Attack of the week: 64-bit ciphers in TLS

A few months ago it was starting to seem like you couldn’t go a week without a new attack on TLS. In that context, this summer has been a blessed relief. Sadly, it looks like our vacation is over, and it’s time to go back to school.

Today brings the news that Karthikeyan Bhargavan and Gaëtan Leurent out of INRIA have a new paper that demonstrates a practical attack on legacy ciphersuites in TLS (it’s called “Sweet32”, website here). What they show is that ciphersuites that use 64-bit blocklength ciphers — notably 3DES — are vulnerable to plaintext recovery attacks that work even if the attacker cannot recover the encryption key.

While the principles behind this attack are well known, there’s always a difference between attacks in principle and attacks in practice. What this paper shows is that we really need to start paying attention to the practice.

So what’s the matter with 64-bit block ciphers?

Block ciphers are one of the most widely-used cryptographic primitives. As the nameimplies, these are schemes designed to encipher data in blocks, rather than a single bit at a time.

The two main parameters that define a block cipher are its block size (the number of bits it processes in one go), and its key size. The two parameters need not be related. So for example, DES has a 56-bit key and a 64-bit block. Whereas 3DES (which is built from DES) can use up to a 168-bit key and yet still has the same 64-bit block. More recent ciphers have opted for both larger blocks and larger keys.

When it comes to the security provided by a block cipher, the most important parameter is generally the key size. A cipher like DES, with its tiny 56-bit key, is trivially vulnerable to brute force attacks that attempt decryption with every possible key (often using specialized hardware). A cipher like AES or 3DES is generally not vulnerable to this sort of attack, since the keys are much longer.

However, as they say: key size is not everything. Sometimes the block size matters too.

You see, in practice, we often need to encrypt messages that are longer than a single block. We also tend to want our encryption to be randomized. To accomplish this, most protocols use a block cipher in a scheme called a mode of operation. The most popular mode used in TLS is CBC mode. Encryption in CBC looks like this:

Source: Wikipedia

The nice thing about CBC is that (leaving aside authentication issues) it can be proven (semantically) secure if we make various assumptions about the security of the underlying block cipher. Yet these security proofs have one important requirement. Namely, the attacker must not receive too much data encrypted with a single key.

The reason for this can be illustrated via the following simple attack.

Imagine that an honest encryptor is encrypting a bunch of messages using CBC mode. Following the diagram above, this involves selecting a random Initialization Vector (IV) of size equal to the block size of the cipher, then XORing IV with the first plaintext block (P), and enciphering the result (P \oplus IV). The IV is sent (in the clear) along with the ciphertext.

Most of the time, the resulting ciphertext block will be unique — that is, it won’t match any previous ciphertext block that an attacker may have seen. However, if the encryptor processes enough messages, sooner or later the attacker will see a collision. That is, it will see a ciphertext block that is the same as some previous ciphertext block. Since the cipher is deterministic, this means the cipher’s input (P \oplus IV) must be identical to the cipher’s previous input (P' \oplus IV') that created the previous block.

In other words, we have (P \oplus IV) = (P' \oplus IV'), which can be rearranged as (P \oplus P') = (IV \oplus IV'). Since the IVs are random and known to the attacker, the attacker has (with high probability) learned the XOR of two (unknown) plaintexts!

What can you do with the XOR of two unknown plaintexts? Well, if you happen to know one of those two plaintext blocks — as you might if you were able to choose some of the plaintexts the encryptor was processing — then you can easily recover the other plaintext. Alternatively, there are known techniques that can sometimes recover useful data even when you don’t know both blocks.

The main lesson here is that this entire mess only occurs if the attacker sees a collision. And the probability of such a collision is entirely dependent on the size of the cipher block. Worse, thanks to the (non-intuitive) nature of the birthday bound, this happens much more quickly than you might think it would. Roughly speaking, if the cipher block is b bits long, then we should expect a collision after roughly 2^{b/2} encrypted blocks.

In the case of a 64-bit blocksize cipher like 3DES, this is somewhere in the vicinity of 2^{32}, or around 4 billion enciphered blocks.

(As a note, the collision does not really need to occur in the first block. Since all blocks in CBC are calculated in the same way, it could be a collision anywhere within the messages.)

Whew. I thought this was a practical attack. 4 billion is a big number!

It’s true that 4 billion blocks seems like an awfully large number. In a practical attack, the requirements would be even larger — since the most efficient attack is for the attacker to know a lot of the plaintexts, in the hope that she will be able to recover one unknown plaintext when she learns the value (P ⊕ P’).

However, it’s worth keeping in mind that these traffic numbers aren’t absurd for TLS. In practice, 4 billion 3DES blocks works out to 32GB of raw ciphertext. A lot to be sure, but not impossible. If, as the Sweet32 authors do, we assume that half of the plaintext blocks are known to the attacker, we’d need to increase the amount of ciphertext to about 64GB. This is a lot, but not impossible.

The Sweet32 authors take this one step further. They imagine that the ciphertext consists of many HTTPS connections, consisting of 512 bytes of plaintext, in each of which is embedded the same secret 8-byte cookie — and the rest of the session plaintext is known. Calculating from these values, they obtain a requirement of approximately 256GB of ciphertext needed to recover the cookie with high probability.

That is really a lot.

But keep in mind that TLS connections are being used to encipher increasingly more data. Moreover, a single open browser frame running attacker-controlled Javascript can produce many gigabytes of ciphertext in a single hour. So these attacks are not outside of the realm of what we can run today, and presumably will be very feasible in the future.

How does the TLS attack work?

While the cryptographic community has been largely pushing TLS away from ciphersuites like CBC, in favor of modern authenticated modes of operation, these modes still exist in TLS. And they exist not only for use not only with modern ciphers like AES, but they are often available for older ciphersuites like 3DES. For example, here’s a connection I just made to Google:

Of course, just because a server supports 3DES does not mean that it’s vulnerable to this attack. In order for a particular connection to be vulnerable, both the client and server must satisfy three main requirements:

    1. The client and server must negotiate a 64-bit cipher. This is a relatively rare occurrence, but can happen in cases where one of the two sides is using an out-of-date client. For example, stock Windows XP does not support any of the AES-based ciphersuites. Similarly, SSL3 connections may negotiate 3DES ciphersuites.
    2. The server and client must support long-lived TLS sessions, i.e., encrypting a great deal of data with the same key. Unfortunately, most web browsers place no limit on the length of an HTTPS session if Keep-Alive is used, provided that the server allows the session. The Sweet32 authors scanned and discovered that many servers (including IIS) will allow sessions long enough to run their attack. Across the Internet, the percentage of vulnerable servers is small (less than 1%), but includes some important sites.
    3. The client must encipher a great deal of known data, including a secret session cookie. This is generally achieved by running adversarial Javascript code in the browser, although it could be done using standard HTML as well.

      Sites vulnerable to Sweet32. (source)

These caveats aside, the authors were able to run their attack using Firefox, sending at a rate of about 1500 connections per second. With a few optimizations, they were able to recover a 16-byte secret cookie in about 30 hours (a lucky result, given an expected 38 hour run time).The client must encipher a great deal of known data, including a secret session cookie. This is generally achieved by running adversarial Javascript code in the browser, although it could be done using standard HTML as well.

So what do we do now?

While this is not an earthshaking result, it’s roughly comparable to previous results we’ve seen with legacy ciphers like RC4.

In short, while these are not the easiest attacks to run, it’s a big problem that there even exist semi-practical attacks that undo the encryption used in standard encryption protocols. This is a problem that we should address, and these attack papers help to make those problems more clear.

Attack of the Week: Apple iMessage

Today’s Washington Post has a story entitled “Johns Hopkins researchers poke a hole in Apple’s encryption“, which describes the results of some research my students and I have been working on over the past few months.

As you might have guessed from the headline, the work concerns Apple, and specifically Apple’s iMessage text messaging protocol. Over the past months my students Christina Garman, Ian Miers, Gabe Kaptchuk and Mike Rushanan and I have been looking closely at the encryption used by iMessage, in order to determine how the system fares against sophisticated attackers. The results of this analysis include some very neat new attacks that allow us to — under very specific circumstances — decrypt the contents of iMessage attachments, such as photos and videos.

The research team. From left: Gabe Kaptchuk, Mike Rushanan, Ian Miers, Christina Garman

Now before I go further, it’s worth noting that the security of a text messaging protocol may not seem like the most important problem in computer security. And under normal circumstances I might agree with you. But today the circumstances are anything but normal: encryption systems like iMessage are at the center of a critical national debate over the role of technology companies in assisting law enforcement.

A particularly unfortunate aspect of this controversy has been the repeated call for U.S. technology companies to add “backdoors” to end-to-end encryption systems such as iMessage. I’ve always felt that one of the most compelling arguments against this approach — an argument I’ve made along with other colleagues — is that we just don’t know how to construct such backdoors securely. But lately I’ve come to believe that this position doesn’t go far enough — in the sense that it is woefully optimistic. The fact of the matter is that forget backdoors: we barely know how to make encryption work at all. If anything, this work makes me much gloomier about the subject.

