Why Bruce Schneier is wrong times infinity

commentary On his Web site, Bruce Schneier describes himself as "an internationally renowned security technologist and author". If Schneier is indeed the "guru" certain parts of the media portrays him to be, when why when interviewed by ZDNet.com.au's sister site Builder AU, did he reveal himself to be so clueless?

In order to watch video content you need to enable javascript and install Flash player version 8 or above.

In the video clip above, Builder AU editor Chris Duckett asks Schneier "why security cost justifications are complete bullshit?" While Duckett isn't known for pulling punches, he's actually quoting Schneier here.

At first, Schneier's explanation of ROI seems sensible, he talks about "measuring the cost of an attack" and "working out the probability of an attack". He then rightfully points out that "it's how all insurance companies build their business models."

But then things get kooky. "This fails when you have very, very rare and very, very expensive events," explained Schneier. "If you have taken any infinity theory — which I don't recommend — you are effectively multiplying zero by infinity."

Now perhaps I don't understand the complexities of Schneier's maths, but if a security threat has a zero probability of occurring, it seems to me that it isn't a security threat. Further, why are you multiplying by infinity? What security attack could possibly have infinite cost? Businesses have a finite value, just as there is a finite amount of money in the world.

Schneier makes a valid point by saying that calculating probabilities and costs of an ROI model is difficult — but it's really nothing a little maths can't solve. Speaking of maths, Schneier goes on to argue that small changes in probability can "completely perturb" IT budgets. Sounds scary.

"If the chance of you being attacked are say one in one million, and I change that to one in two million, who cares? I've suddenly halved the amount of money you should spend... I can completely perturb your budget," he says.

OK, so let's do some maths. Let's take Schneier's example and apply it to a small IT company worth AU$8 million. Let's take the worst case scenario and say that our theoretical one-in-one million attack will cost the complete value of the company.

In this case, the IT company should spend AU$8 dollars defending against the attack — the probability multiplied by the cost. If this probability moves to one-in-two million, then the company should spend AU$4 defending against the attack. As the probabilities get smaller — and harder to calculate — the cost variation become less significant.

If fact the truth is the opposite of what Schneier says — ROI is a problem when attacks have a very high probability of happening, not a very low probability.

To give a practical example — say you buy a shiny new Porsche. It's in all likelihood easier to insure the car against being struck by lightning than to insure it against theft. This is because the cost/probability ratios in insurance are much better for rare events. That is, insuring against rare events costs less.

However, this brings us to another problem with Schneier's argument. If an attack has a high probability of occurring, then it is easy to quantify because such attacks are common and lots of data exists to extrapolate their probability.

Not only that, but you can also calculate the uncertainties in your value, giving you an idea of how accurate any probability is. In probability analysis, values without measured uncertainties are considered meaningless, as any actuary will tell you.

So you can construct meaningful ROI models, because rare events are cheap and common events can be predicted.

Last time I checked, insurance was a multi-billion dollar industry, and remains very lucrative. It is built around the very laws of probability that Schneier disputes.

Disclaimer: Unlike Schneier, I am not an "an internationally renowned security technologist", just a dumb mug journalist. If you want to defend him, please do so in talkback below.

Advertisement

Talkback 11 comments

    Flawed logic Anonymous -- 11/04/08

    Alex, there is probably a reason why you're not internationally renowned. Bruce is indeed internationally renowned, has released several textbooks on security, innumerable papers and has been the keynote speaker at virtually every security conference worldwide at some point in time.

    You seem to be extrapolating beyond what Bruce has said and then attack this point you've assumed he meant. Please stop with the straw-man argument, it makes you look either exceedingly stupid, or like you've got some hidden agenda. Which one is it?

    As for Bruce's comment about infinity and zero, if you had any background in mathematics, you would realise that he was saying that as the probability approaches zero, the cost approaches infinity. Your argument of 'no threat has zero probability' and 'it will never have infinite cost' is the limit case. The point Bruce was making was that with the risk-cost set up in this manner, the closer you get to the limit case the less accurate predictions become at a given precision.

