NSA fails at math

NSA’s recently released backgrounder The National Security Agency: Missions, Authorities, Oversight and Partnerships (9 August 2013) has a short but very interesting section on the “Scope and Scale of NSA Collection”:

According to figures published by a major tech provider, the Internet carries 1,826 Petabytes of information per day. In its foreign intelligence mission, NSA touches about 1.6% of that. However, of the 1.6% of the data, only 0.025% is actually selected for review. The net effect is that NSA analysts look at 0.00004% of the world’s traffic in conducting their mission—that’s less than one part in a million. Put another way, if a standard basketball court represented the global communications environment, NSA’s total collection would be represented by an area smaller than a dime on that basketball court.

Now, there is a lot that could be said about this paragraph, but the first thing that should be said is that its numbers don’t add up.

Let’s do the math. The world’s Internet traffic is estimated at 1,826 petabytes per day. Fair enough. NSA “touches” about 1.6% of that traffic, or about 29.2 petabytes per day. Call it 30 petabytes (i.e., 0.164%), which is probably the round number NSA was working with. Fine. Of those 30 petabytes, 0.025%, or 7.5 terabytes, is “selected for review” per day by NSA analysts. OK. The net effect, we’re then told, is that NSA analysts look at 0.00004% of the world’s traffic, or less than one part in a million. Um, no. The net effect, if the first numbers are accurate, is that NSA analysts look at 0.0004% of the world’s traffic—that’s three zeroes after the decimal point, not four, and the overall math works out to four parts in a million, not "less than one". The NSA’s bottom-line number disagrees with its other numbers by a factor of ten.

With all the mathematicians working at NSA, you would think that the agency could get grade-school arithmetic right in what is, after all, a rather important public document. I guess everyone makes mistakes now and again.

The purpose of the paragraph, of course, is to suggest that the proportion of Internet traffic that the NSA monitors isn’t really very big, and you might consider the point pretty convincing even if the actual number is 0.0004% instead of 0.00004%. I think that number is a lot more significant than it appears, but I’ll leave that question for a future post.

[Update 30 August 2013: The Atlantic Wire also noticed NSA's math (Philip Bump, "The NSA Searches Ten Times as Much of the Internet as It Said It Does," Atlantic Wire, 19 August 2013).]