But enough with the generalities. The TL;DR of our work is this:

Apple iMessage, as implemented in versions of iOS prior to 9.3 and Mac OS X prior to 10.11.4, contains serious flaws in the encryption mechanism that could allow an attacker — who obtains iMessage ciphertexts — to decrypt the payload of certain attachment messages via a slow but remote and silent attack, provided that one sender or recipient device is online. While capturing encrypted messages is difficult in practice on recent iOS devices, thanks to certificate pinning, it could still be conducted by a nation state attacker or a hacker with access to Apple’s servers. You should probably patch now.

For those who want the gory details, I’ll proceed with the rest of this post using the “fun” question and answer format I save for this sort of post.

What is Apple iMessage and why should I care?

Those of you who read this blog will know that I have a particular obsession with Apple iMessage. This isn’t because I’m weirdly obsessed with Apple — although it is a little bit because of that. Mostly it’s because I think iMessage is an important protocol. The text messaging service, which was introduced in 2011, has the distinction of being the first widely-used end-to-end encrypted text messaging system in the world.

To understand the significance of this, it’s worth giving some background. Before iMessage, the vast majority of text messages were sent via SMS or MMS, meaning that they were handled by your cellular provider. Although these messages are technically encrypted, this encryption exists only on the link between your phone and the nearest cellular tower. Once an SMS reaches the tower, it’s decrypted, then stored and delivered without further protection. This means that your most personal messages are vulnerable to theft by telecom employees or sophisticated hackers. Worse, many U.S. carriers still use laughably weak encryption and protocols that are vulnerable to active interception.

So from a security point of view, iMessage was a pretty big deal. In a single stroke, Apple deployed encrypted messaging to millions of users, ensuring (in principle) that even Apple itself couldn’t decrypt their communications. The even greater accomplishment was that most people didn’t even notice this happened — the encryption was handled so transparently that few users are aware of it. And Apple did this at very large scale: today, iMessage handles peak throughput of more than 200,000 encrypted messages per second, with a supported base of nearly one billion devices.

So iMessage is important. But is it any good?

Answering this question has been kind of a hobby of mine for the past couple of years. In the past I’ve written about Apple’s failure to publish the iMessage protocol, and on iMessage’s dependence on a vulnerable centralized key server. Indeed, the use of a centralized key server is still one of iMessage’s biggest weaknesses, since an attacker who controls the keyserver can use it to inject keys and conduct man in the middle attacks on iMessage users.

But while key servers are a risk, attacks on a key server seem fundamentally challenging to implement — since they require the ability to actively manipulate Apple infrastructure without getting caught. Moreover, such attacks are only useful for prospective surveillance. If you fail to substitute a user’s key before they have an interesting conversation, you can’t recover their communications after the fact.A more interesting question is whether iMessage’s encryption is secure enough to stand up against retrospective decryption attacks — that is, attempts to decrypt messages after they have been sent. Conducting such attacks is much more interesting than the naive attacks on iMessage’s key server, since any such attack would require the existence of a fundamental vulnerability in iMessage’s encryption itself. And in 2016 encryption seems like one of those things that we’ve basically figured out how to get right.

Which means, of course, that we probably haven’t.

How does iMessage encryption work?

What we know about the iMessage encryption protocol comes from a previous reverse-engineering effort by a group from Quarkslab, as well as from Apple’s iOS Security Guide. Based on these sources, we arrive at the following (simplified) picture of the basic iMessage encryption scheme:

To encrypt an iMessage, your phone first obtains the RSA public key of the person you’re sending to. It then generates a random AES key k and encrypts the message with that key using CTR mode. Then it encrypts k using the recipient’s RSA key. Finally, it signs the whole mess using the sender’s ECDSA signing key. This prevents tampering along the way.

So what’s missing here?

Well, the most obviously missing element is that iMessage does not use a Message Authentication Code (MAC) or authenticated encryption scheme to prevent tampering with the message. To simulate this functionality, iMessage simply uses an ECDSA signature formulated by the sender. Naively, this would appear to be good enough. Critically, it’s not.

The attack works as follows. Imagine that a clever attacker intercepts the message above and is able to register her own iMessage account. First, the attacker strips off the original ECDSA signature made by the legitimate sender, and replaces it with a signature of her own. Next, she sends the newly signed message to the original recipient using her own account:

The outcome is that the user receives and decrypts a copy of the message, which has now apparently originated from the attacker rather than from the original sender. Ordinarily this would be a pretty mild attack — but there’s a useful wrinkle. In replacing the sender’s signature with one of her own, the attacker has gained a powerful capability. Now she can tamper with the AES ciphertext (red) at will.

Specifically, since in iMessage the AES ciphertext is not protected by a MAC, it is therefore malleable. As long as the attacker signs the resulting message with her key, she can flip any bits in the AES ciphertext she wants — and this will produce a corresponding set of changes when the recipient ultimately decrypts the message. This means that, for example, if the attacker guesses that the message contains the word “cat” at some position, she can flip bits in the ciphertext to change that part of the message to read “dog” — and she can make this change even though she can’t actually read the encrypted message.

Only one more big step to go.

Now further imagine that the recipient’s phone will decrypt the message correctly provided that the underlying plaintext that appears following decryption is correctly formatted. If the plaintext is improperly formatted — for a silly example, our tampering made it say “*7!” instead of “pig” — then on receiving the message, the recipient’s phone might return an error that the attacker can see.

It’s well known that such a configuration capability allows our attacker the ability to learn information about the original message, provided that she can send many “mauled” variants to be decrypted. By mauling the underlying message in specific ways — e.g., attempting to turn “dog” into “pig” and observing whether decryption succeeds — the attacker can gradually learn the contents of the original message. The technique is known as a format oracle, and it’s similar to the padding oracle attack discovered by Vaudenay.

So how exactly does this format oracle work?

The format oracle in iMessage is not a padding oracle. Instead it has to do with the compression that iMessage uses on every message it sends.

You see, prior to encrypting each message payload, iMessage applies a complex formatting that happens to conclude with gzip compression. Gzip is a modestly complex compression scheme that internally identifies repeated strings, applies Huffman coding, then tacks a CRC checksum computed over the original data at the end of the compressed message. It’s this gzip-compressed payload that’s encrypted within the AES portion of an iMessage ciphertext.

It turns out that given the ability to maul a gzip-compressed, encrypted ciphertext, there exists a fairly complicated attack that allows us to gradually recover the contents of the message by mauling the original message thousands of times and sending the modified versions to be decrypted by the target device. The attack turns on our ability to maul the compressed data by flipping bits, then “fix up” the CRC checksum correspondingly so that it reflects the change we hope to see in the uncompressed data. Depending on whether that test succeeds, we can gradually recover the contents of a message — one byte at a time.

While I’m making this sound sort of simple, the truth is it’s not. The message is encoded using Huffman coding, with a dynamic Huffman table we can’t see — since it’s encrypted. This means we need to make laser-specific changes to the ciphertext such that we can predict the effect of those changes on the decrypted message, and we need to do this blind. Worse, iMessage has various countermeasures that make the attack more complex.The complete details of the attack appear in the paper, and they’re pretty eye-glazing, so I won’t repeat them here. In a nutshell, we are able to decrypt a message under the following conditions:

  1. We can obtain a copy of the encrypted message
  2. We can send approximately 2^18 (invisible) encrypted messages to the target device
  3. We can determine whether or not those messages decrypted successfully or not
The first condition can be satisfied by obtaining ciphertexts from a compromise of Apple’s Push Notification Service servers (which are responsible for routing encrypted iMessages) or by intercepting TLS connections using a stolen certificate — something made more difficult due to the addition of certificate pinning in iOS 9. The third element is the one that initially seems the most challenging. After all, when I send an iMessage to your device, there’s no particular reason that your device should send me any sort of response when the message decrypts. And yet this information is fundamental to conducting the attack!

It turns out that there’s a big exception to this rule: attachment messages.

How do attachment messages differ from normal iMessages?

When I include a photo in an iMessage, I don’t actually send you the photograph through the normal iMessage channel. Instead, I first encrypt that photo using a random 256-bit AES key, then I compute a SHA1 hash and upload the encrypted photo to iCloud. What I send you via iMessage is actually just an URL to the encrypted photo, the SHA1 hash, and the decryption key.

Contents of an “attachment” message.


When you successfully receive and decrypt an iMessage from some recipient, your Messages client will automatically reach out and attempt to download that photo. It’s this download attempt, which happens only when the phone successfully decrypts an attachment message, that makes it possible for an attacker to know whether or not the decryption has succeeded.

