worms are able to change their binary representation exponential increase pattern of scan traffic [19], Lakhina et al. or signature as part of their propagation process. This can in [40] proposed schemes to examine other features of scan be achieved with self-encryption mechanisms or semantics- traffic, such as the distribution of destination addresses. Other preserving code manipulation techniques. The C-Worm also works study worms that attempt to take on new patterns to shares some similarity with stealthy port-scan attacks. Such avoid detection [39]. attacks try to find out available services in a target system, Besides the above detection schemes that are based on while avoiding detection [35], [36]. It is accomplished by the global scan traffic monitor by detecting traffic anoma- decreasing the port scan rate, hiding the origin of attackers, lous behavior, there are other worm detection and defense etc. Due to the nature of self-propagation, the C-Worm must schemes such as sequential hypothesis testing for detecting use more complex mechanisms to manipulate the scan traffic worm-infected computers [44], payload-based worm signature volume over time in order to avoid detection. detection [34], [45]. In addition, Cai et al. in [46] presented both theoretical modeling and experimental results on a col- laborative worm signature generation system that employs 2.2 Worm Detection distributed fingerprint filtering and aggregation and multiple Worm detection has been intensively studied in the past and edge networks. Dantu et al. in [47] presented a state-space can be generally classified into two categories: “host-based” feedback control model that detects and control the spread detection and “network-based” detection. Host-based detection of these viruses or worms by measuring the velocity of the systems detect worms by monitoring, collecting, and analyzing number of new connections an infected computer makes. worm behaviors on end-hosts. Since worms are malicious Despite the different approaches described above, we believe programs that execute on these computers, analyzing the that detecting widely scanning anomaly behavior continues to behavior of worm executables plays an important role in host- be a useful weapon against worms, and that in practice multi- based detection systems. Many detection schemes fall under faceted defence has advantages. this category [37], [38]. In contrast, network-based detection systems detect worms primarily by monitoring, collecting, 3 MODELINGOFTHE C-WORM and analyzing the scan traffic (messages to identify vulner- able computers) generated by worm attacks. Many detection 3.1 C-Worm schemes fall under this category [19], [20], [21], [39], [40]. The C-Worm camouflages its propagation by controlling scan Ideally, security vulnerabilities must be prevented to begin traffic volume during its propagation. The simplest way to with, a problem which must addressed by the programming manipulate scan traffic volume is to randomly change the language community. However, while vulnerabilities exist and number of worm instances conducting port-scans. pose threats of large-scale damage, it is critical to also focus As other alternatives, a worm attacker may use an open-loop on network-based detection, as this paper does, to detect wide- control (non-feedback) mechanism by choosing a randomized spreading worms. and time related pattern for the scanning and infection in order In order to rapidly and accurately detect Internet-wide to avoid being detected. Nevertheless, the open-loop control large scale propagation of active worms, it is imperative to approach raises some issues of the invisibility of the attack. monitor and analyze the traffic in multiple locations over First, as we know, worm propagation over the Internet can the Internet to detect suspicious traffic generated by worms. be considered a dynamic system. When an attacker launches The widely adopted worm detection framework consists of worm propagation, it is vey challenging for the attacker to multiple distributed monitors and a worm detection center know the accurate parameters for worm propagation dynamics that controls the former [23], [41]. This framework is well over the Internet. Given the inaccurate knowledge of worm adopted and similar to other existing worm detection systems, propagation over the Internet, the open-loop control system such as the Cyber center for disease controller [11], Internet will not be able to stabilize the scan traffic. This is a known motion sensor [42], SANS ISC (Internet Storm Center) [23], result from control system theory [48]. Consequently, the Internet sink [41], and network telescope [43]. The monitors overall worm scan traffic volume in the open-loop control are distributed across the Internet and can be deployed at end- system will expose a much higher probability to show an hosts, router, or firewalls etc. Each monitor passively records increasing trend with the progress of worm propagation. As irregular port-scan traffic, such as connection attempts to a more and more computers get infected, they, in turn, take range of void IP addresses (IP addresses not being used) and part in scanning other computers. Hence, we consider the C- restricted service ports. Periodically, the monitors send traffic worm as a worst case attacking scenario that uses a closed- logs to the detection center. The detection center analyzes the loop control for regulating the propagation speed based on the traffic logs and determines whether or not there are suspicious feedback propagation status. scans to restricted ports or to invalid IP addresses. In order to effectively evade detection, the overall scan Network-based detection schemes commonly analyze the traffic for the C-Worm should be comparatively slow and collected scanning traffic data by applying certain decision variant enough to not show any notable increasing trends over 4 time. On the other hand, a very slow propagation of the C- B has been infected. Through validating such marks during Worm is also not desirable, since it delays rapid infection the propagation, a C-Worm infected computer can estimate damage to the Internet. Hence, the C-Worm needs to adjust its M(t). Appendix A discusses one alternative how the C- propagation so that it is neither too fast to be easily detected, Worm could estimate M(t) to obtain M¯ (t) as the propagation nor too slow to delay rapid damage on the Internet. proceeds. There are other approaches to achieve this goal, such To regulate the C-Worm scan traffic volume, we introduce as incorporating the Peer-to-Peer techniques to disseminate a control parameter called attack probability P (t) for each information through secured IRC channels [49], [50]. worm-infected computer. P (t) is the probability that a C- Worm instance participates in the worm propagation (i.e., 3.2 Propagation Model of the C-Worm scans and infects other computers) at time t. Our C-Worm model with the control parameter P (t) is generic. P (t) = 1 To analyze the C-Worm, we adopt the epidemic dynamic represents the cases for traditional worms, where all worm model for disease propagation, which has been extensively instances actively participate in the propagation. For the C- used for worm propagation modeling [2], [12]. Based on Worm, P (t) needs not be a constant value and can be set as existing results [2], [12], this model matches the dynamics a time varying function. of real worm propagation over the Internet quite well. For this In order to achieve its camouflaging behavior, the C-Worm reason, similar to other publications, we adopt this model in needs to obtain an appropriate P (t) to manipulate its scan our paper as well. Since our investigated C-Worm is a novel traffic. Specifically, the C-Worm will regulate its overall scan attack, we modified the original Epidemic dynamic formula traffic volume such that: (a) it is similar to non-worm scan to model the propagation of the C-Worm by introducing the traffic in terms of the scan traffic volume over time, (b) it P (t) - the attack probability that a worm-infected computer does not exhibit any notable trends, such as an exponentially participates in worm propagation at time t. We note that there increasing pattern or any mono-increasing pattern even when is a wide scope to notably improve our modified model in the number of infected hosts increases (exponentially) over the future to reflect several characteristics that are relevant in time, and (c) the average value of the overall scan traffic real-world practice. volume is sufficient to make the C-Worm propagate fast Particularly, the epidemic dynamic model assumes that any enough to cause rapid damage on the Internet3. given computer is in one of the following states: immune, We assume that a worm attacker intends to manipulate vulnerable, or infected. An immune computer is one that scan traffic volume so that the number of worm instances cannot be infected by a worm; a vulnerable computer is one participating in the worm propagation follow a random distri- that has the potential of being infected by a worm; an infected computer is one that has been infected by a worm. The simple bution with mean M¯ C . This M¯ C can be regulated in a random epidemic model for a finite population of traditional PRS fashion during worm propagation in order to camouflage the 4 propagation of C-Worm. Correspondingly, the worm instances worms can be expressed as , need to adjust their attack probability P (t) in order to ensure dM(t) = β · M(t) · [N − M(t)], (1) that the total number of worm instances launching the scans dt ¯ is approximately MC . where M(t) is the number of infected computers at time t; To regulate M¯ , it is obvious that P (t) must be decreased C N(= T · P1 · P2) is the number of vulnerable computers on over time since M(t) keeps increasing during the worm the Internet; T is the total number of IP addresses on the propagation. We can express P (t) using a simple function ¯ Internet; P1 is the ratio of the total number of computers on the as follows: P (t) = min( MC , 1), where M¯ (t) represents the M¯ (t) Internet over T ; P2 is the ratio of total number of vulnerable estimation of M(t) at time t. From the above expression, we computers on the Internet over the total number of computers know that the C-Worm needs to obtain the value of M¯ (t) (as on the Internet; β = S/V is called the pairwise infection rate close to M(t) as possible) in order to generate an effective [51]; S is the scan rate defined as the number of scans that P (t). Here, we discuss one approach for the C-Worm to an infected computer can launch in a given time interval. We estimate M(t). The basic idea is as follows: A C-Worm could assume that at t = 0, there are M(0) computers being initially estimate the percentage of computers that have already been infected and N −M(0) computers being susceptible to further infected over the total number of IP addresses as well as M(t), worm infection. through checking a scan attempt as a new hit (i.e., hitting The C-Worm has a different propagation model compared an uninfected vulnerable computer) or a duplicate hit (i.e., to traditional PRS worms because of its P (t) parameter. hitting an already infected vulnerable computer). This method Consequently, Formula (1) needs to be rewritten as, requires each worm instance (i.e., infected computer) to be dM(t) marked indicating that this computer has been infected. Thus, = β · M(t) · P (t) · [N − M(t)]. (2) when a worm instance (for example, computer A) scans one dt ¯ infected computer (for example, computer B), then computer A MC ¯ Recall that P (t) = M¯ (t) , M(t) is the estimation of M(t) at will detect such a mark, thereby becoming aware that computer time t, and assuming that M¯ (t) = (1 + ϵ) · M(t), where ϵ is

