Sunday, June 14, 2009

understanding malware growth

(this is actually kind of old now, but real life has a way of interrupting this whole blogging thing)

alex eckelberry posted some graphs depicting the size and growth of the malware samples collected by andreas marx/ what most people will take away from it is that malware is growing at an incredible rate, and that's kind of depressing. there's more to the graphs than just that however, and not all of it is depressing - in fact it looks pretty good to me.

but to understand this i think i need to point out just how bad the forecast line of the graphs is. the line represents the expected value according to a particular model of malware growth. of course models and reality never match up absolutely perfectly, but the forecast suggests a fairly simplistic model and it appears that as time wears on it diverges more and more from reality. let's construct a model bit by bit based on some reasonable assumptions and see how close it matches reality.

let's first suppose that there are a constant number of malware creators with a fixed amount of resources (i don't mean money or computing power, i mean man-power resources - you can only do so much in a day, that sort of thing). let's further suppose that the amount of malware a malware creator can create with X number of resources is constant. what would that look like?

this depicts constant growth with a linear increase in population over time. this is not the final model, of course, but simply a starting point. one of the basic flaws with it is that it assumes that the population of malware creators themselves is constant. what if we instead suppose that the set of malware creators themselves were growing at a gradual but constant rate, what would that look like?

this depicts linear (rather than constant) growth in the malware because as the set of malware creators increases over time, so too should their malware output. it also shows a curve in the population vs time graph, although the curve isn't quite as pronounced as the one depicted in the forecast on the population graph on alex's blog and that's because in that case the forecast on the growth graph predicted non-linear growth.

how could we get non-linear growth? well another of our starting assumptions that we need modify is that the number of malware samples a malware creator can create with X number of resources is fixed. in reality malware creators come up with innovations and some of those innovations improve the efficiency of their malware creation efforts such that they can create more samples with the same effort as before. minor innovations in this area (minor in the sense that the efficiency improvement is small) probably happen all the time but major innovations are probably rare. furthermore, adoption of such innovations is not immediate, it takes time for the idea to spread amongst the malware creators. finally, such innovations may not apply to all sorts of malware so it may be that only part of the malware creator population ever adopts the new methods.

so now let's suppose one of those rare groundbreaking innovations happens - one malware creator comes up with a way to increase his malware creation rate by an order of magnitude. then he tells 2 friends (it may not actually work quite that way but one way or another the idea gets communicated to others) and they tell 2 friends, and so on until eventually they approach a peak number of creators using the new method and the rate at which creators switch from the old to new method slows to a trickle. what might that look like?

this depicts the same linear growth as before at the beginning (with the scale adjusted) followed by a period of rapid expansion as the new method reaches it's saturation point amongst the malware creators (most, but not all of them adopt the new method), and then it returns to mostly linear growth but with a stepped sort of appearance as individual adopters of the new method gradually continue to trickle in.

now, i don't know about you but to me this is starting to look rather familiar. it's not quite the same shape as the actual figures, mind you, that looks a lot less smooth than this, but it's a better approximation to the shape than the simple curve used in the forecast and it's based on an entirely reasonable set of forces that would affect malware growth.

as a final step, let's try to imagine why the real values don't follow such a smooth curve. so far we've been assuming that the population of malware creators only increases over time, but that's not entirely true, is it. there are any number of reasons why individuals might leave that population either temporarily (due to things like criminal prosecution, or collapse of particular infrastructure they were using), or permanently (due to things like retirement or death). if we were to take some of the malware creators in our model out of the picture temporarily at various points (and assume that the ones that ones that leave permanently will simply be replaced and so have the same effect as a temporary departure) what might that look like?

as you can imagine, because the malware creators using the new methods contribute so much more to the growth of malware than do the ones using old methods, when the population using the new methods drops slightly it has a much more noticeable effect on the graph than when the population using the old methods drop.

so how reasonable are these assumptions? are malware creators resources fixed? i've yet to see a way to increase the number of hours in a day so any individual malware creator is still limited in the number of man-hours he or she can devote to the task of malware creation.

can an innovation have a huge effect on the number of malware samples created? well just look at the massive number of variants that server-side polymorphism has lead to. you can basically think of those setups as variant factories and once they're constructed they really don't require any extra effort on the part of the malware creator in order to create more samples - it can be entirely automated and is then only limited by the number of victims who download samples.

would adoption of such an incredible innovation really be limited? again, look at server-side polymorphism, how well would that innovation apply to malware such as autorun worms? not that great actually. if you think about it you can probably come up with other examples of malware types and malware techniques that don't naturally go well together.

do people really leave the malware creator population either temporarily or permanently? well first of all people do actually die, and malware creators are among them so yes people do leave permanently - and again, with the example of server-side polymorphism, if the servers go down because for example the hosting ISP gets de-peered (as has famously happened a few times now) then yes the creators will temporarily be removed from the malware creator population until such time as they can set their operation back up somewhere else.

so what else can we take away from those graphs at alex's blog besides the fact that malware is increasing at an alarming rate? well, for my money it's that a big chunk of that alarming rate was due to an innovation (probably server-side polymorphism) that created a rapid expansion in the malware creation rate and that that rapid expansion seems to be over (in fact it looks like it came to an end nearly 2 years ago). that's not to say malware growth will begin to slow of course, but simply that the really scary part is behind us - the malware growth rate is still enormous, but it's not increasing at an exponential rate anymore. maybe a new innovation will come along and take us for another rough ride, maybe not, but as it stands right now catching back up to the bad guys (assuming you were of the school of thought that we needed to) looks a lot more feasible than it did before.