One approach for the attacker to detect this download attempt is to gain access to and control your local network connections. But this seems impractical. A more sophisticated approach is to actually maul the URL within the ciphertext so that rather than pointing to, it points to a related URL such as Then the attacker can simply register that domain, place a server there and allow the client to reach out to it. This requires no access to the victim’s local network.

By capturing an attachment message, repeatedly mauling it, and monitoring the download attempts made by the victim device, we can gradually recover all of the digits of the encryption key stored within the attachment. Then we simply reach out to iCloud and download the attachment ourselves. And that’s game over. The attack is currently quite slow — it takes more than 70 hours to run — but mostly because our code is slow and not optimized. We believe with more engineering it could be made to run in a fraction of a day.

Result of decrypting the AES key for an attachment. Note that the ? symbol represents a digit we could not recover for various reasons, typically due to string repetitions. We can brute-force the remaining digits.

The need for an online response is why our attack currently works against attachment messages only: those are simply the messages that make the phone do visible things. However, this does not mean the flaw in iMessage encryption is somehow limited to attachments — it could very likely be used against other iMessages, given an appropriate side-channel.

How is Apple fixing this?

Apple’s fixes are twofold. First, starting in iOS 9.0 (and before our work), Apple began deploying aggressive certificate pinning across iOS applications. This doesn’t fix the attack on iMessage crypto, but it does make it much harder for attackers to recover iMessage ciphertexts to decrypt in the first place.

Unfortunately even if this works perfectly, Apple still has access to iMessage ciphertexts. Worse, Apple’s servers will retain these messages for up to 30 days if they are not delivered to one of your devices. A vulnerability in Apple Push Network authentication, or a compromise of these servers could read them all out. This means that pinning is only a mitigation, not a true fix.

As of iOS 9.3, Apple has implemented a short-term mitigation that my student Ian Miers proposed. This relies on the fact that while the AES ciphertext is malleable, the RSA-OAEP portion of the ciphertext is not. The fix maintains a “cache” of recently received RSA ciphertexts and rejects any repeated ciphertexts. In practice, this shuts down our attack — provided the cache is large enough. We believe it probably is.

In the long term, Apple should drop iMessage like a hot rock and move to Signal/Axolotl.

So what does it all mean?

As much as I wish I had more to say, fundamentally, security is just plain hard. Over time we get better at this, but for the foreseeable future we’ll never be ahead. The only outcome I can hope for is that people realize how hard this process is — and stop asking technologists to add unacceptable complexity to systems that already have too much of it.

Attack of the week: DROWN

To every thing there is a season. And in the world of cryptography, today we have the first signs of the season of TLS vulnerabilities.

This year’s season is off to a roaring start with not one, but two serious bugs announcements by the OpenSSL project, each of which guarantees that your TLS connections are much less than private than you’d like them to be. I can’t talk about both vulnerabilities and keep my sanity, so today I’m going to confine myself to the more dramatic of the two vulnerabilities: a new cross-protocol attack on TLS named “DROWN”.

Technically DROWN stands for “Decrypting RSA using Obsolete and Weakened eNcryption”, but honestly feel free to forget that because the name itself is plenty descriptive. In short, due to a series of dumb mistakes on the part of a vast number of people, DROWN means that TLS connections to a depressingly huge slice of the web (and mail servers, VPNs etc.) are essentially open to attack by fairly modest adversaries.

So that’s bad news. The worse news — as I’ll explain below — is that this whole mess was mostly avoidable.

For a detailed technical explanation of DROWN, you should go read the complete technical paper by Aviram et al. Or visit the DROWN team’s excellent website. If that doesn’t appeal to you, read on for a high level explanation of what DROWN is all about, and what it means for the security of the web. Here’s the TL;DR:

If you’re running a web server configured to use SSLv2, and particularly one that’s running OpenSSL (even with all SSLv2 ciphers disabled!), you may be vulnerable to a fast attack that decrypts many recorded TLS connections made to that box. Most worryingly, the attack does not require the client to ever make an SSLv2 connection itself, and it isn’t a downgrade attack. Instead, it relies on the fact that SSLv2 — and particularly the legacy “export” ciphersuites it incorporates — are pure poison, and simply having these active on a server is enough to invalidate the security of all connections made to that device.

For the rest of this post I’ll use the “fun” question and answer format I save for this kind of attack. First, some background.

What are TLS and SSLv2, and why should I care?

Transport Layer Security (TLS) is the most important security protocol on the Internet. You should care about it because nearly every transaction you conduct on the Internet relies on TLS (v1.0, 1.1 or 1.2) to some degree, and failures in TLS can flat out ruin your day.

But TLS wasn’t always TLS. The protocol began its life at Netscape Communications under the name “Secure Sockets Layer”, or SSL. Rumor has it that the first version of SSL was so awful that the protocol designers collected every printed copy and buried them in a secret New Mexico landfill site. As a consequence, the first public version of SSL is actually SSL version 2. It’s pretty terrible as well — but not (entirely) for the reasons you might think.

Let me explain.

The reason you might think SSLv2 is terrible is because it was a product of the mid-1990s, which modern cryptographers view as the “dark ages of cryptography”. Many of the nastier cryptographic attacks we know about today had not yet been discovered. As a result, the SSLv2 protocol designers were forced to essentially grope their way in the dark, and so were frequently devoured by grues — to their chagrin and our benefit, since the attacks on SSLv2 offered priceless lessons for the next generation of protocols.

And yet, these honest mistakes are not worst thing about SSLv2. The most truly awful bits stem from the fact that the SSLv2 designers were forced to ruin their own protocol. This was the result of needing to satisfy the U.S. government’s misguided attempt to control the export of cryptography. Rather than using only secure encryption, the designers were forced to build in a series of “export-grade ciphersuites” that offered abysmal 40-bit session keys and other nonsense. I’ve previously written about the effect of export crypto on today’s security. Today we’ll have another lesson.

Wait, isn’t SSLv2 ancient history?

For some time in the early 2000s, SSLv2 was still supported by browsers as a fallback protocol, which meant that active attackers could downgrade an SSLv3 or TLS connection by tricking a browser into using the older protocol. Fortunately those attacks are long gone now: modern web browsers have banished SSLv2 entirely — along with export cryptography in general. If you’re using a recent version of Chrome, IE or Safari, you should never have to worry about accidentally making an SSLv2 connection.

The problem is that while clients (such as browsers) have done away with SSLv2, many servers still support the protocol. In most cases this is the result of careless server configuration. In others, the blame lies with crummy and obsolete embedded devices that haven’t seen a software update in years — and probably never will. (You can see if your server is vulnerable here.)

And then there’s the special case of OpenSSL, which helpfully provides a configuration option that’s intended to disable SSLv2 ciphersuites — but which, unfortunately, does no such thing. In the course of their work, the DROWN researchers discovered that even when this option is set, clients may still request arbitrary SSLv2 ciphersuites. (This issue was quietly patched in January. Upgrade.)

The reason this matters is that SSL/TLS servers do a very silly thing. You see, since people don’t like to buy multiple certificates, a server that’s configured to use both TLS and SSLv2 will generally use the same RSA private key to support both protocols. This means any bugs in the way SSLv2 handles that private key could very well affect the security of TLS.

And this is where DROWN comes in.

So what is DROWN?

DROWN is a classic example of a “cross protocol attack”. This type of attack makes use of bugs in one protocol implementation (SSLv2) to attack the security of connections made under a different protocol entirely — in this case, TLS. More concretely, DROWN is based on the critical observation that while SSLv2 and TLS both support RSA encryption, TLS properly defends against certain well-known attacks on this encryption — while SSLv2’s export suites emphatically do not.

I will try to make this as painless as possible, but here we need to dive briefly into the weeds.

You see, both SSLv2 and TLS use a form of RSA encryption padding known as RSA-PKCS#1v1.5. In the late 1990s, a man named Daniel Bleichenbacher proposed an amazing attack on this encryption scheme that allows an attacker to decrypt an RSA ciphertext efficiently — under the sole condition that they can ask an online server to decrypt many related ciphertexts, and give back only one bit of information for each one — namely, the bit representing whether decryption was successful or not.

Bleichenbacher’s attack proved particularly devastating for SSL servers, since the standard SSL RSA-based handshake involves the client encrypting a secret (called the Pre-Master Secret, or PMS) under the server’s RSA public key, and then sending this value over the wire. An attacker who eavesdrops the encrypted PMS can run the Bleichenbacher attack against the server, sending it thousands of related values (in the guise of new SSL connections), and using the server’s error responses to gradually decrypt the PMS itself. With this value in hand, the attacker can compute SSL session keys and decrypt the recorded SSL session.

A nice diagram of the SSL handshake, courtesy of Cloudflare (who don’t know I’m using it. Thanks guys!)

