In general I try to limit this blog to posts that focus on generally-applicable techniques in cryptography. That is, I don’t focus on the deeply wonky. But this post is going to be an exception. Today, I’m going to talk about a topic that most “typical” implementers don’t — and shouldn’t — think about.
Specifically: I’m going to talk about various techniques for making public key encryption schemes chosen ciphertext secure. I see this as the kind of post that would have saved me ages of reading when I was a grad student, so I figured it wouldn’t hurt to write it all down (even though this absolutely shouldn’t serve as a replacement for just reading the original papers!)
Background: CCA(1/2) security
Early (classical) ciphers used a relatively weak model of security, if they used one at all. That is, the typical security model for an encryption scheme was something like the following:
I generate an encryption key (or keypair for public-key encryption)
I give you the encryption of some message of my choice
You “win” if you can decrypt it
This is obviously not a great model in the real world, for several reasons. First off, in some cases the attacker knows a lot about the message to be decrypted. For example: it may come from a small space (like a set of playing cards). For this reason we require a stronger definition like “semantic security” that assumes the attacker can choose the plaintext distribution, and can also obtain the encryption of messages of his/her own choice. I’ve written more about this here.
More relevant to this post, another limitation of the above game is that — in some real-world examples — the attacker has even more power. That is: in addition to obtaining the encryption of chosen plaintexts, they may be able to convince the secret keyholder to decrypt chosen ciphertexts of their choice.
At first blush this seems like a really stupid model. If you can ask the keyholder to decrypt chosen ciphertexts, then isn’t the scheme just obviously broken? Can’t you just decrypt anything you want?
The answer, it turns out, is that there are many real-life examples where the attacker has decryption capability, but the scheme isn’t obviously broken. For example:
Sometimes an attacker can decrypt a limited set of ciphertexts (for example, because someone leaves the decryption machine unattended at lunchtime.) The question then is whether they can learn enough from this access to decrypt other ciphertexts that are generated after she loses access to the decryption machine — for example, messages that are encrypted after the operator comes back from lunch.
Sometimes an attacker can submit any ciphertext she wants — but will only obtain a partial decryption of the ciphertext. For example, she might learn only a single bit of information such as “did this ciphertext decrypt correctly”. The question, then, is whether she can leverage this tiny amount of data to fully decrypt some ciphertext of her choosing.
The first example is generally called a “non-adaptive” chosen ciphertext attack, or a CCA1 attack (and sometimes, historically, a “lunchtime” attack). There are a few encryption schemes that totally fall apart under this attack — the most famous textbook example is Rabin’s public key encryption scheme, which allows you to recover the full secret key from just a single chosen-ciphertext decryption.
The more powerful second example is generally referred to as an “adaptive” chosen ciphertext attack, or a CCA2 attack. The term refers to the idea that the attacker can select the ciphertexts they try to decrypt based on seeing a specific ciphertext that they want to attack, and by seeing the answers to specific decryption queries.
In this article we’re going to use the more powerful “adaptive” (CCA2) definition, because that subsumes the CCA1 definition. We’re also going to focus primarily on public-key encryption.
With this in mind, here is the intuitive definition of the experiment we want a CCA2 public-key encryption scheme to be able to survive:
I generate an encryption keypair for a public-key scheme and give you the public key.
You can send me (sequentially and adaptively) many ciphertexts, which I will decrypt with my secret key. I’ll give you the result of each decryption.
Eventually you’ll send me a pair of messages (of equal length) and I’ll pick a bit at random, and return to you the encryption of , which I will denote as .
You’ll repeat step (2), sending me ciphertexts to decrypt. If you send me I’ll reject your attempt. But I’ll decrypt any other ciphertext you send me, even if it’s only slightly different from .
The attacker outputs their guess . They “win” the game if .
We say that our scheme is secure if the attacker wins only with a significantly greater probability than they would win with if they simply guessed at random. Since they can win this game with probability 1/2 just by guessing randomly, that means we want (Probability attacker wins the game) – 1/2 to be “very small” (typically a negligible function of the security parameter).
You should notice two things about this definition. First, it gives the attacker the full decryption of any ciphertext they send me. This is obviously much more powerful than just giving the attacker a single bit of information, as we mentioned in the example further above. But note that powerful is good. If our scheme can remain secure in this powerful experiment, then clearly it will be secure in a setting where the attacker gets strictly less information from each decryption query.
The second thing you should notice is that we impose a single extra condition in step (4), namely that the attacker cannot ask us to decrypt . We do this only to prevent the game from being “trivial” — if we did not impose this requirement, the attacker could always just hand us back to decrypt, and they would always learn the value of .
(Notice as well that we do not give the attacker the ability to request encryptions of chosen plaintexts. We don’t need to do that in the public key encryption version of this game, because we’re focusing exclusively on public-key encryption here — since the attacker has the public key, she can encrypt anything she wants without my help.)
With definitions out of the way, let’s talk a bit about how we achieve CCA2 security in real schemes.
A quick detour: symmetric encryption
This post is mainly going to focus on public-key encryption, because that’s actually the problem that’s challenging and interesting to solve. It turns out that achieving CCA2 for symmetric-key encryption is really easy. Let me briefly explain why this is, and why the same ideas don’t work for public-key encryption.
(To explain this, we’ll need to slightly tweak the CCA2 definition above to make it work in the symmetric setting. The changes here are small: we won’t give the attacker a public key in step (1), and at steps (2) and (4) we will allow the attacker to request the encryption of chosen plaintexts as well as the decryption.)
The first observation is that many common encryption schemes — particularly, the widely-used cipher modes of operation like CBC and CTR — are semantically secure in a model where the attacker does not have the ability to decrypt chosen ciphertexts. However, these same schemes break completely in the CCA2 model.
The simple reason for this is ciphertext malleability. Take CTR mode, which is particularly easy to mess with. Let’s say we’ve obtained a ciphertext at step (4) (recall that is the encryption of ), it’s trivially easy to “maul” the ciphertext — simply by flipping, say, a bit of the message (i.e., XORing it with “1”). This gives us a new ciphertext that we are now allowed to submit for decryption. We are now allowed (by the rules of the game) to submit this ciphertext, and obtain , which we can use to figure out .
So how do we fix this problem? The straightforward observation is that we need to prevent the attacker from mauling the ciphertext . The generic approach to doing this is to modify the encryption scheme so that it includes a Message Authentication Code (MAC) tag computed over every CTR-mode ciphertext. The key for this MAC scheme is generated by the encrypting party (me) and kept with the encryption key. When asked to decrypt a ciphertext, the decryptor first checks whether the MAC is valid. If it’s not, the decryption routine will output “ERROR”. Assuming an appropriate MAC scheme, the attacker can’t modify the ciphertext (including the MAC) without causing the decryption to fail and produce a useless result.