3. Note that if chooses P (t) below a certain (very low) level, other 4. We would like to remark that we use the PRS worms to compare C- human-scale countermeasures (e.g., signature-based virus detection, machine Worm performance, but our work can be easily extended to compare with quarantine) may become effective to disrupt the propagation. other worm scan techniques, such as hitlist. 5 the estimation error, the Formula (2) can be rewritten as, Number of Detected Scanning Hosts on Camouflaging Worm 100 dM(t) β · M¯ C 90 = · [N − M(t)]. (3) 80 dt 1 + ϵ(t) 70 With Formula (3), we can derive the propagation model 60 · ¯ 50 − β MC (t)·t for the C-Worm as M(t) = N − e 1+ϵ (N − M(0)), 40 30 where M(0) is the number of infected computers at time 20

0. Assume that the worm detection system can monitor Pm Hosts Scanning Detected of # 10 0 (Pm ∈ [0, 1]) of the whole Internet IP address space. Without 200 2000 4000 6000 8000 9000 10000 11000 12000 13000 14000 loss of generality, the probability that at least one scan from a Time (min) worm-infected computer (it generates S scans in unit time PRS C-Worm 1 C-Worm 2 C-Worm 3 on average) will be observed by the detection system is P (t)·S Fig. 1. Observed infected instance number for the C- 1 − (1 − Pm) . We define that MA(t) is the number of worm instances that have been observed by the worm detection Worm and PRS worm system at time t, then there are M(t) − MA(t) unobserved Infection Ratio on Camouflaging Worms infected instances at time t. At the worm propagation early − ≃ 1 stage, M(t) MA(t) M(t). The expected number of newly 0.9 observed infected instances at t + δ (where δ is the interval 0.8 − · − − P (t)·S ≃ 0.7 of monitoring) is (M(t) MA(t)) [1 (1 Pm) ] 0.6 P (t)·S M(i)[1 − (1 − Pm) ]. Thus, we have MA(t + δ) = IR 0.5 − − P (t)·S 0.4 MA(t)+M(t)[1 (1 Pm) ]. Using simple mathematical 0.3 manipulations, the number of worm instances observed by the 0.2 worm detection system at time t is, 0.1 0 200 2000 4000 5000 7000 8100 9100 10200 11800 14000 Pm · M¯ C MA(t) = P (t) · M(t) · Pm = . (4) Time (min) 1 + ϵ(t) PRS C-Worm 1 C-Worm 2 C-Worm 3

Fig. 2. Infected ratio for the C-Worm and PRS-Worm 3.3 Effectiveness of the C-Worm