The main SSL/TLS countermeasure against Bleichenbacher’s attack is basically a hack. When the server detects that an RSA ciphertext has decrypted improperly, it lies. Instead of returning an error, which the attacker could use to implement the attack, it generates a random pre-master secret and continues with the rest of the protocol as though this bogus value was what it actually decrypted. This causes the protocol to break down later on down the line, since the server will compute essentially a random session key. But it’s sufficient to prevent the attacker from learning whether the RSA decryption succeeded or not, and that kills the attack dead.

Anti-Bleichenbacher countermeasure from the TLS 1.2 spec.

Now let’s take a moment to reflect and make an observation.

If the attacker sends a valid RSA ciphertext to be decrypted, the server will decrypt it and obtain some PMS value. If the attacker sends the same valid ciphertext a second time, the server will decrypt and obtain the same PMS value again. Indeed, the server will always get the same PMS even if the attacker sends the same valid ciphertext a hundred times in a row.

On the other hand, if the attacker repeatedly sends the same invalid ciphertext, the server will choose a different PMS every time. This observation is crucial.

In theory, if the attacker holds a ciphertext that might be valid or invalid — and the attacker would like to know which is true — they can send the same ciphertext to be decrypted repeatedly. This will lead to two possible conditions. In condition (1) where the ciphertext is valid, decryption will produce the “same PMS every time”. Condition (2) for an invalid ciphertext will produce a “different PMS each time”. If the attacker could somehow tell the difference between condition (1) and condition (2), they could determine whether the ciphertext was valid. That determination alone would be enough to resurrect the Bleichenbacher attack. Fortunately in TLS, the PMS is never used directly; it’s first passed through a strong hash function and combined with a bunch of random nonces to obtain a Master Secret. This result then used in further strong ciphers and hash functions. Thanks to the strength of the hash function and ciphers, the resulting keys are so garbled that the attacker literally cannot tell whether she’s observing condition (1) or (2).

And here we finally we run into the problem of SSLv2.

You see, SSLv2 implementations include a similar anti-Bleichenbacher countermeasure. Only here there are some key differences. In SSLv2 there is no PMS — the encrypted value is used as the Master Secret and employed directly to derive the encryption session key. Moreover, in export modes, the Master Secret may be as short as 40 bits, and used with correspondingly weak export ciphers. This means an attacker can send multiple ciphertexts, then brute-force the resulting short keys. After recovering these keys for a tiny number of sessions, they will be able to determine whether they’re in condition (1) or (2). This would effectively resurrect the Bleichenbacher attack.

This still sounds like an attack on SSLv2, not on TLS. What am I missing? 

And now we come to the full horror of SSLv2.

Since most servers configured with both SSLv2 and TLS support will use the same RSA private key for decrypting sessions from either protocol, a Bleichenbacher attack on the SSLv2 implementation — with its vulnerable crappy export ciphersuites — can be used to decrypt the contents of a normal TLS-based RSA ciphertext. After all, both protocols are using the same darned secret key. Due to formatting differences in the RSA ciphertext between the two protocols, this attack doesn’t work all the time — but it does work for approximately one out of a thousand TLS handshakes.

To put things succinctly: with access to a whole hell of a lot of computation, an attacker can intercept a TLS connection, then at their leisure make many thousands of queries to the SSLv2-enabled server, and decrypt that connection. The “general DROWN” attack actually requires watching about 1,000 TLS handshakes to find a vulnerable RSA ciphertext, about 40,000 queries to the server, and about 2^50 offline operations.

LOL. That doesn’t sound practical at all. You cryptographers suck.

First off, that isn’t really a question, it’s more a rude statement. But since this is exactly the sort of reaction cryptographers often get when they point out perfectly practical theoretical attacks on real protocols, I’d like to take a moment to push back.

While the attack described above seems costly, it can be conducted in several hours and $440 on Amazon EC2. Are your banking credentials worth $440? Probably not. But someone else’s probably are. Given all the things we have riding on TLS, it’s better for it not to be broken at all.

More urgently, the reason cryptographers spend time on “impractical attacks” is that attacks always get better. And sometimes they get better fast.

The attack described above is called “General DROWN” and yes, it’s a bit impractical. But in the course of writing just this single paper, the DROWN researchers discovered a second variant of their attack that’s many orders of magnitude faster than the general one described above. This attack, which they call “Special DROWN” can decrypt a TLS RSA ciphertext in about one minute on a single CPU core.

This attack relies on a bug in the way OpenSSL handles SSLv2 key processing, a bug that was (inadvertently) fixed in March 2015, but remains open across the Internet. The Special DROWN bug puts DROWN squarely in the domain of script kiddies, for thousands of websites across the Internet.

So how many sites are vulnerable?

This is probably the most depressing part of the entire research project. According to wide-scale Internet scans run by the DROWN researchers, more than 2.3 million HTTPS servers with browser-trusted certificates are vulnerable to special DROWN, and 3.5 million HTTPS servers are vulnerable to General DROWN. That’s a sizeable chunk of the encrypted web, including a surprising chunk of the Chinese and Colombian Internet.

And while I’ve focused on the main attacks in this post, it’s worth pointing out that DROWN also affects other protocol suites, like TLS with ephemeral Diffie-Hellman and even Google’s QUIC. So these vulnerabilities should not be taken lightly.

If you want to know whether your favorite site is vulnerable, you can use the DROWN researchers’ handy test.

What happens now?

In January, OpenSSL patched the bug that allows the SSLv2 ciphersuites to remain alive. Last March, the project inadvertently fixed the bug that makes Special DROWN possible. But that’s hardly the end. The patch they’re announcing today is much more direct: hopefully it will make it impossible to turn on SSLv2 altogether. This will solve the problem for everyone… at least for everyone willing to patch. Which, sadly, is unlikely to be anywhere near enough.

More broadly, attacks like DROWN illustrate the cost of having old, vulnerable protocols on the Internet. And they show the terrible cost that we’re still paying for export cryptography systems that introduced deliberate vulnerabilities in encryption so that intelligence agencies could pursue a small short-term advantage — at the cost of long-term security.

Given that we’re currently in the midst of a very important discussion about the balance of short- and long-term security, let’s hope that we won’t make the same mistake again.

On the Juniper backdoor

You might have heard that a few days ago, Juniper Systems announced the discovery of “unauthorized code” in the ScreenOS software that underlies the NetScreen line of devices. As a result of this discovery, the company announced a pair of separate vulnerabilities, CVE-2015-7755 and CVE-2015-7756 and urged their customers to patch immediately.

The first of these CVEs (#7755) was an authentication vulnerability, caused by a malicious hardcoded password in SSH and Telnet. Rapid7 has an excellent writeup of the issue. This is a pretty fantastic vulnerability, if you measure by the impact on security of NetScreen users. But on the technological awesomeness scale it rates about a two out of ten, maybe a step above ‘hit the guy with a wrench‘.

The second vulnerability is a whole different animal. The advisory notes that CVE-7756 — which is independent of the first issue — “may allow a knowledgeable attacker who can monitor VPN traffic to decrypt that traffic.” This is the kind of vulnerability that makes applied cryptographers cry tears of joy. It certainly did that for me:


And while every reasonable person knows you can’t just drop “passive decryption vulnerability” and expect the world to go on with its business, this is exactly what Juniper tried to do. Since they weren’t talking about it, it fell to software experts to try to work out what was happening by looking carefully at firmware released by the company.

Now I want to be clear that I was not one of those software experts. IDA scares the crap out of me. But I’m fortunate to know some of the right kind of people, like Steve Checkoway, who I was able to get on the job, mostly by encouraging him to neglect his professional obligations. I also follow some talented folks on Twitter, like H.D. Moore and Ralf Philipp Weinmann. So I was fortunate enough to watch them work, and occasionally (I think?) chip in a helpful observation.

And yes, it was worth it. Because what Ralf and Steve et al. found is beyond belief. Ralf’s excellent post provides all of the technical details, and you should honest just stop reading now and go read that. But since you’re still here, the TL;DR is this:

For the past several years, it appears that Juniper NetScreen devices have incorporated a potentially backdoored random number generator, based on the NSA’s Dual_EC_DRBG algorithm. At some point in 2012, the NetScreen code was further subverted by some unknown party, so that the very same backdoor could be used to eavesdrop on NetScreen connections. While this alteration was not authorized by Juniper, it’s important to note that the attacker made no major code changes to the encryption mechanism — they only changed parameters. This means that the systems were potentially vulnerable to other parties, even beforehand. Worse, the nature of this vulnerability is particularly insidious and generally messed up.

In the rest of this post I’m going to try to fill in the last part of that statement. But first, some background.


Pretty much every cryptographic system depends on a secure random number generator, or RNG. These algorithms produce the unpredictable random bits that are consumed by cryptographic protocols. The key word in this description is unpredictable: if an attacker can predict the output of your RNG, then virtually everything you build on it will end up broken.