    As for your argument on insurance, when Bruce talks about cost, he doesn't talk about insurance costs, he is talking about the cost to a business should a security breach occur. The insurance cost is the opposite, so your arguments are actually pomoting Bruce's argument to anyone who's done basic mathematics in highschool.

    Please do some research into the field before attacking one of the greatest minds in it. You attacking Bruce would be like me attacking Stephen Hawking about his ideas on astrophysics. Drop the hidden agenda and just report on the news, please.

    Bruce, is that you? Anonymous -- 11/04/08 (in reply to #320099538)

    come on. if that is you please say

    LOL SECURITY BRUCE SCHNEIER -- 11/04/08 (in reply to #320099558)

    IT'S ME ALRIGHT!
    LOL BRB INVENTING BLOWFISH

    Ignorant logic Anonymous -- 11/04/08

    I'm not internationally renowned either, but my risk management lecturer at university is, so let me explain why your maths is stupid and Bruce is kind of right, that ROI is indeed bullshit to a point.

    Risk is a function of likelihood and magnitude. The point of properly managing risk is NOT to spend money on everything, it's to analyse all the possible risks and determine which should be 'treated' and which should be ignored due to lack of resources or lack of potential return. So you don't spend that $8 you mentioned, you ignore the risk altogether for now, but make sure you review it at a later date to ensure it's not suddenly worth throwing a lot of resources at.

    So generally you'll ignore risks that are low likelihood and low magnitude (of consequence). You then have to be a bit more circumspect about low likelihood, high magnitude events. A September 11 style event is extremely uncommon, but if a plane flies into your building will your business survive? A couple thousand businesses didnt that day, but the big ones who had planned for a total disaster did survive, and many were fully operational within 48 hours.

    ROI can be a useful method for making such analysis, but only up to a point. It also won't help you assess risks that are of a more social nature, it's only really useful from an actuarial (insurer) perspective. In the end there are a number of different methods that can be used, and ROI should only be one of the tools available, not the holy grail.

    Apples and oranges Mike -- 11/04/08 (in reply to #320099552)

    You are right in that the business' insurance cost will drop in this regard, however I believe Bruce was talking about cost TO the insurer. Should a very very rare event occur that is very very very expensive then it's much harder to find a price to put on insuring against such a thing. ie. The closer an event is to the limit case, the harder it is to extrapolate data from that ratio. The data loses precision. I don't believe that Bruce was saying that every rare event will be very expensive to a business, but that very rare AND very expensive events are hard for insurance companies to work with.

    He also goes on to say that what seems like a small difference in probability can mean a huge difference in cost of insurance in the ROI model and from what I understand of the point he was making, this huge difference in cost is what makes ROI so hard to use for very rare events. ie. You get the probability slightly wrong (0.00005% out) and you've doubled the cost to insure. The closer you get to this limit case, the closer it gets to a meaningless number (0 times infinity)

    Despite all this, I question the journalistic integrity of zdnet when you have to resort to personal attacks when you disagree with someone. You even tagged the article with 'idiot'. If you didn't understand his point, you probably could have asked him to explain it better, rather than attempting to discredit him in his field of expertise.

    I don't quite see how some no-name journalist who disagrees with a respected contributor to the security field is newsworthy. Turns out it's only as newsworthy as the journalist in question thinks I guess.

    High school calculus Navin -- 11/04/08 (in reply to #320099552)

    Alex,

    Bruce is pointing out that when you have a very small numbers (the probability of the event) being multiplied by very large numbers (the dollars lost or the expense of the event), and you are actually working with probability distributions rather than hard numbers per se, you are looking at limits of the type zero multiplied by infinity. Such limits can be zero or a constant or infinity - depending on whether the number going to zero is doing this faster than the number going to infinity. My understanding of his point is that the error in estimating probabilities and costs can cause for the resulting calculation to be garbage. The insurance industry relies on actuaries to develop very sophisticated models to figure out their pricing ... something that the security community does not do yet.