We now demonstrate the effectiveness of the C-Worm in evad- For the C-Worm, the trend of observed number of worm ing worm detection through controlling P (t). Given random ¯ instances over time (MA(t)) (defined in Formula (4)) is much selection of Mc, we generate three C-Worm attacks (viz., C- different from that of the traditional PRS worm as shown in Worm 1, C-Worm 2 and C-Worm 3) that are characterized Fig. 2. This clearly demonstrates how the C-Worm success- by different selections of mean and variance magnitudes fully camouflages its increase in the number of worm instances for M¯ C . In our simulations, we assume that the scan rate (MA(t)) and avoids detection by worm detection systems of the traditional PRS worm follow a normal distribution that expect exponential increases in worm instance numbers Sn = N(40, 40) (note that if the scan rate generated by above during large-scale worm propagation. Fig. 3 shows the number distribution is less than 0 , we set the scan rate as 0). We also of scanning computers from normal non-worm port-scanning set the total number of vulnerable computers on the Internet traffic (background traffic) for several well-known ports, (i.e., as 360,000, which is the total number of infected computers 25, 53, 135, and 8080) obtained over several months by the in “Code-Red” worm incident [1]. ISC. Comparing Fig. 3 with Fig. 1, we can observe that it is Fig. 1 shows the observed number of worm-infected com- hard to distinguish the C-Worm port traffic from background puters over time for the PRS worm and the above three C- port-scanning traffic in the time domain. Worm attacks. Fig. 2 shows the infection ratio for the PRS From above Figs. 1 and 2, we also observe that the C- worm and the above three C-Worm attacks. These simulations Worm is still able to maintain a certain magnitude of scan are for a worm detection system discussed in Section 2.2 that traffic so as to cause significant infection on the Internet. As covers a 220 IPv4 address space on the Internet. The reason for 20 a note regarding the speed of C-Worm propagation, we can choosing 2 IP addresses as the coverage space of the worm observe from Fig. 1 that the C-Worm takes approximately 10 detection system is due to the fact that the SANs Internet days to infect 75% of total vulnerable hosts in comparison Storm Center (ISC), a representative ITM system, has similar with the 3.3 days taken by a PRS worm5. Hence, the C-Worm coverage space [23]. In the ITM systems, a large number of could potentially adjust its propagation speed such that it is monitors are commonly deployed all over the Internet and still effective in causing wide-spreading propagation, while each monitor collects the traffic directed to a small set of IP avoiding being detected by the worm detection schemes. address spaces which are not commonly used (also called dark We discussed the “Atak” worm in Section I and mentioned IP addresses). Therefore, the address space of ITM system is that it is similar to the C-Worm since it tries to avoid being not a narrow range address space, rather a large number of small chunks of addresses randomly spread across the global 5. Our simulated PRS worm has less scan rate (mean value of 40) than IP address space. “Code-Red” (mean value of 358). 6

Scanning Traffic Volume: port 25 Scanning Traffic Volume: port 53 2500 500 Sharif et al. [56] presented an obfuscation-based technique that 2000 400 automatically conceals specific condition dependent malicious

1500 300 behavior from virus detectors that have no prior knowledge of

1000 200 program inputs. Popov et al. [57] investigated a technique that Number of Scans Number of Scans 500 100 allows the worm programs to be obfuscated by changing many

0 0 control transfers into signals (traps) and inserting dummy 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Time (unit − 20 min) Time (unit − 20 min) control transfers and “junk” instructions after the signals. Scanning Traffic Volume: port 135 Scanning Traffic Volume: port 8080 3500 3000 The resulting code can significantly reduce the chance to be

3000 2500 detected. Recent studies also showed that existing commercial 2500 2000 anti-worm detection systems fail to detect brand new worms 2000 1500 1500 and can also be easily circumvented by worms that use simple 1000 1000 Number of Scans mutation techniques to manipulate their payload [58]. Number of Scans) 500 500 Although in this paper we only demonstrate effectiveness 0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 of the C-Worm against existing traffic volume-based detection Time (unit − 20 min) Time (unit − 20 min) Fig. 3. Observed infected instance number for back- schemes, the design principle of the C-Worm can be extended ground scanning reported by ISC to defeat other newly developed detection schemes, such as destination distribution-based detection [39], [40]. In the following, we discuss this preliminary concept. Recall that the detected, when it suspects that it is being detected by anti- attack target distribution based schemes analyze the distribu- worm software. However, it differs from the C-Worm in its tion of attack targets (the scanned destination IP addresses) behavior. The “Atak” worm attempts to hide only during as basic detection data to capture the fundamental features times it suspects its propagation will be detected by anti-worm of worm propagation, i.e., they continuously scan different software. Whereas, the C-Worm proactively camouflages itself targets, which is not the expected behavior of non-worm at all times. In addition, the “Self-stopping” worm attempts to scan traffic. However, our initial investigation shows that the hide by co-ordinating with its members to halt propagation worm attacker is still able to defeat such a countermeasure activity only after the vulnerable population is subverted [16]. via manipulating the attack target distribution. For example, This behavior leaves enough evidence for worm detection the attacker may launch a portion of scan traffic bound for systems to recognize its propagation. The C-Worm, on the some IP addresses monitored by ITM system. Recall that other hand, hides itself even during its propagation and thus those dedicated IP addresses monitored by ITM system can keeps the worm detection schemes completely unaware of its be obtained via probing attacks or other means [59], [60], propagation. The C-Worm also has some similarity in spirit [61]. with polymorphic worms that manipulate the byte stream of Using port 135 reported by SANs ISC as an example, we worm payload in order to avoid the detection of signature analyze the traces and obtain the traffic target distribution in a (payload)-based detection scheme [33], [34]. The manipulation window lasting 10 mins. Following existing work [39], [40], of worm payload can be achieved by various mechanisms: (a) we use entropy as the metric to measure the attack target interleaving meaningful instructions with NOP (no operation), distribution. Fig. 4 shows the Probability Density Function (b) using different instructions to achieve the same results, (c) (PDF) of background traffic’s entropy values. We also simulate shuffling the register set in each worm propagation program the worm propagation traffic, which allocates a portion of code copy, and (d) using cryptography mechanisms to change scan traffic bound for IP addresses monitored by the ITM worm payload signature with every infection attempt [33], system. Following this, we obtain the PDF of the entropy [34]. In contrast, the C-Worm tries to manipulate the scan value for combined traffic including both worm propagation traffic pattern to avoid detection. and background traffic. From Fig. 4, we know that when the attacker uses a portion of attack traffic to manipulate the target distribution, the entropy-based detection scheme 3.4 Discussion can degrade significantly. For example, when the attacker In this paper, we focus on a new class of worms, referred to as uses 10% traffic to manipulate the traffic’s entropy value, the the camouflaging worm (C-Worm). The C-Worm adapts their false positive rate of entropy-based detection scheme is 14%. propagation traffic patterns in order to reduce the probability When the attacker uses 30% traffic to manipulate the traffic’s of detection, and to eventually infect more computers. The entropy value, the false positive rate becomes 40%. Hence, C-Worm is different from polymorphic worms that delib- in order to preserve the performance, entropy-based detection erately change their payload signatures during propagation scheme needs to evolve correspondingly and integrate with [34], [52]. For example, MetaPHOR [53] and Zmist [54] other detection schemes. We will perform a more detailed worms intensively metamorphose their payload signature to study of this aspect in our future work. hide themselves from detection schemes that rely on expensive 4 DETECTINGTHE C-WORM packet payload analysis. Bethencourt et al. [55] studied the worm which employs private information retrieval techniques 4.1 Design Rationale to find and retrieve specific pieces of sensitive information In this section, we develop a novel spectrum-based detection from compromised computers while hiding its search criteria. scheme. Recall that the C-Worm goes undetected by detection 7

PDF of C-Worm SFM 100 90 80 70 60 50 40 30 Probability Density Probability 20 10 0 0 0.04 0.08 0.11 0.15 0.19 0.23 0.27 0.3 0.34 0.38 0.42 0.48 0.72 0.96 Fig. 4. Manipulation of attack target distribution entropy SFM Value