This fact has not been lost on attackers! The most famous (alleged) example of deliberate random number generator subversion was discovered in 2007 by Dan Shumow and Neils Ferguson from Microsoft, when they announced the possibility of a backdoor in a NIST standard called Dual_EC_DRBG.

I’ve written extensively about the design of the Dual_EC generator and the process that led to it its standardization. Omitting the mathematics, the short version is that Dual EC relies on a special 32-byte constant called Q, which — if generated by a malicious attacker — can allow said attacker to predict future outputs of the RNG after seeing a mere 30 bytes of raw output from your generator.

The NIST specification of Dual_EC comes with a default value for Q that was generated by the NSA. Nobody has ever been able to determine how NSA generated this value, but leaks by Edward Snowden in 2013 provide strong evidence that NSA may have generated it maliciously. It certainly doesn’t smell good.

But enough with the ancient history. We’re here to talk about Juniper.

Juniper ScreenOS — before the “unauthorized code”

Although it was not widely publicized before this week, Juniper’s ScreenOS devices have used Dual EC for some time — probably since before Juniper acquired NetScreen Technologies. Prior to this week, the only place you might have learned about this was on this tiny page posted by the company after the Snowden leaks.

The decision to use Dual EC is strange all by itself. But it gets weirder.

First, ScreenOS doesn’t use the NSA’s default Q. Instead, they use an alternative Q value that was generated by Juniper and/or NetScreen. If Juniper had really wanted to rule out the possibility of surveillance, this would have been a good opportunity to do so. They could have generated the new constant in a “provably” safe way — e.g., by hashing some English-language string. Since we have no evidence that they did so, a conservative view holds that the Juniper/NetScreen constant may also have been generated maliciously, rendering it useful for eavesdropping.

Next, ScreenOS uses Dual EC in a strange, non-standard way. Rather than generating all of their random numbers with Dual EC (which would be slow), they only use Dual EC to generate a seed for a fast 3DES-based generator called ANSI X9.17. Since that generator is actually FIPS-140 approved and generally believed to be sufficient to the purpose, it’s not clear what value Dual EC is really adding to the system in the first place — except, of course, its usefulness as a potential backdoor.

The good news here is that the post-processing by ANSI X9.17 should kill the Dual EC backdoor, since the attack relies on the attacker seeing raw output from Dual EC. The ANSI generator appears to completely obfuscate this output, thus rendering Dual EC “safe”. This is indeed the argument Juniper made in 2013 when it decided to leave the Dual EC code in ScreenOS.

The problem with this argument is that it assumes that no other code could ever “accidentally” exfiltrate a few bytes bit of raw Dual EC output. Yet this is exactly the kind of threat you’d worry about in a deliberately backdoored system — the threat that, just maybe, the developers are not your friend. Thus Dual EC is safe only if you assume no tiny bug in the code could accidentally leak out 30 bytes or so of raw Dual EC output. If it did, this would make all subsequent seeding calls predictable, and thus render all numbers generated by the system predictable. In general, this would spell doom for the confidentiality of VPN connections.

And unbelievably, amazingly, who coulda thunk it, it appears that such a bug does exist in many versions of ScreenOS, dating to both before and after the “unauthorized code” noted by Juniper. This issue was discovered by Willem Pinckaers and can be illustrated by the following code snippet, which Steve Checkoway decompiled (see full context here):

void prng_generate()
  int index; // eax@4
  unsigned int bytes_generated; // ebx@4
  int v2; // eax@9
  int v3; // eax@12
  char v4; // ST04_1@12
  int time[2]; // [sp+10h] [bp-10h]@1

  time[0] = 0;
  time[1] = get_cycles();
  prng_output_index = 0; // this is a global
  if ( !do_not_need_to_reseed() )
    // the routine below fills a buffer with raw Dual EC output
    prng_reseed(); // internally sets prng_output_index to 32
  for ( ; (unsigned int)prng_output_index <= 0x1F; prng_output_index += 8 )
    // this loop is supposed to process the same buffer
    // through the ANSI (3DES) generator. However, since the
    // value of prng_output_index was set to 32 above, it never executes
    memcpy(prev_prng_seed, prng_seed, 8);
    memcpy(prev_prng_block, prng_block, 8);
    ANSI_X9_31_generate_block(time, prng_seed, prng_key, prng_block);

Thus what comes out from this function is 32 bytes of raw Dual EC output, which is all you need to recover the internal Dual EC generator state and predict all future outputs.

So if this was the authorized code, what the hell was the unauthorized code?

The creepiest thing about CVE-2015-7756 is that there doesn’t seem to be any unauthorized code. Indeed, what’s changed in the modified versions is simply the value of the Q point. According to Ralf this point changed in 2012, presumably to a value that the hacker(s) generated themselves. This would likely have allowed these individuals to passively decrypt ScreenOS VPN sessions.

In the more recent Juniper patch to fix the vulnerability, is simply set back to the the original Juniper/NetScreen value.

The attacker also replaced some test vectors. But that appears to be it.

To sum up, some hacker or group of hackers noticed an existing backdoor in the Juniper software, which may have been intentional or unintentional — you be the judge! They then piggybacked on top of it to build a backdoor of their own, something they were able to do because all of the hard work had already been done for them. The end result was a period in which someone — maybe a foreign government — was able to decrypt Juniper traffic in the U.S. and around the world.

And all because Juniper had already paved the road.

So why does this matter?

For the past several months I’ve been running around with various groups of technologists, doing everything I can to convince important people that the sky is falling. Or rather, that the sky will fall if they act on some of the very bad, terrible ideas that are currently bouncing around Washington — namely, that our encryption systems should come equipped with “backdoors” intended to allow law enforcement and national security agencies to access our communications.

One of the most serious concerns we raise during these meetings is the possibility that encryption backdoors could be subverted. Specifically, that a backdoor intended for law enforcement could somehow become a backdoor for people who we don’t trust to read our messages. Normally when we talk about this, we’re concerned about failures in storage of things like escrow keys. What this Juniper vulnerability illustrates is that the danger is much broader and more serious than that.

The problem with cryptographic backdoors isn’t that they’re the only way that an attacker can break into our cryptographic systems. It’s merely that they’re one of the best. They take care of the hard work, the laying of plumbing and electrical wiring, so attackers can simply walk in and change the drapes.

This post made possible by Ralf Philipp Weinmann, H. D. Moore, Steve Checkoway, Willem Pinckaers, Nadia Heninger, Shaanan Cohney and the letter Q.

Why the Tor attack matters

Earlier today, Motherboard posted a court document filed in a prosecution against a Silk Road 2.0 user, indicating that the user had been de-anonymized on the Tor network thanks to research conducted by a “university-based research institute”.

Source: Motherboard.

As Motherboard pointed out, the timing of this research lines up with an active attack on the Tor network that was discovered and publicized in July 2014. Moreover, the details of that attack were eerily similar to the abstract of a (withdrawn) BlackHat presentation submitted by two researchers at the CERT division of Carnegie Mellon University (CMU).

A few hours later, the Tor Project made the allegations more explicit, posting a blog entry accusing CMU of accepting $1 million to conduct the attack. A spokesperson for CMU didn’t exactly deny the allegations, but demanded better evidence and stated that he wasn’t aware of any payment. No doubt we’ll learn more in the coming weeks as more documents become public.

You might wonder why this is important. After all, the crimes we’re talking about are pretty disturbing. One defendant is accused of possessing child pornography, and if the allegations are true, the other was a staff member on Silk Road 2.0. If CMU really did conduct Tor de-anonymization research for the benefit of the FBI, the people they identified were allegedly not doing the nicest things. It’s hard to feel particularly sympathetic.

Except for one small detail: there’s no reason to believe that the defendants were the only people affected.

If the details of the attack are as we understand them, a group of academic researchers deliberately took control of a significant portion of the Tor network. Without oversight from the University research board, they exploited a vulnerability in the Tor protocol to conduct a traffic confirmation attack, which allowed them to identify Tor client IP addresses and hidden services. They ran this attack for five months, and potentially de-anonymized thousands of users. Users who depend on Tor to protect them from serious harm.

It’s quite possible that the CMU researchers exercised strict protocols to ensure that they didn’t accidentally de-anonymize innocent bystanders. This would be standard procedure in any legitimate research involving human subjects, particularly research that has the potential to do harm. If the researchers did take such steps, it would be nice to know about them. CMU hasn’t even admitted to the scope of the research project, nor have they published any results, so we just don’t know.

While most of the computer science researchers I know are fundamentally ethical people, as a community we have a blind spot when it comes to the ethical issues in our field. There’s a view in our community that Institutional Review Boards are for medical researchers, and we’ve somehow been accidentally caught up in machinery that wasn’t meant for us. And I get this — IRBs are unpleasant to work with. Sometimes the machinery is wrong.

But there’s also a view that computer security research can’t really hurt people, so there’s no real reason for sort of ethical oversight machinery in the first place. This is dead wrong, and if we want to be taken seriously as a mature field, we need to do something about it.