So in short: in the symmetric encryption setting, the answer to CCA2 security is simply for the encrypting parties to authenticate each ciphertext using a secret authentication (MAC) key they generate. Since we’re talking about symmetric encryption, that extra (secret) authentication key can be generated and stored with the decryption key. (Some more efficient schemes make this all work with a single key, but that’s just an engineering convenience.) Everything works out fine.
So now we get to the big question.
CCA security is easy in symmetric encryption. Why can’t we just do the same thing for public-key encryption?
As we saw above, it turns out that strong authenticated encryption is sufficient to get CCA(2) security in the world of symmetric encryption. Sadly, when you try this same idea generically in public key encryption, it doesn’t always work. There’s a short reason for this, and a long one. The short version is: it matters whois doing the encryption.
Let’s focus on the critical difference. In the symmetric CCA2 game above, there is exactly one person who is able to (legitimately) encrypt ciphertexts. That person is me. To put it more clearly: the person who performs the legitimate encryption operations (and has the secret key) is also the same person who is performing decryption.
Even if the encryptor and decryptor aren’t literally the same person, the encryptor still has to be honest. (To see why this has to be the case, remember that the encryptor has shared secret key! If that party was a bad guy, then the whole scheme would be broken, since they could just output the secret key to the bad guys.) And once you’ve made the stipulation that the encryptor is honest, then you’re almost all the way there. It suffices simply to add some kind of authentication (a MAC or a signature) to any ciphertext she encrypts. At that point the decryptor only needs to determine whether any given ciphertexts actually came from the (honest) encryptor, and avoid decrypting the bad ones. You’re done.
Public key encryption (PKE) fundamentally breaks all these assumptions.
In a public-key encryption scheme, the main idea is that anyone can encrypt a message to you, once they get a copy of your public key. The encryption algorithm may sometimes be run by good, honest people. But it can also be run by malicious people. It can be run by parties who are adversarial. The decryptor has to be able to deal with all of those cases. One can’t simply assume that the “real” encryptor is honest.
Let me give a concrete example of how this can hurt you. A couple of years ago I wrote a post about flaws in Apple iMessage, which (at the time) used simple authenticated (public key) encryption scheme. The basic iMessage encryption algorithm used public key encryption (actually a combination of RSA with some AES thrown in for efficiency) so that anyone could encrypt a message to my key. For authenticity, it required that every message be signed with an ECDSA signature by the sender.
When I received a message, I would look up the sender’s public key and first make sure the signature was valid. This would prevent bad guys from tampering with the message in flight — e.g., executing nasty stuff like adaptive chosen ciphertext attacks. If you squint a little, this is almost exactly a direct translation of the symmetric crypto approach we discussed above. We’re simply swapping the MAC for a digital signature.
The problems with this scheme start to become apparent when we consider that there might be multiple people sending me ciphertexts. Let’s say the adversary is on the communication path and intercepts a signed message from you to me. They want to change (i.e., maul) the message so that they can execute some kind of clever attack. Well, it turns out this is simple. They simply rip off the honest signature and replace it one they make themselves:
The new message is identical, but now appears to come from a different person (the attacker). Since the attacker has their own signing key, they can maul the encrypted message as much as they want, and sign new versions of that message. If you plug this attack into (a version) of the public-key CCA2 game up top, you see they’ll win quite easily. All they have to do is modify the challenge ciphertext at step (4) to be signed with their own signing key, then they can change it by munging with the CTR mode encryption, and request the decryption of that ciphertext.
Of course if I only accept messages from signed by some original (guaranteed-to-be-honest) sender, this scheme might work out fine. But that’s not the point of public key encryption. In a real public-key scheme — like the one Apple iMessage was trying to build — I should be able to (safely) decrypt messages from anyone, and in that setting this naive scheme breaks down pretty badly.
Ok, this post has gotten a bit long, and so far I haven’t actually gotten to the various “tricks” for adding chosen ciphertext security to real public key encryption schemes. That will have to wait until the next post, to come shortly.
Over the past several years I’ve been privileged to observe two contradictory and fascinating trends. The first is that we’re finally starting to use the cryptography that researchers have spent the past forty years designing. We see this every day in examples ranging from encrypted messaging to phone security to cryptocurrencies.
But before I get to all of that — much further below — let me stress that this is not a post about the quantum computing apocalypse, nor is it about the success of cryptography in the 21st century. Instead I’m going to talk about something much more wonky. This post will be about one of the simplest (and coolest!) cryptographic technologies ever developed: hash-based signatures.
Hash-based signature schemes were first invented in the late 1970s by Leslie Lamport, and significantly improved by Ralph Merkle and others. For many years they were largely viewed as an interesting cryptographic backwater, mostly because they produce relatively large signatures (among other complications). However in recent years these constructions have enjoyed something of a renaissance, largely because — unlike signatures based on RSA or the discrete logarithm assumption — they’re largely viewed as resistant to serious quantum attacks like Shor’s algorithm.
First some background.
Background: Hash functions and signature schemes
In order to understand hash-based signatures, it’s important that you have some familiarity with cryptographic hash functions. These functions take some input string (typically or an arbitrary length) and produce a fixed-size “digest” as output. Common cryptographic hash functions like SHA2, SHA3 or Blake2 produce digests ranging from 256 bits to 512 bits.
In order for a function to be considered a ‘cryptographic’ hash, it must achieve some specific security requirements. There are a number of these, but here we’ll just focus on three common ones:
1. Pre-image resistance (sometimes known as “one-wayness”): given some output , it should be time-consuming to find an input such that . (There are many caveats to this, of course, but ideally the best such attack should require a time comparable to a brute-force search of whatever distribution is drawn from.)
2. Second-preimage resistance: This is subtly different than pre-image resistance. Given some input , it should be hard for an attacker to find a different input such that .
3. Collision resistance: It should be hard to find any two values such that . Note that this is a much stronger assumption than second-preimage resistance, since the attacker has complete freedom to find any two messages of its choice.
The example hash functions I mentioned above are believed to provide all of these properties. That is, nobody has articulated a meaningful (or even conceptual) attack that breaks any of them. That could always change, of course, in which case we’d almost certainly stop using them. (We’ll discuss the special case of quantum attacks a bit further below.)
Since our goal is to use hash functions to construct signature schemes, it’s also helpful to briefly review that primitive.
A digital signature scheme is a public key primitive in which a user (or “signer”) generates a pair of keys, called the public key and private key. The user retains the private key, and can use this to “sign” arbitrary messages — producing a resulting digital signature. Anyone who has possession of the public key can verify the correctness of a message and its associated signature.
From a security perspective, the main property we want from a signature scheme is unforgeability, or “existential unforgeability“. This requirement means that an attacker (someone who does not possess the private key) should not be able to forge a valid signature on a message that you did not sign. For more on the formal definitions of signature security, see this page.