Fig. 5. PDF of SFM on C-Worm traffic schemes that try to determine the worm propagation only in PDF of Normal Non-worm Scanning Traffic the time domain. Our detection scheme captures the distinct 70 pattern of the C-Worm in the frequency domain, and thereby 60 has the potential of effectively detecting the C-Worm propa- 50 gation. In order to identify the C-Worm propagation in the fre- 40 quency domain, we use the distribution of Power Spectral Den- 30 sity (PSD) and its corresponding Spectral Flatness Measure Density Probability 20

(SFM) of the scan traffic. Particularly, PSD describes how the 10 power of a time series is distributed in the frequency domain. 0 Mathematically, it is defined as the Fourier transform of the 0 0.15 0.3 0.4 0.43 0.47 0.5 0.54 0.57 0.61 0.64 0.68 0.71 0.75 0.8 0.96 auto-correlation of a time series. In our case, the time series SFM Value corresponds to the changes in the number of worm instances Fig. 6. PDF of SFM on normal non-worm traffic that actively conduct scans over time. The SFM of PSD is defined as the ratio of geometric mean to arithmetic mean of the coefficients of PSD. The range of SFM values is [0, 1] the fact that the power of C-Worm scan traffic is within a and a larger SFM value implies flatter PSD distribution and narrow-band frequency range. Such concentration within a vice versa. narrow range of frequencies is unavoidable since the C-Worm To illustrate SFM values of both the C-Worm and normal adapts to the dynamics of the Internet in a recurring manner non-worm scan traffic, we plot the Probability Density Func- for manipulating the overall scan traffic volume. In reality, tion (PDF) of SFM for both C-Worm and normal non-worm the above recurring manipulations involve steady increase scan traffic as shown in Fig. 5 and Fig. 6, respectively. The followed by a decrease in the scan traffic volume. normal non-worm scan traffic data shown in Fig. 6 is based Notice that the frequency domain analysis will require on real-world traces collected by the ISC 6. Note that we more samples in comparison with the time domain analysis, only show the data for port 8080 as an example, and other since the frequency domain analysis technique such as the ports show similar observations. From this figure, we know Fourier transform, needs to derive power spectrum amplitude that the SFM value for normal non-worm traffic is very small for different frequencies. In order to generate the accurate (e.g., SFM ∈ (0.02, 0.04) has much higher density compared spectrum amplitude for relatively high frequencies, a high with other magnitudes). The C-Worm data shown in Fig. 5 is granularity of data sampling will be required. In our case, we based on 800 C-Worms attacks generated by varying attack rely on Internet threat monitoring (ITM) systems to collect parameters defined in Section 3 such as P (t) and Mc(t). traffic traces from monitors (motion sensors) in a timely From this figure, we know that the SFM value of the C-Worm manner. As a matter of fact, other existing detection schemes attacks is high (e.g., SFM ∈ 0.5, 0.6 has high density). From based on the scan traffic rate [20], variance [21] or trend [19] the above two figures, we can observe that there is a clear will also demand a high sampling frequency for ITM systems demarcation range of SFM ∈ (0.3, 0.38) between the C-Worm in order to accurately detect worm attacks. Enabling the ITM and normal non-worm scan traffic. As such, the SFM can be system with timely data collection will benefit worm detection used to sensitively detect the C-Worm scan traffic. in real-time. The large SFM values of normal non-worm scan traffic can be explained as follows. The normal non-worm scan 4.2 Spectrum-based Detection Scheme traffic does not tend to concentrate at any particular frequency We now present the details of our spectrum-based detection since its random dynamics is not caused by any recurring scheme. Similar to other detection schemes [19], [21], we use phenomenon. The small value of SFM can be reasoned by a “destination count” as the number of the unique destination 6. The traces used in this paper contain log files which have over 100 IP addresses targeted by launched scans during worm propaga- million records and the total size exceeds 40 GB. tion. To understand how the destination count data is obtained, 8 we recall that an ITM system collects logs from distributed non-worm scan traffic. The PSD of C-Worm scan traffic shows monitors across the Internet. On a side note, Internet Threat spikes or noticeably higher concentrations at a certain range Monitoring (ITM) systems are a widely deployed facility to of the spectrum. detect, analyze, and characterize dangerous Internet threats such as worms. In general, an ITM system consists of one 4.2.2 Spectral Flatness Measure (SFM) centralized data center and a number of monitors distributed We measure the flatness of PSD to distinguish the scan traffic across the Internet. Each monitor records traffic that addressed of the C-Worm from the normal non-worm scan traffic. For to a range of IP addresses (which are not commonly used IP this, we introduce the Spectral Flatness Measure (SFM), which address also called the dark IP addresses) and periodically can capture anomaly behavior in certain range of frequencies. sends the traffic logs to the data center. The data center then The SFM is defined as the ratio of the geometric mean to the analyzes the collected traffic LOGS and publishes reports (e.g., arithmetic mean of the PSD coefficients [62], [63]. It can be statistics of monitored traffic) to ITM system users. Therefore expressed as, ∏ the baseline traffic in our study is scan traffic. With reports in n 1 n [ k=1 S(fk)] a sampling window Ws, the source count X(t) is obtained by SFM = ∑ , (7) 1 n S(f ) counting the unique source IP addresses in received logs. n k=1 k

