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With a simple network model, the impact of the following commonly used security measures can be evaluated mathematically against the spread of malware:. A network is a set of nodes that may be interconnected. The examination of a large network mainly provides statistical properties with which its behavior can be better understood and predicted. There are different types of networks. The behavior of computer networks e. The Internet is designed to be robust against a random failure of nodes. However, the Internet is vulnerable if nodes are attacked in descending order of their number of links to other nodes.

E-mail, peer-to-peer P2P computing and web browsing form a social network. Malware can spread via both the Internet and in-person social networks. An Internet worm can infect an online server or workstation without any user interaction, or a user can unintentionally infect a computer with malware by downloading and using an infected file. Using the results of previous research, 4 , 5 three simple network models are compared.

The three network models are:. The SIS model divides the population into two parts: infected i and the rest s , which are susceptible to this infection. The SIS model indicates that, at first, the infection grows slowly because there are few infected computers that can transmit the infection. In the final phase, the infection slowly reaches the maximum because the probability decreases that an infected node can contact an uninfected node.

Therefore, infection growth is proportional to the product. The number of infected computers is reduced by the detection and removal of malware. This decrease is proportional to the number of infected computers i. The following formulas describe the SIS model. The solution of formula 1 is the logistic function 6 or S-curve see figure 3.

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When the product R0. However, if R 0. The battle between cybercriminals and security vendors is at full throttle. Recent studies show that even with up-to-date malware signatures, the detection rates of AV software over time have dropped to approximately 40 percent of new malware. Because all AV products show about the same time lag behind malware, malware detection is only marginally improved by deploying multiple virus scanners simultaneously.

Math on Malware

Also, more virus scanners will produce more potential false positives. Although modern AV software can sometimes detect malware even when its signatures are unknown, the added value of these heuristic techniques is limited. AV software cannot produce many false positives because, after a short time, the average user will begin to ignore these warnings. Moreover, both closed-source software and malware are often wrapped in encrypted zip files, making malware detection much more difficult.

There are just too many criminals active on the Internet underground, in China, Latin America, right here in Russia. We have to work all day and all night just to keep up. The rapid production and implementation of patches is an absolute necessity, but patches also indicate that software development is not mature.

The quality of software can be expressed as the number of errors per 10, lines of code.


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Due to the increasing computer capacity, more complex applications with tens of millions of lines of code are developed and used. At the same time, as products must go to market faster, there is less time to test them. Even after many patches, there remain enough vulnerabilities in software for malware exploitation. Sometimes, software companies have such a backlog on the development of patches that so-called zero-day exploits can circulate for months before the vulnerability is patched.

Math on Malware

For instance, using a patch that repairs a buffer overflow, it takes about 30 seconds to generate a malicious input file that triggers the buffer overflow in unpatched computers. Worse still, some organizations have a delay in the implementation of patches. Their computers can be infected by malware misusing vulnerabilities for which patches have been issued long ago. Therefore, good change management procedures have a positive effect on security.

The malware problem continues to grow rapidly. For instance, Symantec created 2,, new malicious code signatures in This represents 51 percent of all malicious code signatures ever created by Symantec. Due to the large amount of malware in circulation, a computer can already be infected with various exploits before the infection is noticed. If the disinfection does not remove all malware, it lowers the value of g.

Incident management procedures should, therefore, rely on a proven incident response plan. This improves the effectiveness of a disinfection because the need to reinvent in stressful conditions becomes unnecessary. In this way, more computers are infected i max and the infection lasts longer.

Yet, it can also be advantageous for cybercriminals to let infections grow slowly and unnoticed because fast-growing malware infections appear on the radar of AV software vendors. By varying the contamination rate not every malware contact with a susceptible computer leads to an infection , three scenarios have been defined and are discussed in the following section see figure 3.