We may need different machinery, but we need something. That something begins with the understanding that active attacks that affect vulnerable users can be dangerous, and should never be conducted without rigorous oversight — if they must be conducted at all. It begins with the idea that universities should have uniform procedures for both faculty researchers and quasi-government organizations like CERT, if they live under the same roof. It begins with CERT and CMU explaining what went on with their research, rather than treating it like an embarrassment to be swept under the rug.

Most importantly, it begins with researchers looking beyond their own research practices. So far the response to the Tor news has been a big shrug. It’s wonderful that most of our community is responsible. But none of that matters if we look the other way when others in our community fail to act responsibly.

Attack of the week: Logjam

Credit: Sharon Mollerus (cc)

In case you haven’t heard, there’s a new SSL/TLS vulnerability making the rounds. Nicknamed Logjam, the new attack is ‘special’ in that it may admit complete decryption or hijacking of any TLS connection you make to an improperly configured web or mail server. Worse, there’s at least circumstantial evidence that similar (and more powerful) attacks might already be in the toolkit of some state-level attackers such as the NSA.

This work is the result of an unusual collaboration between a fantastic group of co-authors spread all around the world, including institutions such as the University of Michigan, INRIA Paris-Rocquencourt, INRIA Paris-Nancy, Microsoft Research, Johns Hopkins and the University Of Pennsylvania. It’s rare to see this level of collaboration between groups with so many different areas of expertise, and I hope to see a lot more like it. (Disclosure: I am one of the authors.)

The absolute best way to understand the Logjam result is to read the technical research paper. This post is mainly aimed at people who want a slightly less technical form. For those with even shorter attention spans, here’s the TL;DR:

It appears that the the Diffie-Hellman protocol, as currently deployed in SSL/TLS, may be vulnerable to a serious downgrade attack that restores it to 1990s “export” levels of security, and offers a practical “break” of the TLS protocol against poorly configured servers. Even worse, extrapolation of the attack requirements — combined with evidence from the Snowden documents — provides some reason to speculate that a similar attack could be leveraged against protocols (including TLS, IPSec/IKE and SSH) using 768- and 1024-bit Diffie-Hellman.

I’m going to tackle this post in the usual ‘fun’ question-and-answer format I save for this sort of thing.

What is Diffie-Hellman and why should I care about TLS “export” ciphersuites?

Diffie-Hellman is probably the most famous public key cryptosystem ever invented. Publicly discovered by Whit Diffie and Martin Hellman in the late 1970s (and a few years earlier, in secret, by UK GCHQ), it allows two parties to negotiate a shared encryption key over a public connection.

Diffie-Hellman is used extensively in protocols such as SSL/TLS and IPSec, which rely on it to establish the symmetric keys that are used to transport data. To do this, both parties must agree on a set of parameters to use for the key exchange. In traditional (‘mod p‘) Diffie-Hellman, these parameters consist of a large prime number p, as well as a ‘generator’ g. The two parties now exchange keys as shown below:

Classical Diffie-Hellman (source).

TLS supports several variants of Diffie-Hellman. The one we’re interested in for this work is the ‘ephemeral’ non-elliptic (“DHE”) protocol variant, which works in a manner that’s nearly identical to the diagram above. The server takes the role of Alice, selecting (p, g, ga mod p) and signing this tuple (and some nonces) using its long-term signing key. The client responds gb mod p and the two sides then calculate a shared secret.

Just for fun, TLS also supports an obsolete ‘export’ variant of Diffie-Hellman. These export ciphersuites are a relic from the 1990s when it was illegal to ship strong encryption out of the country. What you need to know about “export DHE” is simple: it works identically to standard DHE, but limits the size of p to 512 bits. Oh yes, and it’s still out there today. Because the Internet.

How do you attack Diffie-Hellman?

The best known attack against a correct Diffie-Hellman implementation involves capturing the value gand solving to find the secret key a. The problem of finding this value is known as the discrete logarithm problem, and it’s thought to be a mathematically intractable, at least when Diffie-Hellman is implemented in cryptographically strong groups (e.g., when p is of size 2048 bits or more).

Unfortunately, the story changes dramatically when p is relatively small — for example, 512 bits in length. Given a value gmod p for a 512-bit p, itshould at least be possible to efficiently recover the secret a and read traffic on the connection.

Most TLS servers don’t use 512-bit primes, so who cares?

The good news here is that weak Diffie-Hellman parameters are almost never used purposely on the Internet. Only a trivial fraction of the SSL/TLS servers out there today will organically negotiate 512-bit Diffie-Hellman. For the most part these are crappy embedded devices such as routers and video-conferencing gateways.

However, there is a second class of servers that are capable of supporting 512-bit Diffie-Hellman when clients request it, using a special mode called the ‘export DHE’ ciphersuite. Disgustingly, these servers amount to about 8% of the Alexa top million sites (and a whopping 29% of SMTP/STARTLS mail servers). Thankfully, most decent clients (AKA popular browsers) won’t willingly negotiate ‘export-DHE’, so this would also seem to be a dead end.

It isn’t.
ServerKeyExchange message (RFC 5246)

You see, before SSL/TLS peers can start engaging in all this fancy cryptography, they first need to decide which ciphers they’re going to use. This is done through a negotiation process in which the client proposes some options (e.g., RSA, DHE, DHE-EXPORT), and the server picks one.

This all sound simple enough. However, one of the early, well known flaws in SSL/TLS is the protocol’s failure to properly authenticate these ‘negotiation’ messages. In very early versions of SSL they were not authenticated at all. SSLv3 and TLS tacked on an authentication process — but one that takes place only at the end of the handshake.*

This is particularly unfortunate given that TLS servers often have the ability to authenticate their messages using digital signatures, but don’t really take advantage of this. For example, when two parties negotiate Diffie-Hellman, the parameters sent by the server are transmitted within a signed message called the ServerKeyExchange (shown at right). The signed portion of this message covers the parameters, but neglects to include any information about which ciphersuite the server thinks it’s negotiating. If you remember that the only difference between DHE and DHE-EXPORT is the size of the parameters the server sends down, you might start to see the problem.

Here it is in a nutshell: if the server supports DHE-EXPORT, the attacker can ‘edit’ the negotiation messages sent from the a client — even if the client doesn’t support export DHE — replacing the client’s list of supported ciphers with only export DHE. The server will in turn send back a signed 512-bit export-grade Diffie-Hellman tuple, which the client will blindly accept — because it doesn’t realize that the server is negotiating the export version of the ciphersuite. From its perspective this message looks just like ‘standard’ Diffie-Hellman with really crappy parameters.

Overview of the Logjam active attack (source: paper).

All this tampering should run into a huge snag at the end of the handshake, when he client and server exchange Finished messages embedding include a MAC of the transcript. At this point the client should learn that something funny is going on, i.e., that what it sent no longer matches what the server is seeing. However, the loophole is this: if the attacker can recover the Diffie-Hellman secret quickly — before the handshake ends — she can forge her own Finished messages. In that case the client and server will be none the wiser.

The upshot is that executing this attack requires the ability to solve a 512-bit discrete logarithm before the client and server exchange Finished messages. That seems like a tall order.

Can you really solve a discrete logarithm before a TLS handshake times out?

In practice, the fastest route to solving the discrete logarithm in finite fields is via an algorithm called the Number Field Sieve (NFS). Using NFS to solve a single 512-bit discrete logarithm instance requires several core-years — or about week of wall-clock time given a few thousand cores — which would seem to rule out solving discrete logs in real time.

However, there is a complication. In practice, NFS can actually be broken up into two different steps:

  1. Pre-computation (for a given prime p). This includes the process of polynomial selection, sieving, and linear algebra, all of which depend only on p. The output of this stage is a table for use in the second stage.
  2. Solving to find a (for a given gmod p). The final stage, called the descent, uses the table from the precomputation. This is the only part of the algorithm that actually involves a specific g andga.

The important thing to know is that the first stage of the attack consumes the vast majority of the time, up to a full week on a large-scale compute cluster. The descent stage, on the other hand, requires only a few core-minutes. Thus the attack cost depends primarily on where the server gets its Diffie-Hellman parameters from. The best case for an attacker is when p is hard-coded into the server software and used across millions of machines. The worst case is when p is re-generated routinely by the server.

I’ll let you guess what real TLS servers actually do.

In fact, large-scale Internet scans by the team at University of Michigan show that most popular web servers software tends to re-use a small number of primes across thousands of server instances. This is done because generating prime numbers is scary, so implementers default to using a hard-coded value or a config file supplied by your Linux distribution. The situation for export Diffie-Hellman is particularly awful, with only two (!) primes used across up 92% of enabled Apache/mod_ssl sites.

Number of seconds to solve a 512-bit discrete log (source: paper).