To conduct spectrum analysis, we consider a detection where S(fk) is an PSD coefficient for the PSD obtained from sliding window Wd in the worm detection system. Wd consists the results in Formula (6). SFM is a widely existing measure of q (> 1) continuous detection sampling windows and each for discriminating frequencies in various applications such sampling window lasts Ws. The detection sampling window as voiced frame detection in speech recognition [63], [64]. is the unit time interval to sample the detection data (e.g., the In general, small values of SFM imply the concentration of destination count). Hence, at time i, within a sliding window data at narrow frequency spectrum ranges. Note that the C- Wd, there are q samples denoted by (X(i − q − 1),X(i − Worm has unpreventable recurring behavior in its scan traffic; q − 2),...,X(i)), where X(i − j − 1) (j ∈ (1, q)) is the j-th consequently its SFM values are comparatively smaller than destination count from time i − j − 1 to i − j. the SFM values of normal non-worm scan traffic. To be useful In our spectrum-based detection scheme, the distribution of in detecting C-Worms, we introduce a sliding window to PSD and its corresponding SFM are used to distinguish the C- capture a noticeably higher concentrations at a small range of Worm scan traffic from the non-worm scan traffic. Recall that spectrum. When such noticeably concentration is recognized, the definition of PSD distribution and its corresponding SFM we derive the SFM within a wider frequency range. From are introduced in Section 4.1. In our worm detection scheme, Fig. 5, we can observe that the SFM value for the C-Worm is the detection data (e.g., destination counter), is further pro- very small (e.g., with a mean value of approximately 0.075). cessed in order to obtain its PSD and SFM. In the following, A formal analysis of SFM for the C-Worm is presented in the we detail how the PSD and SFM are determined during the Appendix B. processing of the detection data. 4.2.3 Detection Decision Rule 4.2.1 Power Spectral Density (PSD) We now describe the method of applying an appropriate To obtain the PSD distribution for worm detection data, detection rule to detect C-Worm propagation. As the SFM we need to transform data from the time domain into the value can be used to sensitively distinguish the C-Worm frequency domain. To do so, we use a random process and normal non-worm scan traffic, the worm detection is X(t), t ∈ [0, n] to model the worm detection data. Assuming performed by comparing the SFM with a predefined threshold X(t) is the source count in time period [t − 1, t] (t ∈ [1, n]), Tr. If the SFM value is smaller than a predefined threshold we define the auto-correlation of X(t) by Tr, then a C-Worm propagation alert is generated. The value of the threshold Tr used by the C-Worm detection can be RX (L) = E[X(t)X(t + L)]. (5) fittingly set based on the knowledge of statistical distribution (e.g., PDF) of SFM values that correspond to the non-worm In Formula (5), R (L) is the correlation of worm detection X scan traffic. Notice that the T value for the non-worm traffic data in an interval L. If a recurring behavior exists, a Fourier r can be derived by analyzing the historical data provided by transform of the auto-correlation function of R (L) can reveal X SANs Internet Storm Center (ISC). In the worm detection such behavior. Thus, the PSD function (also represented by systems, monitors collect port-scan traffic to certain area of S (f); where f refers to frequency) of the scan traffic data X dark IP addresses and periodically reports scan traffic log to is determined using the Discrete Fourier Transform (DFT) of the data center. Then the data center aggregates the data from its auto-correlation function as follows, different monitors on the same port and publishes the data. N∑−1 Based on the historical data for different ports, we can build · −j2πKn/N ψ(RX [L],K) = (RX [L]) e , (6) the statistical profiles of port-scan traffic on different ports and n=0 then derive the Tr value for the non-worm traffic. Based on where K = 0, 1,...,N − 1. the continuous reported data, the value of Tr will be tuned As the PSD inherently captures any recurring pattern in the and adaptively used to carry out worm detection. frequency domain, the PSD function shows a comparatively If we can obtain the PDF of SFM values for the C- even distribution across a wide spectrum range for the normal Worm through comprehensive simulations and even real-world 9 profiled data in the future, the optimal threshold can be 5.1 Evaluation Methodology obtained by applying the Bayes classification [65]. If the PDF 5.1.1 Evaluation Metrics of SFM values for the C-Worm is not available, based on the PDF of SFM values of the normal non-worm scan traffic, we In order to evaluate the performance of any given detection scheme against the C-Worm, we use the following three can set an appropriate Tr value. For example, the Tr value can be determined by the Chebyshev inequality [65] in order metrics listed in Table II. The first metric is the worm Infection to obtain a reasonable false positive rate for worm detection. Ratio (IR), which is defined as the ratio of the number of Hence in Section 5, we evaluate our spectrum-based detection infected computers to the total number of vulnerable comput- scheme against the C-Worm on two cases: (a) the PDF of SFM ers, assuming there is no worm detection/defense system in values are known for both the normal non-worm scan traffic place. The other two metrics are the Detection Time (DT ) and the C-Worm scan traffic, (b) the PDF of SFM values is and the Maximal Infection Ratio (MIR). DT is defined as only known for the normal non-worm scan traffic. the time taken to successfully detect a wide-spreading worm from the moment the worm propagation starts. It quantifies In addition, our spectrum-based scheme is also generic for the detection speed of a detection scheme. MIR defines the detecting the PRS worms. This is due to the fact that propa- ratio of an infected computer number over the total number gation traffic of PRS worms has an exponentially increasing of vulnerable computers up to the moment when the worm pattern. Thus, in the propagation traffic of PRS worms, the spreading is detected. It quantifies the damage caused by a PSD values in the low frequency range are much higher worm before being detected. The objective of any detection compared with other frequency ranges. A formal analysis of scheme is to minimize the damage caused by a rapid worm SFM for the PRS worm is presented in Appendix C. propagation. Hence, MIR and DT can be used to quantify Notice that even if the C-Worm monitors the port-scan the effectiveness of any worm detection scheme. The higher traffic report, it will be hard for the C-Worm to make the the values, the more effective the worm attack and the less SFM similar to the background traffic. This can be reasoned effective the detection. In addition, we use two more metrics - by two factors. First, the low value of SFM is mainly caused by Detection Rate (PD) and False Positive Rate (PF ). The PD is the closed-loop control nature of C-worm. The concentration defined as the probability that a detection scheme can correctly within a narrow range of frequencies is unavoidable since the identify a worm attack. The PF is defined as the probability C-Worm adapts to the dynamics of the Internet in a recurring that a detection scheme mistakenly identifies a non-existent manner for manipulating the overall scan traffic volume. Based worm attack. on our analysis, the non-worm traffic on a port is rather random and its SFM has a flat pattern. That means that the non-worm 5.1.2 Simulation Setup traffic on the port distributes similar power across different frequencies. Second, as we indicated in other responses, with- In our evaluation we considered both experiments with real- out introducing the closed-loop control, it will be difficult for world “non-worm” traffic and simulated c-worm traffic. To the attacker to hide the irregularity of worm propagation traffic make our experiments reflect real-world practice, some key in the time domain. When the worm attacks incorporate the parameters that we used to generate C-worm traffic in our closed-loop control mechanism to camouflage their traffic, it simulation were based on previous results from a real-worm will expose a relative small value of SFM. Hence, integrating incidence - “Code-Red” worm in 2001 [1]. Specifically, we our spectrum-based detection with existing traffic rate-based set the total number of vulnerable computers on the Internet anomaly detection in the time domain, we can force the worm as 360,000, which is the maximum number of computers attacker into a dilemma: if the worm attacker does not use the which could be infected by “Code-Red” worm. Additionally, S closed-loop control, the existing traffic rate-based detection we set the scan rate (number of scans per minute) to scheme will be able to detect the worm; if the worm attacker be variable within a range, this allows us to emulate the adopt the closed-loop control, it will cause the relatively small infected computers in different network environments. In our SFM due to the process of closed-loop control. This makes evaluation, the scan rates are predetermined and follow a S = N(S ,S2) S S2 the worm attack to be detected by our spectrum-based scheme Gaussian distribution m σ , where m and σ are [(20, 70] along with other existing traffic-rate based detection schemes. in , similar to those used in [19]. In our evaluation, we merged the simulated C-worm attack traffic into replayed “non-worm” traffic traces and carried out evaluation study. We simulate the C-Worm attacks by varying the attack parameters, such as attack probability (P (t)) and the number 5 PERFORMANCE EVALUATION of worm instances participating in the scan (M¯ C ) defined in Section 3. The M¯ C follows the Gaussian distribution N(m, σ) In this section, we report our evaluation results that illustrate and are changed dynamically by the C-Worm during its the effectiveness of our spectrum-based detection scheme propagation. Particularly, for N(m, σ), m is randomly selected against both the C-Worm and the PRS worm in comparison in (12000, 75000) and σ is randomly selected in (0.2, 100). with existing representative detection schemes for detecting We simulate different C-Worm attacks by varying the values wide-spreading worms. In addition, we also take into consid- of m and σ. The detection sampling window Ws is set to eration destination distribution based detection schemes and 5 minutes and the detection sliding window Wd is set to evaluate their performance against the C-Worm. be incremental from 80 min to 800 min. The incremental 10