Large-scale infections do appear on the radar of AV software vendors, but that does not mean that the malware can be rapidly eliminated. The experience with the Conficker worm has made that clear. To avoid detection of the malware, it is essential that the infection not be spread widely so that the abused vulnerabilities are not picked up by the system users, other cybercriminals, AV software vendors or software manufacturers.

Network theory predicts that, when the nodes with the most links are disabled, the function of the network will deteriorate rapidly. Thus, the proliferation of spam and malware is best reduced by engaging the source. While malware sources are difficult to control, it remains possible to periodically reinstall clean software on computers, which replaces infected computers with uninfected ones. The security improvement of replacing all the software can be determined by adjusting the SIS model. However, such labor-intensive operations are efficient only when automated. A lesser impact of malware means fewer economic damages and more profit.

It is a fact that employees cause many incidents. Personal computers of employees at home are often linked directly to business computers by e-mail and Universal Serial Bus USB drives.

Explained! Computer Viruses

For example, if employees edit business documents on infected personal computers PCs at home, the information being edited could be disclosed. The population of computer users can be divided into two parts: one with sufficient security knowledge and the other with little security knowledge. Because the SIS model becomes complex in heterogeneous populations, the quantitative analysis is not complete.

On average, a computer user knows little about security. However, when inexperienced computer users suffer more frequently and longer from malware infections, this also affects the computers of security experts and enterprises using the same software. This is because malware can be exchanged between users. When the security knowledge and awareness of inexperienced users is improved, the impact of malware for the entire population significantly decreases, especially when combined with the reinstallation of clean software, as mentioned previously.

This does not mean that everyone has to become a security expert. With a periodic security lecture for personnel that states what should and should not be done, including how to secure home PCs, employees quickly become wise about using the Internet.


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For example, an important rule of thumb is not to start using new software immediately. If, four weeks after the download, the updated AV software still does not find malware in the quarantined downloads, it is far more likely that the downloads are actually free from malware. Additionally, some enterprises impose rules for working at home and provide employees with business software and security software for free.

Enterprises that select freeware or open-source software as standard products avoid the extra license costs for private usage. Experts can assess the effectiveness and efficiency of the implemented security measures. If the security is properly designed and implemented, inexperienced users cannot easily infect their PCs. If employees know why their access rights are limited and why business software is white-listed, and if the lessons learned from incidents are widely communicated, support is created and security awareness improves. Even so, the malware risk remains at maximum for security experts and enterprises using market-leading software.

All software contains vulnerabilities, and computers that use the same software share the same vulnerabilities. For malware, all computers using the same software form a separate population. While software compartments may be linked by common code for hardware drivers and network functions, in practice, it is unlikely that Windows malware can infect a Mac. This is because there is little shared source code, which has often been rigorously reviewed to eliminate vulnerabilities. The larger the population, the more attractive it is for cybercriminals to develop exploits that misuse the vulnerabilities in that population.

To maximize their profits, cybercriminals are targeting their malware on the generally used software with the largest market share. Therefore, it is obvious that the economics of malware can be reduced by creating more software diversity. To enable this, enterprises must abandon the idea that the interchangeability of information depends on using the same software. Instead, enterprises must dare to rely on data standards to break vendor lock-in. The use of open standards also ensures that data in electronic archives can still be processed in the future.

The SIS model can predict the effect on the spread of malware if the software population is made more diverse. Suppose that q is the part of the population that becomes immune to the malware targeting the market-leading software by migrating to alternative software. If the value of q does not affect the software monopoly, the vast majority of malware continues to target the market-leading software used by the rest of the population 1 - q. This creates more reaction time for the software industry to respond to new malware. The number of infections in formula 2 is also reduced:.

Therefore, the number of infections in the steady state will be reduced by q , the same as the reduction in susceptible computers. If q is greater than or equal to the i max of a malware variant, then this malware dies out.

I had this same annoying problem with Chrome. It was in my Windows 8 desktop, but not in my Windows 7 laptop. I tried all Solutios with no result. Then I downloaded and run Microsoft Safety Scanner in both computers.