The upshot of all of this is that about two weeks of pre-computation is sufficient to build a table that allows you to perform the downgrade against most export-enabled servers in just a few minutes (see the chart at right). This is fast enough that it can be done before the TLS connection timeout. Moreover, even if this is not fast enough, the connection can often be held open longer by using clever protocol tricks, such as sending TLS warning messages to reset the timeout clock.

Keep in mind that none of this shared prime craziness matters when you’re using sufficiently large prime numbers (on the order of 2048 bits or more). It’s only a practical issue you’re using small primes, like 512-bit, 768-bit or — and here’s a sticky one I’ll come back to in a minute — 1024 bit.

How do you fix the downgrade to export DHE?

The best and most obvious fix for this problem is to exterminate export ciphersuites from the Internet. Unfortunately, these awful configurations are the default in a number of server software packages (looking at you Postfix), and getting people to update their configurations is surprisingly difficult (see e.g., FREAK).

A simpler fix is to upgrade the major web browsers to resist the attack. The easy way to do this is to enforce a larger minimum size for received DHE keys. The problem here is that the fix itself causes some collateral damage — it will break a small but significant fraction of lousy servers that organically negotiate (non-export) DHE with 512 bit keys.

The good news here is that the major browsers have decided to break the Internet (a little) rather than allow it to break them. Each has agreed to raise the minimum size limit to at least 768 bits, and some to a minimum of 1024 bits. It’s still not perfect, since 1024-bit DHE may not be cryptographically sound against powerful attackers, but it does address the immediate export attack. In the longer term the question is whether to use larger negotiated DHE groups, or abandon DHE altogether and move to elliptic curves.

What does this mean for larger parameter sizes?

The good news so far is that 512-bit Diffie-Hellman is only used by a fraction of the Internet, even when you account for active downgrade attacks. The vast majority of servers use Diffie-Hellman moduli of length at least 1024 bits. (The widespread use of 1024 is largely due to a hard-cap in older Java clients. Go away Java.)

While 2048-bit moduli are generally believed to be outside of anyone’s reach, 1024-bit DHE has long been considered to be at least within groping range of nation-state attackers. We’ve known this for years, of course, but the practical implications haven’t been quite clear. This paper tries to shine some light on that, using Internet-wide measurements and software/hardware estimates.

If you recall from above, the most critical aspect of the NFS attack is the need to perform large amounts of pre-computation on a given Diffie-Hellman prime p, followed by a relatively short calculation to break any given connection that uses p. At the 512-bit size the pre-computation only requires about a week. The question then is, how much does it cost for a 1024-bit prime, and how common are shared primes?

While there’s no exact way to know how much the 1024-bit attack would cost, the paper attempts to provide some extrapolations based on current knowledge. With software, the cost of the pre-computation seems quite high — on the order of 35 million core-years. Making this happen for a given prime within a reasonable amount of time (say, one year) would appear to require billions of dollars of computing equipment if we assume no algorithmic improvements. Even if we rule out such improvements, it’s conceivable that this cost might be brought down to a few hundred million dollars using hardware. This doesn’t seem out of bounds when you consider leaked NSA cryptanalysis budgets.

What’s interesting is that the descent stage, required to break a given Diffie-Hellman connection, is much faster. Based on some implementation experiments by the CADO-NFS team, it may be possible to break a Diffie-Hellman connection in as little as 30 core-days, with parallelization hugely reducing the wall-clock time. This might even make near-real-time decryption of Diffie-Hellman connections practical.

Is the NSA actually doing this?

So far all we’ve noted is that NFS pre-computation is at least potentially feasible when 1024-bit primes are re-used. That doesn’t mean the NSA is actually doing any of it.

There is some evidence, however, that suggests the NSA has decryption capability that’s at least consistent with such a break. This evidence comes from a series of Snowden documents published last winter in Der Spiegel. Together they describe a large-scale effort at NSA and GCHQ, capable of decrypting ‘vast’ amounts of Internet traffic, including IPSec, SSH and HTTPS connections.

NSA slide illustrating exploitation
of IPSec encrypted traffic (source: Spiegel).

While the architecture described by the documents mentions attacks against many protocols, the bulk of the energy seems to be around the IPSec and IKE protocols, which are used to establish Virtual Private Networks (VPNs) between individuals and corporate networks such as financial institutions.

The nature of the NSA’s exploit is never made clear in the documents, but diagram at right gives a lot of the architectural details. The system involves collecting Internet Key Exchange (IKE) handshakes, transmitting them to the NSA’s Cryptanalysis and Exploitation Services (CES) enclave, and feeding them into a decryption system that controls substantial high performance computing resources to process the intercepted exchanges. This is at least circumstantially consistent with Diffie-Hellman cryptanalysis.

Of course it’s entirely possible that the attack is based on a bad random number generator, weak symmetric encryption, or any number of engineered backdoors. There are a few pieces of evidence that militate towards a Diffie-Hellman break, however:

  1. IPSec (or rather, the IKE key exchange) uses Diffie-Hellman for every single connection, meaning that it can’t be broken without some kind of exploit, although this doesn’t rule out the other explanations.
  2. The IKE exchange is particularly vulnerable to pre-computation, since IKE uses a small number of standardized prime numbers called the Oakley groups, which are going on 17 years old now. Large-scale Internet scanning by the Michigan team shows that a majority of responding IPSec endpoints will gladly negotiate using Oakley Group 1 (768 bit) or Group 2 (1024 bit), even when the initiator offers better options.
  3. The NSA’s exploit appears to require the entire IKE handshake as well as any pre-shared key (PSK). These inputs would be necessary for recovery of IKEv1 session keys, but are not required in a break that involves only symmetric cryptography.
  4. The documents explicitly rule out the use of malware, or rather, they show that such malware (‘TAO implants’) is in use — but that malware allows the NSA to bypass the IKE handshake altogether.

I would stipulate that beyond the Internet measurements and computational analysis, this remains firmly in the category of  ‘crazy-eyed informed speculation’. But while we can’t rule out other explanations, this speculation is certainly consistent with a hardware-optimized break of Diffie-Hellman 768 and 1024-bit, along with some collateral damage to SSH and related protocols.

So what next?

The paper gives a detailed set of recommendations on what to do about these downgrade attacks and (relatively) weak DHE groups. The website provides a step-by-step guide for server administrators. In short, probably the best long-term move is to switch to elliptic curves (ECDHE) as soon as possible. Failing this, clients and servers should enforce at least 2048-bit Diffie-Hellman across the Internet. If you can’t do that, stop using common primes.

Making this all happen on anything as complicated as the Internet will probably consume a few dozen person-lifetimes. But it’s something we have to do, and will do, to make the Internet work properly.


* There are reasons for this. Some SSL/TLS ciphersuites (such as the RSA encryption-based ciphersuites) don’t use signatures within the protocol, so the only way to authenticate the handshake is to negotiate a ciphersuite, run the key exchange protocol, then use the resulting shared secret to authenticate the negotiation messages after the fact. But SSL/TLS DHE involves digital signatures, so it should be possible to achieve a stronger level of security than this. It’s unfortunate that the protocol does not.

Attack of the week: FREAK (or ‘factoring the NSA for fun and profit’)

This is the story of how a handful of cryptographers ‘hacked’ the NSA. It’s also a story of encryption backdoors, and why they never quite work out the way you want them to.

But I think I’m getting ahead of myself a bit here.

Today’s Washington Post has the story of a nasty bug in some TLS/SSL servers and clients, one that has the potential to downgrade the security of your TLS connections to something that isn’t really secure at all. In this post I’m going to talk about the technical aspects of the attack, why it matters, and how bad it is.
If you don’t want to read a long blog post, let me give you a TL;DR:

A group of cryptographers at INRIA, Microsoft Research and IMDEA have discovered some serious vulnerabilities in OpenSSL (e.g., Android) clients and Apple TLS/SSL clients (e.g., Safari) that allow a ‘man in the middle attacker’ to downgrade connections from ‘strong’ RSA to ‘export-grade’ RSA. These attacks are real and exploitable against a shocking number of websites — including government websites. Patch soon and be careful. 

You can find a detailed description of the work by the researchers — Beurdouche, Bhargavan, Delignat-Lavaud, Fournet, Kohlweiss, Pironti, Strub, Zinzindohoue, Zanella-Béguelin — at their site You should go visit that site and read about the exploits directly. The proof of concept implementation also involved contributions from Nadia Heninger at U. Penn.

I’m going to explain the rest of it in the ‘fun’ question and answer format I save for this kind of attack.

What is SSL/TLS and what are ‘EXPORT cipher suites’ anyway?

In case you’re not familiar with SSL and its successor TLS, what you should know is that they’re the most important security protocols on the Internet. In a world full of untrusted networks, SSL and TLS are what makes modern communication possible.

Or rather, that’s the theory. In practice, SSL and TLS have been a more like a work in progress. In part this is because they were developed during an era when modern cryptographic best practices weren’t nailed down yet. But more to the point: it’s because even when the crypto is right, many software implementations still get things wrong.