TABLE 1 Evaluation Metrics

Notation Definition Infection Ratio (IR) Ratio of worm-infection over time without the presence of detection/defense system Maximal Infection Ratio (MIR) Ratio of worm infection at the moment that worm is being detected Detection time (DT ) Time taken to successfully detect a wide-spreading worm from its birth

selection of Ws from a comparatively small window to a large SPEC(W)) and the other has knowledge of C-Worm attacks window can adaptively reflect the worm scan traffic dynamics through an off-line training process (denoted by SPEC). For caused by the C-Worm propagation at various speeds. We the off-line training, we use 1000 worm attacks that include choose the setting of the detection sampling window to be both the C-Worm (800 C-Worm attacks) and PRS worms short enough in order to provide enough sampling accuracy (200 PRS worm attacks). For fairness, we set the detection as prescribed by Nyquist’s sampling theory. Also, we choose parameters for our SPEC scheme and the other three detection the detection sliding window to be long enough to capture schemes, so that all detection schemes achieve a similar false adequate information for spectrum-based analysis [63]. positive rate (PF ) below 1%. In practice, since detection systems analyze port scan traffic In the following subsections, we first evaluate the perfor- blended with the non-worm scan traffic, we replay the real- mance of our spectrum-based detection scheme in the context world traces as non-worm scan traffic (background noise to of detecting C-Worm attacks. We then evaluate the perfor- attack traffic) in our simulations. In particular, we used the mance of our spectrum-based detection scheme in the context ISC real-world trace (Shield logs dataset) from 01/01/2005 of detecting traditional PRS worms, followed by performance to 01/15/2005. Note that SANs ISC, maintained by the SANs comparison between traffic volume based detection and traffic Institute, have gained popularity among the Internet security distribution based detection. community in recent years. ISC collects firewall and Intrusion 5.2.1 Detection Performance for C-Worm Attacks detection system logs, which indicate port-scan trends from approximately 2000 organizations that monitor up to 1 million Table 2 shows the detection results of different detection IP addresses. We choose the scan traffic logs for port 8080 as schemes against the C-Worm. The results have been averaged an example for profiling the non-worm scan traffic. over 500 C-Worm attacks. From this table, we can observe In order to provide the creditability of such data, we did the that existing detection schemes are not able to effectively following effort before using the data in our experiments. First, detect the C-Worm and their detection rate (PD) values are we had the 15 days traces from 01/01/2005 to 01/15/2005 significantly lower in comparison with our spectrum-based provided by SANs ISC. We checked with the SANs website detection schemes (SPEC and SPEC(W)). For example, SPEC and found that there were no worm attack incidents within achieves the detection rate of 99%, which is at least 3-4 those 15 days. Second, we obtained the statistical profile of times more accurate than detection schemes such as VAR and traffic traces, including the mean value and standard deviation MEAN that achieve detection rate values of only 48% and of traffic rates. Based on the statistical profile, we set a 14%, respectively. threshold which is the summary of mean value and four times Our SPEC and SPEC(W) detection schemes also achieve that of the standard derivation, and filtered out some data good detection time (DT ) performance in addition to the high which had unusual large values. Third, we conducted our detection rate values indicated above. In contrast, the detection evaluation 15 times based on data randomly combined with time of existing detection schemes have relatively larger different dates. The results we showed in the paper are the values. As a consequence of the detection time values, we can mean values of experimental results from different rounds. see that the C-Worm propagation is effectively contained by SPEC and SPEC(W), as demonstrated by the lower values of maximal infection ratio (MIR) for the SPEC and SPEC(W). 5.2 Performance of Detection Schemes Since the detection rate values for the existing detection We evaluate our proposed spectrum-based detection scheme by schemes are relatively small, obtaining low values of MIR comparing its performance with three existing representative for those schemes are not as significant as those for SPEC traffic volume-based detection schemes. The first scheme is and SPEC(W). Furthermore, we can notice that the detection the volume mean-based (MEAN) detection scheme which uses performance of the SPEC(W) is worse than the SPEC. This is mean of scan traffic to detect worm propagation [20]; the because the SPEC(W) lacks off-line training knowledge for the second scheme is the trend-based (TREND) detection scheme C-Worm scan traffic. Nonetheless, the SPEC(W) still performs which uses the increasing trend of scan traffic to detect worm much better than existing detection schemes. propagation [19]; and the third scheme is the victim number variance based (VAR) detection scheme which uses the vari- 5.2.2 Detection Performance for Traditional PRS Worms ance of the scan traffic to detect worm propagation [21]. We evaluate the detection performance of different detection We define our spectrum-based detection scheme as SPEC. schemes for traditional PRS worm attacks. The detection per- We evaluate two types of SPEC: one has no knowledge of formance results have been averaged over 500 PRS worm at- any C-Worm attacks or C-Worm scan traffic (denoted by tacks. We observe that both our SPEC and SPEC(W) schemes 11

TABLE 2 Detection results for the C-Worm Schemes VAR TREND MEAN SPEC(W) SPEC Detection Rate (DR) 48% 0% 14% 96.4% 99.3% Maximal Infection Ratio (MIR) 14.4% 100% 7.5% 4.4% 2.8% Detection Time (DT) in minutes 2367 ∞ 1838 1707 1460

Maximal Infection Ratio of of PRS Worm based on the fact that traditional PRS worm scanning traffic 0.1 shows a constantly rapid increase. Thus, SFM values are 0.09 relatively small due to PSD concentration at the low frequency 0.08 0.07 bands in the case of the traditional PRS worm scanning. 0.06 0.05 MIR 0.04 6 FINAL REMARKS 0.03 In this paper, we studied a new class of smart-worm called C- 0.02 0.01 Worm, which has the capability to camouflage its propagation 0 and further avoid the detection. Our investigation showed that, 20 30 40 50 60 70 Scan Rate although the C-Worm successfully camouflages its propagation VAR TREND MEAN SPEC(W) in the time domain, its camouflaging nature inevitably mani- fests as a distinct pattern in the frequency domain. Based on Fig. 7. Maximal Infection Ratio of detection schemes observation, we developed a novel spectrum-based detection against PRS worm scheme to detect the C-Worm. Our evaluation data showed that our scheme achieved superior detection performance against Detection Time of PRS Worm the C-Worm in comparison with existing representative de-