The Lamport One-Time Signature
The first hash-based signature schemes was invented in 1979 by a mathematician named Leslie Lamport. Lamport observed that given only simple hash function — or really, a one-way function — it was possible to build an extremely powerful signature scheme.
Powerful that is, provided that you only need to sign one message! More on this below.
For the purposes of this discussion, let’s suppose we have the following ingredient: a hash function that takes in, say, 256-bit inputs and produces 256-bit outputs. SHA256 would be a perfect example of such a function. We’ll also need some way to generate random bits.
Let’s imagine that our goal is to sign 256 bit messages. To generate our secret key, the first thing we need to do is generate a series of 512 separate random bitstrings, each of 256 bits in length. For convenience, we’ll arrange those strings into two separate lists and refer to each one by an index as follows:
The lists represent the secret key that we’ll use for signing. To generate the public key, we now simply hash every one of those random strings using our function . This produces a second pair of lists:
We can now hand out our public key to the entire world. For example, we can send it to our friends, embed it into a certificate, or post it on Keybase.
Now let’s say we want to sign a 256-bit message using our secret key. The very first thing we do is break up and represent as a sequence of 256 individual bits:
The rest of the signing algorithm is blindingly simple. We simply work through the message from the first bit to the last bit, and select a string from one of the two secret key list. The list we choose from depends on value of the message bit we’re trying to sign.
Concretely, for i=1 to 256: if the message bit , we grab the secret key string from the list, and output that string as part of our signature. If the message bit we copy the appropriate string from the list. Having done this for each of the message bits, we concatenate all of the strings we selected. This forms our signature.
Here’s a toy illustration of the process, where (for simplicity) the secret key and message are only eight bits long. Notice that each colored box below represents a different 256-bit random string:
When a user — who already has the public key — receives a message and a signature, she can verify the signature easily. Let represent the component of the signature: for each such string. She simply checks the corresponding message bit and computes hash . If the result should match the corresponding element from . If the result should match the element in .
The signature is valid if every single element of the signature, when hashed, matches the correct portion of the public key. Here’s an (admittedly) sketchy illustration of the verification process, for at least one signature component:
If your initial impression of Lamport’s scheme is that it’s kind of insane, you’re both a bit right and a bit wrong.
Let’s start with the negative. First, it’s easy to see that Lamport signatures and keys are be quite large: on the order of thousands of bits. Moreover — and much more critically — there is a serious security limitation on this scheme: each key can only be used to sign one message. This makes Lamport’s scheme an example of what’s called a “one time signature”.
To understand why this restriction exists, recall that every Lamport signature reveals exactly one of the two possible secret key values at each position. If I only sign one message, the signature scheme works well. However, if I ever sign two messages that differ at any bit position , then I’m going to end up handing out both secret key values for that position. This can be a problem.
Imagine that an attacker sees two valid signatures on different messages. She may be able to perform a simple “mix and match” forgery attack that allows her to sign a third message that I never actually signed. Here’s how that might look in our toy example:
The degree to which this hurts you really depends on how different the messages are and how many of them you’ve given the attacker to play with. But it’s rarely good news.
So to sum up our observations about the Lamport signature scheme. It’s simple. It’s fast. And yet for various practical reasons it kind of sucks. Maybe we can do a little better.
From one-time to many-time signatures: Merkle’s tree-based signature
While the Lamport scheme is a good start, our inability to sign many messages with a single key is a huge drawback. Nobody was more inspired by this than Martin Hellman’s student Ralph Merkle. He quickly came up with a clever way to address this problem.
While we can’t exactly retrace Merkle’s steps, let’s see if we can recover some of the obvious ideas.
Let’s say our goal is to use Lamport’s signature to sign many messages — say of them. The most obvious approach is to simply generate different keypairs for the original Lamport scheme, then concatenate all the public keys together into one mega-key.
(Mega-key is a technical term I just invented).
If the signer holds on to all secret key components, she can now sign different messages by using exactly one secret Lamport key per message. This seems to solve the problem without ever requiring her to re-use a secret key. The verifier has all the public keys, and can verify all the received messages. No Lamport keys are ever used to sign twice.
Obviously this approach sucks big time.
Specifically, in this naive approach, signing times requires the signer to distribute a public key that is times as large as a normal Lamport public key. (She’ll also need to hang on to a similar pile of secret keys.) At some point people will get fed up with this, and probably won’t every get to be very large. Enter Merkle.
What Merkle proposed was a way to retain the ability to sign different messages, but without the linear-cost blowup of public keys. Merkle’s idea worked like this:
First, generate separate Lamport keypairs. We can call those .
Next, place each public key at one leaf of a Merkle hash tree (see below), and compute the root of the tree. This root will become the “master” public key of the new Merkle signature scheme.
The signer retains all of the Lamport public and secret keys for use in signing.
Merkle trees are described here. Roughly speaking, what they provide is a way to collect many different values such that they can be represented by a single “root” hash (of length 256 bits, using the hash function in our example). Given this hash, it’s possible to produce a simple “proof” that an element is in a given hash tree. Moreover, this proof has size that is logarithmic in the number of leaves in the tree.
To sign the message, the signer simply selects the public key from the tree, and signs the message using the corresponding Lamport secret key. Next, she concatenates the resulting signature to the Lamport public key and tacks on a “Merkle proof” that shows that this specific Lamport public key is contained within the tree identified by the root (i.e., the public key of the entire scheme). She then transmits this whole collection as the signature of the message.
(To verify a signature of this form, the verifier simply unpacks this “signature” as a Lamport signature, Lamport public key, and Merkle Proof. She verifies the Lamport signature against the given Lamport public key, and uses the Merkle Proof to verify that the Lamport public key is really in the tree. With these three objectives achieved, she can trust the signature as valid.)
This approach has the disadvantage of increasing the “signature” size by more than a factor of two. However, the master public key for the scheme is now just a single hash value, which makes this approach scale much more cleanly than the naive solution above.
As a final optimization, the secret key data can itself be “compressed” by generating all of the various secret keys using the output of a cryptographic pseudorandom number generator, which allows for the generation of a huge number of (apparently random) bits from a single short ‘seed’.
Making signatures and keys (a little bit) more efficient
Merkle’s approach allows any one-time signature to be converted into an -time signature. However, his construction still requires us to use some underlying one-time signature like Lamport’s scheme. Unfortunately the (bandwidth) costs of Lamport’s scheme are still relatively high.
There are two major optimizations that can help to bring down these costs. The first was also proposed by Merkle. We’ll cover this simple technique first, mainly because it helps to explain the more powerful approach.