    Rather than turning up such a banal attack on Bruce it would have been so much more interesting to think through the alternatives to the straight ROI calculation in business cases - perhaps the means by which security related metrics might help quantify risk in a manner that is accurate enough and comprehensible by management.

    Please lift your game - articles of this quality make me want to not advertise with you ...

    Sneering tone Anonymous -- 13/04/08

    Alex, I'm not going to take issue with your logic. I'm more concerned about the sneering tone of this column.

    Attacking the man rather the argument's also pretty poor form. In fact the whole article reads more like a web forum or usenet flame.

    You can do better than that and I hope you do in future articles.

    Alex Serpo's Bio for Comparision Anonymous -- 13/04/08

    Serpo joined last last year, Prior to landing the job at ZDNet, Serpo was freelancing at publications including The Australian Financial Review and Fast Thinking magazine and recently graduated from the University of NSW with a background in science, during which time he also studied synthetic chemistry and international politics.

    In particular, Serpo is interested in new technologies such as "quantum computers, synchrotrons, carbon nanotubes, fusion reactors and man-made genomes", to name a few.

    Whatever you think, this article is plain rude. I assume the tag of idiot is for the reporter and not the subject?

    Bruce is right, Alex is dead wrong Keong (not internationally renowned either) Lim -- 14/04/08

    Alex,

    Bruce Scheier is absolutely right in what he said. If you take an infinitesimal number (i.e. extremely close to zero) and multiply it by an extremely large number, then with tiny changes to the small number you can make the product of the two numbers be equal to any other number you choose.

    The problem is that those tiny, tiny changes are so easy to make and so tiny that no-one will notice and call you out for doing it. It's creative accounting to the max! Hence, it's bullshit!

    Why don't you try it out for yourself?

    You don't need to know infinity theory, but it does help if you've done some numerical analysis and know how to estimate the error range of your calculations. The error range in this case is nearly infinite, meaning that the true value is somewhere in between zero and infinity (not very exact, is it? Allows for *very* creative accounting!).

    FYI, if you look up some things on Wikipedia, you get the sense of how mathematically rigorous the analysis of these numbers are:

    http://en.wikipedia.org/wiki/Infinitesimal

    http://en.wikipedia.org/wiki/Infinity

    Alex, please apologise to Bruce. I will also be asking ZDNet to pull this article offline.

    Thanks,
    Keong

    Apology Anonymous -- 14/04/08

    Hi Everyone,

    Just to clarify, I mean no disrespect to Bruce, and yes, the "idiot" label does apply to me, in this instance the "dumb mug journalist." I removed the tag in case it caused offense. If I have caused Bruce offense, I apologise.

    There is no doubt "creative" accounting will make for problematic ROI models, and that could be a big problem. Bruce points out in another video that companies often don't accurately report data for fear of loss of reputation.

    However, I stand by the fact that you can make a statistically meaningful ROI model. My point here is that the mathematics isn't the problem. If the error is big, the model is invalid.

    Alex

    Better to read this other article instead Ignoring Alex Serpo -- 14/04/08

    http://www.zdnet.com.au/insight/software/soa/Making-the-security-ROI-model-work/0,139023769,339287987,00.htm

Add your opinion

Latest Videos

Sponsored content

Power Centre - Content from our premier sponsors

Blogs

  • Suzanne Tindal IT: Govt's cost-cutting bitch
    The government needs to stop looking at IT as a necessary evil or the place to remove costs when the Treasurer comes calling.
  • Array Can complaints on mobile content be cut?
    On 1 July this year the new Mobile Premium Services Code was introduced. It sounds like it's had a good impact, but is it enough?
  • Array NZ farmers: Bleating about broadband
    As we know, farmers are such bleaters. They bleat as much as the four-legged woolly things in their paddocks. If it's not the weather, it's the strength of the dollar! Nothing is ever right. Likewise with rural broadband.
  • More blogs »

Tags

Back to top

Featured