2900 tection schemes. This paper lays the foundation for ongoing studies of “smart” worms that intelligently adapt their propa- 2500 gation patterns to reduce the effectiveness of countermeasures

2100 DT

1700 ACKNOWLEDGMENTS This work was supported in part by the National Science Foun- 1300 dation under grants ACI-0329155, CCF-0546668 0808419, 900 0324988, 0721571, and 0329181. Any opinions, findings, con- 20 30 40 50 60 70 Scan Rate clusions, and/or recommendations expressed in this material, VAR TREND MEAN SPEC(W) either expressed or implied, are those of the authors and do

not necessarily reflect the views of the sponsors listed above. Fig. 8. Detection Time of detection schemes against PRS The authors would like to acknowledge Ms. Larisa Archer for worm her dedicated help to improve the paper.

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[58] M. Christodorescu and S. Jha, “Testing malware detectors,” in (identified by duplicate hits). We model the number of infected Proceedings of the 2004 ACM SIGSOFT International Symposium on computers indicated by watermarks during the scanning pro- Software Testing and Analysis (ISSTA), Boston, MA, July 2004. cess as binomial process. Then H(t) scanning tries and each [59] X. Wang, W. Yu, X. Fu, D. Xuan, and W. Zhao, “iloc: An invisible local- ¯ ization attack to internet threat monitoring systems,” in Proceedings of M(t) scanning try has successful probability T to be indicated the 27th IEEE International Conference on Computer Communications by watermarks, where M¯ (t) is the estimated M(t) at time (INFOCOM) Mini-conference, Phoenix, AZ, April 2008. · M¯ (t) [60] J. Bethencourt, J. Frankin, and M. Vernon, “Mapping internet sensors t. Thus K(t) = H(t) T . With the above equation, we · with probe response attacks,” in Proceedings of the 14-th USNIX have M¯ (t) = T K(t) . Note that the above watermarking-based Security Symposium, Baltimore, MD, July-August 2005. H(t) [61] Y. Shinoda, K. Ikai, and M. Itoh, “Vulnerabilities of passive internet method might lack the accuracy for the worm propagator to threat monitors,” in Proceedings of the 14-th USNIX Security Sympo- track the accurate status of worm propagation. Nevertheless, sium, Baltimore, MD, July-August 2005. this approach can provide a rough estimation for the worm [62] S. Soundararajan and D. L. Wang, “A schema-based model for phonemic restoration,” Tech. Report, OSU-CISRC-1/04-TR03, Department of propagation status and can be integrated with other strategies Computer Science and Engineering, The Ohio State University, January to improve the accuracy of tracking worm propagation status. 2004. [63] N. S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall, 1984. [64] R. E. Yantorno, K. R. Krishnamachari, J. M. Lovekin, D. S. Benincasa, Appendix B: SFM of the C-Worm and S. J. Wenndt, “The spectral autocorrelation peak valley ratio (sapvr) - a usable speech measure employed as a co-channel detection system,” We present a formal analysis of SFM for the C-Worm as in Proceedings of IEEE International Workshop on Intelligent Signal follows: Let the observation Z1 be given by Z1 = X1 + Y1, Processing (WISP), Budapest, Hungary, May 2001. where X is the random variable representing the C-Worm [65] S. Theodoridis and K. Koutroumbas, Pattern Recognition, Second 1 Edition, Elsevier Science, 2003. scanning traffic (e.g., volume, destination counter) in one sampling window and Y1 is the random variable representing the background scanning traffic (e.g., volume, source counter) APPENDIX in one sampling window. We define X = X1 − E[X1], where Appendix A: Estimation of M(t) E[X1] is the mean value of X1 and Y = Y − E[Y1]. Thus, We now discuss how the C-Worm can estimate M(t) (number we have Z = X + Y , where X and Y are independent zero- of worm instances or infected computers) during run-time (i.e, mean random variables. We assume that the total frequency is − ≤ ≤ during C-Worm propagation). While there are many possible within the W f W range. ways to estimate M(t), we only discuss one approach the C- Based on the observations in Section 4.1, we approximately Worm could use based on the limited network and computing represent Y1(t) by white Gaussian noise, which is widely resources available during its propagation. There are other used in modeling wide-band noise in communication systems. approaches, such as incorporating the Peer-to-Peer techniques Thus, Y can be approximately represented by a Gaussian white to disseminate information through secured IRC channels [49], noise with zero mean and a variance of σ. Thus, in the total ∈ − ≤ ≤ [50]. Actually, a worm could take advantage of the knowledge frequency band limited within the range [ W f W ], that an infection attempt was a new hit (reaching a previously the PSD of Y is SY (f) = σ shows that Y has a constant uninfected vulnerable computer) and duplicate hit (reaching a power spectrum and each frequency has the average power previously infected vulnerable computer). value σ. To estimate M(t), we use an approach that is similar in Considering the fact that all C-Worm instances adopt a nature to the approach used by the “self-stopping” worms similar control mechanism strategy to manipulate the overall that do not require a global overlay control network [16] for scanning traffic volume, we explained how a distinct trend realizing their behavior in practice. We call our approach to can be noticed in the frequency domain, i.e., the trend being estimate M(t) as the Distributed Co-ordination method. In this a concentration in the scanning traffic frequency of the C- method, there is no centralized co-ordination between the C- Worm within a narrow range of frequencies. Assume that C- Worm instances to obtain feedback information about the value Worm scanning traffic counter is referred as m (denoted by of M(t). The distributed co-ordination requires each C-Worm fk, where k = 1, . . . , m and m < W ) in the total (narrow- infected computer to be marked with a watermark indicating band) frequency range. Without loss∑ of generality, X(t) is ap- 2m that the C-Worm infection code has already been installed proximately represented by X(t) = k=1 ak cos(2πfkt + θ), on the scanned host as with “Code-Red” worms. Thus, when where θ is uniformly distributed in the interval [0, 2π]) and − an already infected computer (say for example, host A) scans ak is uniformly distributed in the interval [ l, l]. Based on another infected computer (say for example, computer B), then the relationship among autocorrelation, mean, and autoconva- computer A will detect the watermark and know that computer riance, we have RX (τ) = CX (t1, t2) + E[X(t1)]E[X(t2)], − B has already been infected. By scanning vulnerable computers where τ = t2 t1, E[X(t1)] = E[X(t2)] = 0, and − − and obtaining the watermarks information during the scanning, CX (t1, t2) = E[(X(t1) EX (t1))(X(t2) EX (t2))] is the auto-covariance of a random process X(t). Thus, it a C-Worm instance can estimate M(t) at run-time as follows. ∑ 2 m ak Let us assume that T , which refers to the whole Internet is easy to verify that RX (τ) = k=1[ 2 cos(2πfkτ)]. IP address space, is the C-Worm scanning target space. In Thus,∑ the PSD of X(t) can be represented by SX (f) = k=m 2 2 ak − ak this scanning target space, assume we have the case where k=1 [ 4 δ(f fk) + 4 δ(f + fk)]. As X(t) and Y (t) H(t) number of scans in time t resulted in K(t) number are independent∑ random process (SY (f) = σ), we have k=m 2 2 ak − ak of infected computers indicated by presence of watermarks SZ (f) = k=1 [ 4 δ(f fk) + 4 δ(f + fk)] + σ. 14

