Today’s paper is not primary research, but an expert opinion on a matter of public policy; three of its authors have posted their own summaries [1] [2] [3], the general press has picked it up [4] [5] [6] [7] [8], and it was mentioned during Congressional hearings on the topic [9]. I will, therefore, only briefly summarize it, before moving on to some editorializing of my own. I encourage all of you to read the paper itself; it’s clearly written, for a general audience, and you can probably learn something about how to argue a position from it.

The paper is a direct response to FBI Director James Comey, who has for some time been arguing that data storage and communications systems must be designed for exceptional access by law enforcement agencies (quote from paper); his recent Lawfare editorial can be taken as representative. British politicians have also been making similar noises (see the above general-press articles). The paper, in short, says that this would cause much worse technical problems than it solves, and that even if, by some magic, those problems could be avoided, it would still be a terrible idea for political reasons.

At slightly more length, exceptional access means: law enforcement agencies (like the FBI) and espionage agencies (like the NSA) want to be able to wiretap all communications on the ’net, even if those communications are encrypted. This is a bad idea technically for the same reasons that master-key systems for doors can be more trouble than they’re worth. The locks are more complicated, and easier to pick than they would be otherwise. If the master key falls into the wrong hands you have to change all the locks. Whoever has access to the master keys can misuse them—which makes the keys, and the people who control them, a target. And it’s a bad idea politically because, if the USA gets this capability, every other sovereign nation gets it too, and a universal wiretapping capability is more useful to a totalitarian state that wants to suppress the political opposition, than it is to a detective who wants to arrest murderers. I went into this in more detail toward the end of my review of RFC 3514.

I am certain that James Comey knows all of this, in at least as much detail as it is explained in the paper. Moreover, he knows that the robust democratic debate he calls for already happened, in the 1990s, and wiretapping lost. [10] [11] [12] Why, then, is he trying to relitigate it? Why does he keep insisting that it must somehow be both technically and politically feasible, against all evidence to the contrary? Perhaps most important of all, why does he keep insisting that it’s desperately important for his agency to be able to break encryption, when it was only an obstacle nine times in all of 2013? [13]

On one level, I think it’s a failure to understand the scale of the problems with the idea. On the technical side, if you don’t live your life down in the gears it’s hard to bellyfeel the extent to which everything is broken and therefore any sort of wiretap requirement cannot help but make the situation worse. And it doesn’t help, I’m sure, that Comey has heard (correctly) that what he wants is mathematically possible, so he thinks everyone saying this is impossible is trying to put one over on him, rather than just communicate this isn’t practically possible.

The geopolitical problems with the idea are perhaps even harder to convey, because the Director of the FBI wrestles with geopolitical problems every day, so he thinks he does know the scale there. For instance, the paper spends quite some time on a discussion of the jurisdictional conflict that would naturally come up in an investigation where the suspect is a citizen of country A, the crime was committed in B, and the computers involved are physically in C but communicate with the whole world—and it elaborates from there. But we already have treaties to cover that sort of investigation. Comey probably figures they can be bent to fit, or at worst, we’ll have to negotiate some new ones.

If so, what he’s missing is that he’s imagining too small a group of wiretappers: law enforcement and espionage agencies from countries that are on reasonably good terms with the USA. He probably thinks export control can keep the technology out of the hands of countries that aren’t on good terms with the USA (it can’t) and hasn’t even considered non-national actors: local law enforcement, corporations engaged in industrial espionage, narcotraficantes, mafiosi, bored teenagers, Anonymous, religious apocalypse-seekers, and corrupt insiders in all the above. People the USA can’t negotiate treaties with. People who would already have been thrown in jail if anyone could make charges stick. People who may not even share premises like what good governance or due process of law or basic human decency mean. There are a bit more than seven billion people on the planet today, and this is the true horror of the Internet: roughly 40% of those people [14] could, if they wanted, ruin your life, right now. It’s not hard. [15] (The other 60% could too, if they could afford to buy a mobile, or at worst a satellite phone.)

But these points, too, have already been made, repeatedly. Why does none of it get through? I am only guessing, but my best guess is: the War On Some Drugs [16] and the aftermath of 9/11 [17] (paywalled, sorry; please let me know if you have a better cite) have both saddled the American homeland security complex with impossible, Sisyphean labors. In an environment where failure is politically unacceptable, yet inevitable, the loss of any tool—even if it’s only marginally helpful—must seem like an existential threat. To get past that, we would have to be prepared to back off on the must never happen again / must be stopped at all cost posturing; the good news is, that has an excellent chance of delivering better, cheaper law enforcement results overall. [18]

Diffie-Hellman key exchange is a cryptographic primitive used in nearly all modern security protocols. Like many cryptographic primitives, it is difficult to break because it is difficult to solve a particular mathematical problem; in this case, the discrete logarithm problem. Generally, when people try to break a security protocol, they either look at the pure math of it—searching for an easier way to solve discrete logarithms—or they look for mistakes in how the protocol is implemented—something that will mean you don’t have to solve a discrete logarithm to break the protocol.

