There's a delicious irony in some of the testimony on cybersecurity that the Senate Homeland Security and Governmental Affairs Committee will hear today (starting at 2:30 Eastern --- it's unclear from the hearing's page whether it will be live-streamed). Former National Security Agency general counsel Stewart Baker flubs a basic mathematical concept.



If Congress credits his testimony, is it really equipped to regulate the Internet in the name of "cybersecurity"?



Baker's written testimony (not yet posted) says, stirringly, "Our vulnerabilities, and their consequences, are growing at an exponential rate." He's stirring cake batter, though. Here's why.



Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value. It's nicely illustrated with rabbits. If in week one you have two rabbits, and in week two you have four, you can expect eight rabbits in week three and sixteen in week four. That's exponential growth. The number of rabbits each week dictates the number of rabbits the following week. By the end of the year, the earth will be covered in rabbits. (The Internet provides us an exponents calculator, you see. Try calculating 2^52.)



The vulnerabilities of computers, networks, and data may be growing. But such vulnerabilities are not a function of the number of transistors that can be placed on an integrated circuit. Baker is riffing on Moore's Law, which describes long-term exponential growth in computing power.



Instead, vulnerabilities will generally be a function of the number of implementations of information technology. A new protocol may open one or more vulnerabilities. A new piece of software may have one or more vulnerabilities. A new chip design may have one or more vulnerabilities. Interactions between various protocols and pieces of hardware and software may create vulnerabilities. And so on. At worst, in some fields of information technology, there might be something like cubic growth in vulnerabilities, but it's doubtful that such a trend could last.



Why? Because vulnerabilities are also regularly closing. Protocols get ironed out. Software bugs get patched. Bad chip designs get fixed.



There's another dimension along which vulnerabilities are also probably growing. This would be a function of the "quantity" of information technology out there. If there are 10,000 instances of a given piece of software in use out there with a vulnerability, that's 10,000 vulnerabilities. If there are 100,000 instances of it, that's 10 times more vulnerabilities---but that's still linear growth, not exponential growth. The number of vulnerabilities grows in direct proportion to the number of instances of the technology.



Ignore the downward pressure on vulnerabilities, though, and put growth in the number of vulnerabilities together with the growth in the propogation of vulnerabilities. Don't you have exponential growth? No. You still have linear growth. The growth in vulnerability from new implementations of information technology and new instances of that technology multiply. Across technologies, they sum. They don't act as exponents to one another.



Baker uses "vulnerability" and "threat" interchangeably, but careful thinkers about risk wouldn't do this, I don't think. Vulnerability is the existence of weakness. Threat is someone or something animated to exploit it (a "hazard" if that thing is inanimate). Vulnerabilities don't really matter, in fact, if there isn't anyone to exploit them. Do you worry about the number of hairs on your body being a source of pain? No, because nobody is going to come along and pluck them all. You need to have a threat vector, or vulnerability is just idle worry.



Now, threats can multiply quickly online. When exploits to some vulnerabilities are devised, their creators can propogate them quickly to others, such as "script kiddies" who will run such exploits everywhere they can. Hence, the significance of the "zero-day threat" and the importance of patching software promptly.



As to consequence, Baker cites examples of recent hacks on HBGary, RSA, Verisign, and DigiNotar, as well as weakness in industrial control systems. This says nothing about growth rates, much less how the number of hacks in the last year forms the basis for more in the next. If some hacks allow other hacks to be implemented, that, again, would be a multiplier, not an exponent. (Generally, these most worrisome hacks can't be executed by script kiddes, so they are not soaring in numerosity. You know what happens to consequential hacks that do soar in numerosity? They're foreclosed by patches.)



Vulnerability and threat analyses are inputs into determinations about the likelihood of bad things happening. The next step is to multiply that likelihood against consequence. The product is a sense of how important a given risk is. That's risk assessment.



But Baker isn't terribly interested in acute risk management. During his years as Assistant Secretary for Policy at the Department of Homeland Security, the agency didn't do the risk management work that would validate or invalidate the strip-search machine/intrusive pat-down policy (and it still hasn't, despite a court order). The bill he's testifying in support of wouldn't manage cybersecurity risks terribly well, either, for reasons I'll articulate in a forthcoming post.



Do your representatives in Congress get the math involved here? Do they know the difference between exponential growth and linear growth? Do they "get" risk management? Chances are they don't. They may even parrot the "statistic" that Baker is putting forth. How well equipped do you suppose a body like that is for telling you how to do your cybersecurity?