If you recall Lamport’s scheme, in order sign a 256-bit message we required a vector consisting of 512 separate secret key (and public key) bitstrings. The signature itself was a collection of 256 of the secret bitstrings. (These numbers were motivated by the fact that each bit of the message to be signed could be either a “0” or a “1”, and thus the appropriate secret key element would need to be drawn from one of two different secret key lists.)
But here’s a thought: what if we don’t sign all of the message bits?
Let’s be a bit more clear. In Lamport’s scheme we sign every bit of the message — regardless of its value — by outputting one secret string. What if, instead of signing both zero values and one values in the message, we signed only the message bits were equal to one? This would cut the public and secret key sizes in half, since we could get rid of the list entirely.
We would now have only a single list of bitstrings in our secret key. For each bit position of the message where we would output a string . For every position where we would output… zilch. (This would also tend to reduce the size of signatures, since many messages contain a bunch of zero bits, and those would now ‘cost’ us nothing!)
An obvious problem with this approach is that it’s horrendously insecure. Please do not implement this scheme!
As an example, let’s say an attacker observes a (signed) message that begins with “1111…”, and she want to edit the message so it reads “0000…” — without breaking the signature. All she has to do to accomplish this is to delete several components of the signature! In short, while it’s very difficult to “flip” a zero bit into a one bit, it’s catastrophically easy to do the reverse.
But it turns out there’s a fix, and it’s quite elegant.
You see, while we can’t prevent an attacker from editing our message by turning one bits into zero bits, we can catch them. To do this, we tack on a simple “checksum” to the message,then sign the combination of the original message and the checksum. The signature verifier must verify the entire signature over both values, and also ensure that the received checksum is correct.
The checksum we use is trivial: it consists of a simple binary integer that represents the total number of zero bits in the original message.
If the attacker tries to modify the content of the message (excluding the checksum) in order to turn some one bit into a zero bit, the signature scheme won’t stop her. But this attack have the effect of increasing the number of zero bits in the message. This will immediately make the checksum invalid, and the verifier will reject the signature.
Of course, a clever attacker might also try to mess with the checksum (which is also signed along with the message) in order to “fix it up” by increasing the integer value of the checksum. However — and this is critical — since the checksum is a binary integer, in order to increase the value of the checksum, she would always need to turn some zero bit of the checksum into a one bit. But since the checksum is also signed, and the signature scheme prevents this kind of change, the attacker has nowhere to go.
(If you’re keeping track at home, this does somewhat increase the size of the ‘message’ to be signed. In our 256-bit message example, the checksum will require an additional eight bits and corresponding signature cost. However, if the message has many zero bits, the reduced signature size will typically still be a win.)
Winternitz: Trading space for time
The trick above reduces the public key size by half, and reduces the size of (some) signatures by a similar amount. That’s nice, but not really revolutionary. It still gives keys and signatures that are thousands of bits long.
It would be nice if we could make a bigger dent in those numbers.
The final optimization we’ll talk about was proposed by Robert Winternitz as a further optimization of Merkle’s technique above. In practical use it gives a 4-8x reduction in the size of signatures and public keys — at a cost of increasing both signing and verification time.
Winternitz’s idea is an example of a technique called a “time-space tradeoff“. This term refers to a class of solutions in which space is reduced at the cost of adding more computation time (or vice versa). To explain Winternitz’s approach, it helps to ask the following question:
What if, instead of signing messages composed of bits (0 or 1), we treated our messages as though they were encoded using larger symbol alphabets? For example, what if we signed four-bit ‘nibbles’? Or eight-bit bytes?
In Lamport’s original scheme, we had two lists of bitstrings as part of the signing (and public) key. One was for signing zero message bits, and the other was for one bits.
Now let’s say we want to sign bytes rather than bits. An obvious idea would be to increase the number of secret key lists (and public key) from two such list to 256 such lists — one list for each possible value of a message byte. The signer could work through the message one byte at a time, and pick from the much larger menu of key values.
Unfortunately, this solution really stinks. It reduces the size of the signature by a factor of eight, at a cost of increasing the public and secret key size by a factor of 256. Even this might be fine if the public keys could be used for many signatures, but they can’t — when it comes to key re-use, this “byte signing version of Lamport” suffers from the same limitations as the original Lamport signature.
All of which brings us to Winternitz’s idea.
Since it’s too expensive to store and distribute 256 truly random lists, what if we generated those lists programatically only when we needed them?
Winternitz’s idea was to generate single list of random seeds for our initial secret key. Rather than generating additional lists randomly, he proposed to use the hash function on each element of that initial secret key, in order to derive the next such list for the secret key: . And similarly, one can use the hash function again on that list to get the next list . And so on for many possible lists.
This is helpful in that we now only need to store a single list of secret key values , and we can derive all the others lists on-demand just by applying the hash function.
But what about the public key? This is where Winternitz gets clever.
Specifically, Winternitz proposed that the public key could be derived by applying the hash function one more time to the final secret key list. This would produce a single public key list . (In practice we only need 255 secret key lists, since we can treat the final secret key list as the public key.) The elegance of this approach is that given any one of the possible secret key values it’s always possible to check it against the public key, simply by hashing forward multiple times and seeing if we reach a public key element.
The whole process of key generation is illustrated below:
To sign the first byte of a message, we would pick a value from the appropriate list. For example, if the message byte was “0”, we would output a value from in our signature. If the message byte was “20”, we would output a value from . For bytes with the maximal value “255” we don’t have a secret key list. That’s ok: in this case we can output an empty string, or we can output the appropriate element of .
Note as well that in practice we don’t really need to store each of these secret key lists. We can derive any secret key value on demand given only the original list . The verifier only holds the public key vector and (as mentioned above) simply hashes forward an appropriate number of times — depending on the message byte — to see whether the result is equal to the appropriate component of the public key.
Like the Merkle optimization discussion in the previous section, the scheme as presented so far has a glaring vulnerability. Since the secret keys are related (i.e., ), anyone who sees a message that signs the message “0” can easily change the corresponding byte of the message to a “1”, and update the signature to match. In fact, an attacker can increment the value of any byte(s) in the message. Without some check on this capability, this would allow very powerful forgery attacks.
The solution to this problem is similar to the we discussed just above. To prevent an attacker from modifying the signature, the signer calculates and also signs a checksum of the original message bytes. The structure of this checksum is designed to prevent the attacker from incrementing any of the bytes, without invalidating the checksum. I won’t go into the gory details right now, but you can find them here.
It goes without saying that getting this checksum right is critical. Screw it up, even a little bit, and some very bad things can happen to you. This would be particularly unpleasant if you deployed these signatures in a production system.
Illustrated in one terrible picture, a 4-byte toy example of the Winternitz scheme looks like this:
What are hash-based signatures good for?
Throughout this entire discussion, we’ve mainly been talking about the how of hash-based signatures rather than the why of them. It’s time we addressed this. What’s the point of these strange constructions?