a 2δ(f ) k k ≫ Xun Wang Dr. Xun Wang received the BS and Define 4σ ∑= R( 1), SZ (f) can be rewritten by S (f) = σ{ k=m [Rδ(f − f ) + Rδ(f + f )] + 1} MS in computer engineering from The East Z k=1 k k China Normal University, Shanghai, China, in and the SFM of Z(t) can be represented by SZ (f) = 1999 and 2002, and the PhD degree in Com- − 1 m σ2W 2mRσ2m 2W R W puter Science and Engineering from The Ohio 1 − = m (R−1)+1 . We can rewrite SZ (f) 2W [2mσR+σ(2W 2m)] W State University in 2007. He has been working t in above formula as the function of R as F (x) = x , for Cisco Systems, Inc. since 2007. His research t(x−1)+1 interests include network security, overlay net- t−1 − − m ′ tx (x 1)(t 1) works, and wireless sensor networks. where x = R, t = W < 1. As F (x) = [t(x−1)+1]2 < 0, the function SZ (f) is a decreasing function of x (= R) and it 2 ak 4δ(f) ≫ is observable that R1 = σ + 1 1 (due to the Dirac’s δ function property), SZ (f) → 0. Thus, the SFM of C-Worm is close to 0. Prasad Calyam Dr. Prasad Calyam received the BS degree in Electrical and Electronics Appendix C: SFM of PRS Worm Engineering from Bangalore University, India, In the following, we conduct analysis on the spectrum-based and the MS and Ph.D. degrees in Electrical and Computer Engineering from The Ohio State detection scheme to detection PRS worms. Let the input for University, in 1999, 2002, and 2007 respec- detection data Z1 in one sample window be given by Z1 = tively. He is currently a Senior Systems Devel- X + Y , where X is the random variable representing the oper/Engineer at the Ohio Supercomputer Cen- 1 1 1 ter, The Ohio State University. His current re- attack traffic (e.g., scan volume) for PRS worms and Y1 is search interests include multimedia networking, the random variable representing the background traffic (e.g., cyber security, cyber infrastructure systems, and network management. scan volume). We define X = X1 − E[X1], where E[X1] is the mean value of X1. We also define Y = Y1 −E[Y1], where E[Y1] is the mean value of Y1. Thus, we have Z = X + Y , where X and Y are independent zero-mean random variables. We assume the overall frequency is within −W ≤ F ≤ W Dong Xuan Dr. Dong Xuan received the BS range. Similarly, we approximately represent Y1(t) by white and MS degrees in electronic engineering from Shanghai Jiao Tong University (SJTU), China, in Gaussian noise. Thus, Y can be approximately represented by 1990 and 1993, and the PhD degree in computer a white noise with zero mean and a standard derivation of σ. engineering from Texas A&M University in 2001. Thus, in the frequency band limited within [−W ≤ F ≤ W ], Currently, he is an associate professor in the De- partment of Computer Science and Engineering, the PSD of Y is SY (F ) = σ, which shows that frequency The Ohio State University. He was on the faculty Y ∈ [−W, W ] has a constant power spectrum. Based on the of Electronic Engineering at SJTU from 1993 to 1997. In 1997, he worked as a visiting research SFM definition, it is easy to observe that SFM of Y is close scholar in the Department of Computer Science, to 1. City University of Hong Kong. From 1998 to 2001, he was a research According to PRS worm propagation dynamics in For- assistant/associate in Real-Time Systems Group of the Department mula (1), the result is M(t) ≃ eβ·N·t at the early stage of Computer Science, Texas A&M University. He is a recipient of the · · ≪ US National Science Foundation (NSF) CAREER award. His research of worm propagation. As β N t 1 at the early stage, interests include distributed computing, computer networks and cyber M(t) ≃ 1+β ·N ·t. Follow the similar procedure, the PSD of space security. − · · 1 X = f(t) E(f(t)) can be represented by SX (F ) = β N F 2 , ∈ − · · 1 where F [ W, W ]. Thus, the PSD of Z is β N F 2 + σ. According to Formula (7), we can observe that the value of SFM for PRS worms is close to 0. It indicates that spectrum- Wei Zhao Dr. Wei Zhao is currently the Rector based scheme can detect the PRS worm propagation at the of the University of Macau. Before joining the early stage as well. University of Macau, he served as the Dean of the School of Science at Rensselaer Polytechnic Institute. Between 2005 and 2006, he served as the director for the Division of Computer and Network Systems in the US National Science Foundation when he was on leave from Texas A&M University, where he served as Senior As- Wei Yu Dr. Wei Yu is an assistant professor sociate Vice President for Research and Profes- in the Department of Computer and Informa- sor of Computer Science. He was the founding tion Sciences, Towson University, Towson, MD director of the Texas A&M Center for Information Security and Assur- 21252. Before that, He worked for Cisco Sys- ance, which has been recognized as a Center of Academic Excellence tems Inc. for almost nine years. He received in Information Assurance Education by the National Security Agency. the BS degree in Electrical Engineering from Dr. Zhao completed his undergraduate program in physics at Shaanxi Nanjing University of Technology in 1992, the Normal University, Xian, China, in 1977. He received the MS and PhD MS degree in Electrical Engineering from Tongji degrees in Computer and Information Sciences at the University of University in 1995, and the PhD degree in com- Massachusetts at Amherst in 1983 and 1986, respectively. Since then, puter engineering from Texas A&M University in he has served as a faculty member at Amherst College, the University 2008. His research interests include cyber space of Adelaide, and Texas A&M University. As an elected IEEE fellow, Wei security, computer network, and distributed systems. Zhao has made significant contributions in distributed computing, real- time systems, computer networks, and cyber space security.