This paper does a bit of both. It observes something about the way Diffie-Hellman is used in Internet security protocols that makes it unusually easy to solve the discrete logarithms that will break the protocol. Concretely: to break an instance of Diffie-Hellman as studied in this paper, you have to solve for $x$ in the equation

${g}^{x}\equiv y\phantom{\rule{0.278em}{0ex}}\left(\mathrm{\text{mod}}\phantom{\rule{0.167em}{0ex}}p\right)$

where all numbers are positive integers, $g$ and $p$ are fixed in advance, and $y$ is visible on the wire. The trouble is with the fixed in advance part. It turns out that the most efficient known way to solve this kind of equation, the general number field sieve, can be broken into two stages. The first stage is much more expensive than the second, and it depends only on $g$ and $p$. So if the same $g$ and $p$ were reused for many communications, an eavesdropper could do the first stage in advance, and then breaking individual communications would be much easier—perhaps easy enough to do on the fly, as needed.

At least three common Internet security protocols (TLS, IPsec, and SSH) do reuse $g$ and $p$, if they are not specifically configured otherwise. As the paper puts it, if the attacker can precompute for one 1024-bit group, they can compromise 37% of HTTPS servers in the Alexa Top 1 million, 66% of all probeable IPsec servers, and 26% of all probeable SSH servers. A group is a specific pair of values for $g$ and $p$, and the number of bits essentially refers to how large $p$ is. 1024 bits is the smallest size that was previously considered secure; this paper demonstrates that the precomputation for one such group would cost only a little less than a billion dollars, most of which goes to constructing the necessary supercomputer—the incremental cost for more groups is much smaller. As such we have to move 1024 bits onto the not secure anymore pile. (There’s an entire section devoted to the possibility that the NSA might already have done this.)

(Another section of the paper demonstrates that 512-bit groups can be precomputed by a small compute cluster, and 768-bit groups by a substantial (but not enormous) cluster: 110 and 36,500 core-years of computation, respectively. The former took one week of wall-clock time with the equipment available to the authors. We already knew those groups were insecure; unfortunately, they are still accepted by ~10% of servers.)

What do we do about it? If you’re running a server, the thing you should do right now is jump to a 2048-bit group; the authors have instructions for common TLS servers and SSH, and generic security configuration guidelines for HTTPS servers and SSH also cover this topic. (If you know where to find instructions for IPsec, please let me know.) 2048 bits is big enough that you probably don’t need to worry about using the same group as anyone else, but generating your own groups is also not difficult. It is also important to make sure that you have completely disabled support for export ciphersuites. This eliminates the 512- and 768-bit groups and also several other primitives that we know are insecure.

At the same time, it would be a good idea turn on support for TLSv1.2 and modern ciphersuites, including elliptic curve Diffie-Hellman, which requires an attacker to solve a more complicated equation and is therefore much harder to break. It’s still a discrete logarithm problem, but in a different finite field that is harder to work with. I don’t understand the details myself, but an elliptic curve group only needs 256 bits to provide the same security as a 2048-bit group for ordinary Diffie-Hellman. There is a catch: the general number field sieve works for elliptic curves, too. I’m not aware of any reason why the precomputation attack in this paper wouldn’t apply, and I wish the authors had estimated how big your curve group needs to be for it to be infeasible. 256 bits is almost certainly big enough; but how about 128 bits, which is usually considered equivalent to 1024 bits for ordinary DH?

In the longer timeframe, where we think about swapping out algorithms entirely, I’m going to say this paper means cryptographers should take precomputation should not help the attacker as a design principle. We already do this for passwords, where the whole point of salt is to make precomputation not help; it’s time to start thinking about that in a larger context.

Also in the longer timeframe, this is yet another paper demonstrating that old clients and servers, that only support old primitives that are now insecure, hurt everyone’s security. Just about every time one peer continues to support a broken primitive for backward compatibility, it has turned out that a man in the middle can downgrade it—trick it into communicating insecurely even with counterparties that do support good primitives. (There’s a downgrade attack to 512-bit Diffie-Hellman groups in this paper.) This is one of those thorny operational/incentive alignment problems that hasn’t been solved to anyone’s satisfaction. Windows XP makes an instructive example: it would have been technically possible for Microsoft to backport basically all of the security improvements (and other user-invisible improvements) in later versions of Windows, and there are an enormous number of people who would have benefited from that approach. But it wouldn’t have been in Microsoft’s own best interest, so instead they did things geared to force people onto newer versions of the OS even at the expense of security for people who didn’t want to budge, and people who needed to continue interoperating with people who didn’t want to budge (`schannel.dll` in XP still doesn’t support TLS 1.2). I could spin a similar story for basically every major player in the industry.