One early argument in favor of hash-based signatures is that they’re remarkably fast and simple. Since they only require only the evaluation of a hash function and some data copying, from a purely computational cost perspective they’re highly competitive with schemes like ECDSA and RSA. This could hypothetically be important for lightweight devices. Of course, this efficiency comes at a huge tradeoff in bandwidth efficiency.
More concretely: the imminent arrival of quantum computers is going to have a huge impact on the security of nearly all of our practical signature schemes, ranging from RSA to ECDSA and so on. This is due to the fact that Shor’s algorithm (and its many variants) provides us with a polynomial-time algorithm for solving the discrete logarithm and factoring problems, which is likely to render most of these schemes insecure.
Most implementations of hash-based signatures are not vulnerable to Shor’s algorithm. That doesn’t mean they’re completely immune to quantum computers, of course. The best general quantum attacks on hash functions are based on a search technique called Grover’s algorithm, which reduces the effective security of a hash function. However, the reduction in effective security is nowhere near as severe as Shor’s algorithm (it ranges between the square root and cube root), and so security can be retained by simply increasing the internal capacity and output size of the hash function. Hash functions like SHA3 were explicitly developed with large digest sizes to provide resilience against such attacks.
So at least in theory, hash-based signatures are interesting because they provide us with a line of defense against future quantum computers — for the moment, anyway.
What about the future?
Note that so far I’ve only discussed some of the “classical” hash-based signature schemes. All of the schemes I described above were developed in the 1970s or early 1980s. This hardly brings us up to present day.
After I wrote the initial draft of this article, a few people asked for pointers on more recent developments in the field. I can’t possibly give an exhaustive list here, but let me describe just a couple of the more recent ideas that others brought up (thanks to Zooko and Claudio Orlandi):
Signatures without state. A limitation of all the signature schemes above is that they require the signer to keep state between signatures. In the case of one-time signatures the reasoning is obvious: you have to avoid using any key more than once. But even in the multi-time Merkle signature, you have to remember which leaf public key you’re using, so you can avoid using any leaf twice. Even worse, the Merkle scheme requires the signer to construct all the keypairs up front, so the total number of signatures is bounded.
In the 1980s, Oded Goldreich pointed out that one can build signatures without these limitations. The idea is as follows: rather than generate all signatures up front, one can generate a short “certification tree” of one-time public keys. Each of these keys can be used to sign additional one-time public keys at a lower layer of the tree, and so on and so forth. Provided all of the private keys are generated deterministically using a single seed, this means that the full tree need not exist in full at key generation time, but can be built on-demand whenever a new key is generated. Each signature contains a “certificate chain” of signatures and public keys starting from the root and going down to a real signing keypair at the bottom of the tree.
This technique allows for the construction of extremely “deep” trees with a vast (exponential) number of possible signing keys. This allows us to construct so many one-time public keys that if we pick a signing key randomly (or pseudorandomly), then with high probability the same signing will never be used twice. This is intuition, of course. For a highly optimized and specific instantiation of this idea, see the SPHINCS proposal by Bernstein et al. The concrete SPHINCS-256 instantiation gives signatures that are approximately 41KB in size.
Picnic: post-quantum zero-knowledge based signatures. In a completely different direction lies Picnic. Picnic is based on a new non-interactive zero-knowledge proof system called ZKBoo. ZKBoo is a new ZK proof system that works on the basis of a technique called “MPC in the head”, where the prover uses multi-party computation to calculate a function with the prover himself. This is too complicated to explain in a lot of detail, but the end result is that one can then prove complicated statements using only hash functions.
The long and short of it is that Picnic and similar ZK proof systems provide a second direction for building signatures out of hash functions. The cost of these signatures is still quite large — hundreds of kilobytes. But future improvements in the technique could substantially reduce this size.
Epilogue: the boring security details
If you recall a bit earlier in this article, I spent some time describing the security properties of hash functions. This wasn’t just for show. You see, the security of a hash-based signature depends strongly on which properties a hash function is able to provide.
(And by implication, the insecurity of a hash-based signature depends on which properties of a hash function an attacker has managed to defeat.)
Most original papers discussing hash-based signatures generally hang their security arguments on the preimage-resistance of the hash function. Intuitively, this seems pretty straightforward. Let’s take the Lamport signature as an example. Given a public key element , an attacker who is able to compute hash preimages can easily recover a valid secret key for that component of the signature. This attack obviously renders the scheme insecure.
However, this argument considers only the case where an attacker has the public key but has not yet seen a valid signature. In this case the attacker has a bit more information. They now have (for example) both the public key and a portion of the secret key: and . If such an attacker can find a second pre-image for the public key she can’t sign a different message. But she has produced a new signature. In the strong definition of signature security (SUF-CMA) this is actually considered a valid attack. So SUF-CMA requires the slightly stronger property of second-preimage resistance.
Of course, there’s a final issue that crops up in most practical uses of hash-based signature schemes. You’ll notice that the description above assumes that we’re signing 256-bit messages. The problem with this is that in real applications, many messages are longer than 256 bits. As a consequence, most people use the hash function to first hash the message as and then the sign the resulting value instead of the message.
This leads to a final attack on the resulting signature scheme, since the existential unforgeability of the scheme now depends on the collision-resistance of the hash function. An attacker who can find two different messages such that has now found a valid signature on two different messages. This leads to a trivial break of EUF-CMA security.
In Fall 2016 I was invited to come to Miami as part of a team that independently validated some alleged flaws in implantable cardiac devices manufactured by St. Jude Medical (now part of Abbott Labs). These flaws were discovered by a company called MedSec. The story got a lot of traction in the press at the time, primarily due to the fact that a hedge fund called Muddy Waters took a large short position on SJM stock as a result of these findings. SJM subsequently sued both parties for defamation. The FDA later issued a recall for many of the devices.
Due in part to the legal dispute (still ongoing!), I never had the opportunity to write about what happened down in Miami, and I thought that was a shame: because it’s really interesting. So I’m belatedly putting up this post, which talks a bit MedSec’s findings, and implantable device security in general.
By the way: “we” in this case refers to a team of subject matter experts hired by Bishop Fox, and retained by legal counsel for Muddy Waters investments. I won’t name the other team members here because some might not want to be troubled by this now, but they did most of the work — and their names can be found in this public expert report (as can all the technical findings in this post.)
Quick disclaimers: this post is my own, and any mistakes or inaccuracies in it are mine and mine alone. I’m not a doctor so holy cow this isn’t medical advice. Many of the flaws in this post have since been patched by SJM/Abbot. I was paid for my time and travel by Bishop Fox for a few days in 2016, but I haven’t worked for them since. I didn’t ask anyone for permission to post this, because it’s all public information.
A quick primer on implantable cardiac devices
Implantable cardiac devices are tiny computers that can be surgically installed inside a patient’s body. Each device contains a battery and a set of electrical leads that can be surgically attached to the patient’s heart muscle.