With all that in mind, there’s a third aspect of SSL/TLS that doesn’t get nearly as much attention. That is: the SSL protocol itself was deliberately designed to be broken.

Let me explain what I mean by that.

Back in the early 1990s when SSL was first invented at Netscape Corporation, the United States maintained a rigorous regime of export controls for encryption systems. In order to distribute crypto outside of the U.S., companies were required to deliberately ‘weaken’ the strength of encryption keys. For RSA encryption, this implied a maximum allowed key length of 512 bits.*

The 512-bit export grade encryption was a compromise between dumb and dumber. In theory it was designed to ensure that the NSA would have the ability to ‘access’ communications, while allegedly providing crypto that was still ‘good enough’ for commercial use. Or if you prefer modern terms, think of it as the original “golden master key“.

The need to support export-grade ciphers led to some technical challenges. Since U.S. servers needed to support both strong and weak crypto, the SSL designers used a ‘cipher suite’ negotiation mechanism to identify the best cipher both parties could support. In theory this would allow ‘strong’ clients to negotiate ‘strong’ ciphersuites with servers that supported them, while still providing compatibility to the broken foreign clients.

This story has a happy ending, after a fashion. The U.S eventually lifted the most onerous of its export policies. Unfortunately, the EXPORT ciphersuites didn’t go away. Today they live on like zombies — just waiting to eat our flesh.

If EXPORT ciphers are known to be broken, what’s the news here?

We don’t usually worry about export-grade cipher suites very much, because supposedly they aren’t very relevant to the modern Internet. There are three general reasons we don’t think they matter anymore:

  1. Most ‘modern’ clients (e.g., web browsers) won’t offer export grade ciphersuites as part of the negotiation process. In theory this means that even if the server supports export-grade crypto, your session will use strong crypto.
  2. Almost no servers, it was believed, even offer export-grade ciphersuites anymore.
  3. Even if you do accidentally negotiate an export-grade RSA ciphersuite, a meaningful attack still requires the attacker to factor a 512-bit RSA key (or break a 40-bit symmetric cipher). This is doable, but it’s generally considered too onerous if you have to do it for every single connection.
This was the theory anyway. It turns out that theory is almost always different than practice. Which brings us to the recent work by Beurdouche et al. from INRIA, Microsoft Research and IMDEA.

What these researchers did was develop a fairly beautiful piece of formal analysis tooling that allows them to ‘fuzz’ the state machines of most modern SSL/TLS implementations. They found a bunch of wonderful things in the course of doing this — some of them quite nasty. I’m not going to cover all of them in this post, but the one we care about here is quite simple.

You see, it turns out that some modern TLS clients — including Apple’s SecureTransport and OpenSSL — have a bug in them. This bug causes them to accept RSA export-grade keys even when the client didn’t ask for export-grade RSA. The impact of this bug can be quite nasty: it admits a ‘man in the middle’ attack whereby an active attacker can force down the quality of a connection, provided that the client is vulnerable and the server supports export RSA.

The MITM attack works as follows:
  1. In the client’s Hello message, it asks for a standard ‘RSA’ ciphersuite.
  2. The MITM attacker changes this message to ask for ‘export RSA’.
  3. The server responds with a 512-bit export RSA key, signed with its long-term key.
  4. The client accepts this weak key due to the OpenSSL/SecureTransport bug.
  5. The attacker factors the RSA modulus to recover the corresponding RSA decryption key.
  6. When the client encrypts the ‘pre-master secret’ to the server, the attacker can now decrypt it to recover the TLS ‘master secret’.
  7. From here on out, the attacker sees plaintext and can inject anything it wants.
So that’s bad news and it definitely breaks our assumption in point (1) above. But at least in theory we should still be safe based on points (2) and (3).

How common are export-enabled TLS servers?

No matter how bad you think the Internet is, it can always surprise you. The surprise in this case is that export-grade RSA is by no means as extinct as we thought it was.

Based on some recent scans by Alex Halderman, Zakir Durumeric and David Adrian at University of Michigan, it seems that export-RSA is supported by as many as 5.2% 36.7% (!!!!) of the 14 million sites serving browser-trusted certs. The vast majority of these sites appear to be content distribution networks (CDN) like Akamai. Those CDNs are now in the process of removing export grade suites.
While the numbers are impressive, the identity of those sites is a bit more worrying. They include U.S. government sites like (Oy vey), and It turns out that the FBI tip reporting site ( was also vulnerable.

(Facebook have updated their configuration as a result of this work.)

Factoring an RSA key seems pretty expensive for breaking one session.

This brings us to the most awful part of this attack. You don’t have to be that fast.

 You see, it turns out that generating fresh RSA keys is a bit costly. So modern web servers don’t do it for every single connection. In fact, Apache mod_ssl by default will generate a single export-grade RSA key when the server starts up, and will simply re-use that key for the lifetime of that server.
What this means is that you can obtain that RSA key once, factor it, and break every session you can get your ‘man in the middle’ mitts on until the server goes down. And that’s the ballgame.

PoC or GTFO.

Fortunately, a proof of concept for this attack requires only a few ingredients. First, you need some tooling to actually run the MITM attack. Then you need the ability to (quickly) factor 512-bit RSA keys. From there it’s just a question of finding a vulnerable client and server.

This is what happens to EC2 spot pricing
when Nadia runs 75 ‘large’ instances
to factor a 512-bit key.

Just because someone says an implementation is vulnerable doesn’t mean it actually is. You should ask for proof.

The guts of the PoC were put together by Karthik Bhargavan and Antoine Delignat-Lavaud at INRIA. They assembled an MITM proxy that can intercept connections and re-write them to use export-RSA against a willing website.

To factor the 512-bit export keys, the project enlisted the help of Nadia Heninger at U. Penn, who has been working on “Factoring as a Service” for exactly this purpose. Her platform uses cado-nfs on a cluster of EC2 virtual servers, and (with Nadia doing quite a bit of handholding to deal with crashes) was able to factor a bunch of 512-bit keys — each in about 7.5 hours for $104 in EC2 time.

From there all you need is a vulnerable website.

Since the NSA was the organization that demanded export-grade crypto, it’s only fitting that they should be the first site affected by this vulnerability. There’s great video on the SmackTLS site. After a few hours of factoring, one can take the original site (which looked like this):


And change it into this:

Attack images courtesy Karthik, Antoine INRIA.

Very dramatic.

Some will point out that an MITM attack on the NSA is not really an ‘MITM attack on the NSA’ because NSA outsources its web presence to the Akamai CDN (see obligatory XKCD at right). These people may be right, but they also lack poetry in their souls.

Is it patched?

The most recent of OpenSSL does have a patch. This was announced (though not very loudly) in January of this year.

Apple is working on a patch.

Akamai and other CDNs are also rolling out a patch to solve these problems. Over the next two weeks we will hopefully see export ciphersuites extinguished from the Internet. In the mean time, try to be safe.

What does it all mean?

You might think this is all a bit absurd and doesn’t affect you very much. In a strictly technical sense you’re probably right. The client bugs will soon be patched (update your devices! unless you have Android in which case you’re screwed). With good luck, servers supporting export-grade RSA cipher suites will soon be rare curiosity.

Still, to take this as the main lesson of the work would, I think, be missing the forest for the trees. There’s a much more important moral to this story.

The export-grade RSA ciphers are the remains of a 1980s-vintage effort to weaken cryptography so that intelligence agencies would be able to monitor foreign traffic. This was done badly. So badly, that while the policies were ultimately scrapped, they’re still hurting us today.

This might be an academic point if it was only a history lesson. However, for the past several months, U.S. and European politicians have been publicly mooting the notion of a new set of cryptographic backdoors in systems we use today. While the proposals aren’t explicit, they would presumably involve deliberately weakening encryption tech so that governments can intercept and read our conversations. While officials carefully avoid the term “back door” — or any suggestion of weakening our encryption systems against real attackers — this is wishful thinking. These systems are already so complex that even normal issues stress them to the breaking point. There’s just no room for new backdoors.

To be blunt about it, the moral is pretty simple:

Encryption backdoors will always turn around and bite you in the ass. They are never worth it.


Special thanks to Karthik and Antoine for sharing this with me, Nadia for factoring, Ivan Ristic for interrupting his vacation to get us data, and the CADO-NFS team for the software that made this possible.


* Export controls might have made some sense in the days when ‘encryption’ meant big clunky pieces of hardware, but it was nonsensical in a world of software. Non-U.S. users could easily skirt the paltry IP-address checks to download strong versions of browsers such as Netscape, and — when that was too much trouble — they could easily re-implement the crypto themselves or use foreign open source libraries. (The requirements became so absurd that mainstream U.S. companies like RSA Security wound up hiring foreign developers to build their encryption libraries, since it was easier to import strong encryption than to export it.)