When people think about these devices, they’re probably most familiar with the cardiacpacemaker. Pacemakers issue small electrical shocks to ensure that the heart beats at an appropriate rate. However, the pacemaker is actually one of the least powerful implantable devices. A much more powerful type of device is the Implantable Cardioverter-Defibrillator (ICD). These devices are implanted in patients who have a serious risk of spontaneously entering a dangerous state in which their heart ceases to pump blood effectively. The ICD continuously monitors the patient’s heart rhythm to identify when the patient’s heart has entered this condition, and applies a series of increasingly powerful shocks to the heart muscle to restore effective heart function. Unlike pacemakers, ICDs can issue shocks of several hundred volts or more, and can both stop and restart a patient’s normal heart rhythm.
Like most computers, implantable devices can communicate with other computers. To avoid the need for external data ports – which would mean a break in the patient’s skin – these devices communicate via either a long-range radio frequency (“RF”) or a near-field inductive coupling (“EM”) communication channel, or both. Healthcare providers use a specialized hospital device called a Programmer to update therapeutic settings on the device (e.g., program the device, turn therapy off). Using the Programmer, providers can manually issue commands that cause an ICD to shock the patient’s heart. One command, called a “T-Wave shock” (or “Shock-on-T”) can be used by healthcare providers to deliberately induce ventrical fibrillation. This capability is used after a device is implanted, in order to test the device and verify it’s functioning properly.
Because the Programmer is a powerful tool – one that could cause harm if misused – it’s generally deployed in a physician office or hospital setting. Moreover, device manufacturers may employ special precautions to prevent spurious commands from being accepted by an implantable device. For example:
Some devices require that all Programmer commands be received over a short-range communication channel, such as the inductive (EM) channel. This limits the communication range to several centimeters.
Other devices require that a short-range inductive (EM) wand must be used to initiate a session between the Programmer and a particular implantable device. The device will only accept long-range RF commands sent by the Programmer after this interaction, and then only for a limited period of time.
From a computer security perspective, both of these approaches have a common feature: using either approach requires some form of close-proximity physical interaction with the patient before the implantable device will accept (potentially harmful) commands via the long-range RF channel. Even if a malicious party steals a Programmer from a hospital, she may still need to physically approach the patient – at a distance limited to perhaps centimeters – before she can use the Programmer to issue commands that might harm the patient.
In addition to the Programmer, most implantable manufacturers also produce some form of “telemedicine” device. These devices aren’t intended to deliver commands like cardiac shocks. Instead, they exist to provide remote patient monitoring from the patient’s home. Telematics devices use RF or inductive (EM) communications to interrogate the implantable device in order to obtain episode history, usually at night when the patient is asleep. The resulting data is uploaded to a server (via telephone or cellular modem) where it can be accessed by healthcare providers.
What can go wrong?
Before we get into specific vulnerabilities in implantable devices, it’s worth asking a very basic question. From a security perspective, what should we even be worried about?
There are a number of answers to this question. For example, an attacker might abuse implantable device systems or infrastructure to recover confidential patient data (known as PHI). Obviously this would be bad, and manufacturers should design against it. But the loss of patient information is, quite frankly, kind of the least of your worries.
A much scarier possibility is that an attacker might attempt to harm patients. This could be as simple as turning off therapy, leaving the patient to deal with their underlying condition. On the much scarier end of the spectrum, an ICD attacker could find a way to deliberately issue dangerous shocks that could stop a patient’s heart from functioning properly.
Now let me be clear: this isn’t not what you’d call a high probability attack. Most people aren’t going to be targeted by sophisticated technical assassins. The concerning thing about this the impact of such an attack is significantly terrifying that we should probably be concerned about it. Indeed, some high-profile individuals have already taken precautions against it.
The real nightmare scenario is a mass attack in which a single resourceful attacker targets thousands of individuals simultaneously — perhaps by compromising a manufacturer’s back-end infrastructure — and threatens to harm them all at the same time. While this might seem unlikely, we’ve already seen attackers systematically target hospitals with ransomware. So this isn’t entirely without precedent.
Securing device interaction physically
The real challenge in securing an implantable device is that too much security could hurt you. As tempting as it might be to lard these devices up with security features like passwords and digital certificates, doctors need to be able to access them. Sometimes in a hurry.
This is a big deal. If you’re in a remote emergency room or hospital, the last thing you want is some complex security protocol making it hard to disable your device or issue a required shock. This means we can forget about complex PKI and revocation lists. Nobody is going to have time to remember a password. Even merely complicated procedures are out — you can’t afford to have them slow down treatment.
At the same time, these devices obviously must perform some sort of authentication: otherwise anyone with the right kind of RF transmitter could program them — via RF, from a distance. This is exactly what you want to prevent.
Many manufacturers have adopted an approach that cut through this knot. The basic idea is to require physical proximity before someone can issue commands to your device. Specifically, before anyone can issue a shock command (even via a long-range RF channel) they must — at least briefly — make close physical contact with the patient.
This proximity be enforced in a variety of ways. If you remember, I mentioned above that most devices have a short-range inductive coupling (“EM”) communications channel. These short-range channels seem ideal for establishing a “pairing” between a Programmer and an implantable device — via a specialized wand. Once the channel is established, of course, it’s possible to switch over to long-range RF communications.
This isn’t a perfect solution, but it has a lot going for it: someone could still harm you, but they would have to at least get a transmitter within a few inches of your chest before doing so. Moreover, you can potentially disable harmful commands from an entire class of device (like telemedecine monitoring devices) simply by leaving off the wand.
St. Jude Medical and MedSec
So given this background, what did St. Jude Medical do? All of the details are discussed in a full expert report published by Bishop Fox. In this post we I’ll focus on the most serious of MedSec’s claims, which can be expressed as follows:
Using only the hardware contained within a “Merlin @Home” telematics device, it was possible to disable therapy and issue high-power “shock” commands to an ICD from a distance, and without first physically interacting with the implantable device at close range.
This vulnerability had several implications:
The existence of this vulnerability implies that – through a relatively simple process of “rooting” and installing software on a Merlin @Home device – a malicious attacker could create a device capable of issuing harmful shock commands to installed SJM ICD devices at a distance. This is particularly worrying given that Merlin @Home devices are widely deployed in patients’ homes and can be purchased on eBay for prices under $30. While it might conceivably be possible to physically secure and track the location of all PCS Programmer devices, it seems challenging to physically track the much larger fleet of Merlin @Home devices.
More critically, it implies that St. Jude Medical implantable devices do not enforce a close physical interaction (e.g., via an EM wand or other mechanism) prior to accepting commands that have the potential to harm or even kill patients. This may be a deliberate design decision on St. Jude Medical’s part. Alternatively, it could be an oversight. In either case, this design flaw increases the risk to patients by allowing for the possibility that remote attackers might be able to cause patient harm solely via the long-range RF channel.
If it is possible – using software modifications only – to issue shock commands from the Merlin @Home device, then patients with an ICD may be vulnerable in the hypothetical event that their Merlin @Home device becomes remotely compromised by an attacker. Such a compromise might be accomplished remotely via a network attack on a single patient’s Merlin @Home device. Alternatively, a compromise might be accomplished at large scale through a compromise of St. Jude Medical’s server infrastructure.
We stress that the final scenario is strictly hypothetical. MedSec did not allege a specific vulnerability that allows for the remote compromise of Merlin @Home devices or SJM infrastructure. However, from the perspective of software and network security design, these attacks are one of the potential implications of a design that permits telematics devices to send such commands to an implantable device. It is important to stress that none of these attacks would be possible if St. Jude Medical’s design prohibited the implantable from accepting therapeutic commands from the Merlin @Home device (e.g., by requiring close physical interaction via the EM wand, or by somehow authenticating the provenance of commands and restricting critical commands to be sent by the Programmer only).
Validating MedSec’s claim
To validate MedSec’s claim, we examined their methodology from start to finish. This methodology included extracting and decompiling Java-based software from a single PCS Programmer; accessing a Merlin @Home device to obtain a root shell via the JTAG port; and installing a new package of custom software written by MedSec onto a used Merlin @Home device.
We then observed MedSec issue a series of commands to an ICD device using a Merlin @Home device that had been customized (via software) as described above. We used the Programmer to verify that these commands were successfully received by the implantable device, and physically confirmed that MedSec had induced shocks by attaching a multimeter to the leads on the implantable device.
Finally, we reproduced MedSec’s claims by opening the case of a second Merlin @Home device (after verifying that the tape was intact over the screw holes), obtaining a shell by connecting a laptop computer to the JTAG port, and installing MedSec’s software on the device. We were then able to issue commands to the ICD from a distance of several feet. This process took us less than three hours in total, and required only inexpensive tools and a laptop computer.
What are the technical details of the attack?
Simply reproducing a claim is only part of the validation process. To verify MedSec’s claims we also needed to understand why the attack described above was successful. Specifically, we were interested in identifying the security design issues that make it possible for a Merlin @Home device to successfully issue commands that are not intended to be issued from this type of device. The answer to this question is quite technical, and involves the specific way that SJM implantable devices verify commands before accepting them.
MedSec described to us the operation of SJM’s command protocol as part of their demonstration. They also provided us with Java JAR executable code files taken from the hard drive of the PCS Programmer. These files, which are not obfuscated and can easily be “decompiled” into clear source code, contain the software responsible for implementing the Programmer-to-Device communications protocol.
By examining the SJM Programmer code, we verified that Programmer commands are authenticated through the inclusion of a three-byte (24 bit) “authentication tag” that must be present and correct within each command message received by the implantable device. If this tag is not correct, the device will refuse to accept the command.
From a cryptographic perspective, 24 bits is a surprisingly short value for an important authentication field. However, we note that even this relatively short tag might be sufficient to prevent forgery of command messages – provided the tag ws calculated using a secure cryptographic function (e.g., a Message Authentication Code) using a fresh secret key that cannot be predicted by an the attacker.
Based on MedSec’s demonstration, and on our analysis of the Programmer code, it appears that SJM does not use the above approach to generate authentication tags. Instead, SJM authenticates the Programmer to the implantable with the assistance of a “key table” that is hard-coded within the Java code within the Programmer. At minimum, any party who obtains the (non-obfuscated) Java code from a legitimate SJM Programmer can gain the ability to calculate the correct authentication tags needed to produce viable commands – without any need to use the Programmer itself.
Moreover, MedSec determined – and successfully demonstrated – that there exists a “Universal Key”, i.e., a fixed three-byte authentication tag, that can be used in place of the calculated authentication tag. We identified this value in the Java code provided by MedSec, and verified that it was sufficient to issue shock commands from a Merlin @Home to an implantable device.
While these issues alone are sufficient to defeat the command authentication mechanism used by SJM implantable devices, we also analyzed the specific function that is used by SJM to generate the three-byte authentication tag. To our surprise, SJM does not appear to use a standard cryptographic function to compute this tag. Instead, they use an unusual and apparently “homebrewed” cryptographic algorithm for the purpose.
Specifically, the PCS Programmer Java code contains a series of hard-coded 32-bit RSA public keys. To issue a command, the implantable device sends a value to the Programmer. This value is then “encrypted” by the Programmer using one of the RSA public keys, and the resulting output is truncated to produce a 24-bit output tag.
The above is not a standard cryptographic protocol, and quite frankly it is difficult to see what St. Jude Medical is trying to accomplish using this technique. From a cryptographic perspective it has several problems:
The RSA public keys used by the PCS Programmers are 32 bits long. Normal RSA keys are expected to be a minimum of 1024 bits in length. Some estimates predict that a 1024-bit RSA key can be factored (and thus rendered insecure) in approximately one year using a powerful network of supercomputers. Based on experimentation, we were able to factor the SJM public keys in less than one second on a laptop computer.
Even if the RSA keys were of an appropriate length, the SJM protocol does not make use of the corresponding RSA secret keys. Thus the authentication tag is not an RSA signature, nor does it use RSA in any way that we are familiar with.
As noted above, since there is no shared session key established between the specific implantable device and the Programmer, the only shared secret available to both parties is contained within the Programmer’s Java code. Thus any party who extracts the Java code from a PCS Programmer will be able to transmit valid commands to any SJM implantable device.
Our best interpretation of this design is that the calculation is intended as a form of “security by obscurity”, based on the assumption that an attacker will not be able to reverse engineer the protocol. Unfortunately, this approach is rarely successful when used in security systems. In this case, the system is fundamentally fragile – due to the fact that code for computing the correct authentication tag is likely available in easily-decompiled Java bytecode on each St. Jude Medical Programmer device. If this code is ever extracted and published, all St. Jude Medical devices become vulnerable to command forgery.
How to remediate these attacks?
To reiterate, the fundamental security concerns with these St. Jude Medical devices (as of 2016) appeared to be problems of design. These were:
SJM implantable devices did not require close physical interaction prior to accepting commands (allegedly) sent by the Programmer.
SJM did not incorporate a strong cryptographic authentication mechanism in its RF protocol to verify that commands are truly sent by the Programmer.
Even if the previous issue was addressed, St. Jude did not appear to have an infrastructure for securely exchanging shared cryptographic keys between a legitimate Programmer and an implantable device.
There are various ways to remediate these issues. One approach is to require St. Jude implantable devices to exchange a secret key with the Programmer through a close-range interaction involving the Programmer’s EM wand. A second approach would be to use a magnetic sensor to verify the presence of a magnet on the device, prior to accepting Programmer commands. Other solutions are also possible. I haven’t reviewed the solution SJM ultimately adopted in their software patches, and I don’t know how many users patched.
Implantable devices offer a number of unique security challenges. It’s naturally hard to get these things right. At the same time, it’s important that vendors take these issues seriously, and spend the time to get cryptographic authentication mechanisms right — because once deployed, these devices are very hard to repair, and the cost of a mistake is extremely high.
Last week Apple made an announcement describing changes to the iCloud service for users residing in mainland China. Beginning on February 28th, all users who have specified China as their country/region will have their iCloud data transferred to the GCBD cloud services operator in Guizhou, China.
Chinese news sources optimistically describe the move as a way to offer improved network performance to Chinese users, while Apple admits that the change was mandated by new Chinese regulations on cloud services. Both explanations are almost certainly true. But neither answers the following question: regardless of where it’s stored, how secure is this data?
Apple has strong data privacy and security protections in place and no backdoors will be created into any of our systems”
That sounds nice. But what, precisely, does it mean? If Apple is storing user data on Chinese services, we have to at least accept the possibility that the Chinese government might wish to access it — and possibly without Apple’s permission. Is Apple saying that this is technically impossible?
This is a question, as you may have guessed, that boils down to encryption.
Does Apple encrypt your iCloud backups?
Unfortunately there are many different answers to this question, depending on which part of iCloud you’re talking about, and — ugh — which definition you use for “encrypt”. The dumb answer is the one given in the chart on the right: all iCloud data probably is encrypted. But that’s the wrong question. The right question is: who holds the key(s)?
There’s a pretty simple thought experiment you can use to figure out whether you (or a provider) control your encryption keys. I call it the “mud puddle test”. It goes like this:
Imagine you slip in a mud puddle, in the process (1) destroying your phone, and (2) developing temporary amnesia that causes you to forget your password. Can you still get your iCloud data back? If you can (with the help of Apple Support), then you don’t control the key.
With one major exception — iCloud Keychain, which I’ll discuss below — iCloud fails the mud puddle test. That’s because most Apple files are not end-to-end encrypted. In fact, Apple’s iOS security guide is clear that it sends the keys for encrypted files out to iCloud.
However, there is a wrinkle. You see, iCloud isn’t entirely an Apple service, not even here in the good-old U.S.A. In fact, the vast majority of iCloud data isn’t actually stored by Apple at all. Every time you back up your phone, your (encrypted)
data is transmitted directly to a variety of third-party cloud service providers including Amazon, Google and Microsoft.
And this is, from a privacy perspective, mostly** fine! Those services act merely as “blob stores”, storing unreadable encrypted data files uploaded by Apple’s customers. At least in principle, Apple controls the encryption keys for that data, ideally on a server located in a dedicated Apple datacenter.*
So what exactly is Apple storing in China?
You see, it’s entirely possible that the new Chinese cloud stores will perform the same task that Amazon AWS, Google, or Microsoft do in the U.S. That is, they’re storing encrypted blobs of data that can’t be decrypted without first contacting the iCloud mothership back in the U.S. That would at least be one straightforward reading of Apple’s announcement, and it would also be the most straightforward mapping from iCloud’s current architecture and whatever it is Apple is doing in China.
Of course, this interpretation seems hard to swallow. In part this is due to the fact that some of the new Chinese regulations appear to include guidelines for user monitoring. I’m no lawyer, and certainly not an expert in Chinese law — so I can’t tell you if those would apply to backups. But it’s at least reasonable to ask whether Chinese law enforcement agencies would accept the total inability to access this data without phoning home to Cupertino, not to mention that this would give Apple the ability to instantly wipe all Chinese accounts. Solving these problems (for China) would require Apple to store keys as well as data in Chinese datacenters.
The critical point is that these two interpretations are not compatible. One implies that Apple is simply doing business as usual. The other implies that they may have substantially weakened the security protections of their system — at least for Chinese users.
And here’s my problem. If Apple needs to fundamentally rearchitect iCloud to comply with Chinese regulations, that’s certainly an option. But they should say explicitly and unambiguously what they’ve done. If they don’t make things explicit, then it raises the possibility that they could make the same changes for any other portion of the iCloud infrastructure without announcing it.
It seems like it would be a good idea for Apple just to clear this up a bit.
You said there was an exception. What about iCloud Keychain?
I said above that there’s one place where iCloud passes the mud puddle test. This is Apple’s Cloud Key Vault, which is currently used to implement iCloud Keychain. This is a special service that stores passwords and keys for applications, using a much stronger protection level than is used in the rest of iCloud. It’s a good model for how the rest of iCloud could one day be implemented.
For a description, see here. Briefly, the Cloud Key Vault uses a specialized piece of hardware called a Hardware Security Module (HSM) to store encryption keys. This HSM is a physical box located on Apple property. Users can access their own keys if and only if they know their iCloud Keychain password — which is typically the same as the PIN/password on your iOS device. However, if anyone attempts to guess this PIN too many times, the HSM will wipe that user’s stored keys.
The critical thing is that the “anyone” mentioned above includes even Apple themselves. In short: Apple has designed a key vault that even they can’t be forced to open. Only customers can get their own keys.
What’s strange about the recent Apple announcement is that users in China will apparently still have access to iCloud Keychain. This means that either (1) at least some data will be totally inaccessible to the Chinese government, or (2) Apple has somehow weakened the version of Cloud Key Vault deployed to Chinese users. The latter would be extremely unfortunate, and it would raise even deeper questions about the integrity of Apple’s systems.
Probably there’s nothing funny going on, but this is an example of how Apple’s vague (and imprecise) explanations make it harder to trust their infrastructure around the world.
So what should Apple do?
Unfortunately, the problem with Apple’s disclosure of its China’s news is, well, really just a version of the same problem that’s existed with Apple’s entire approach to iCloud.
Where Apple provides overwhelming detail about their best security systems (file encryption, iOS, iMessage), they provide distressingly little technical detail about the weaker links like iCloud encryption. We know that Apple can access and even hand over iCloud backups to law enforcement. But what about Apple’s partners? What about keychain data? How is this information protected? Who knows.
This vague approach to security might make it easier for Apple to brush off the security impact of changes like the recent China news (“look, no backdoors!”) But it also confuses the picture, and calls into doubt any future technical security improvements that Apple might be planning to make in the future. For example, this article from 2016 claims that Apple is planning stronger overall encryption for iCloud. Are those plans scrapped? And if not, will those plans fly in the new Chinese version of iCloud? Will there be two technically different versions of iCloud? Who even knows?
And at the end of the day, if Apple can’t trust us enough to explain how their systems work, then maybe we shouldn’t trust them either.
* This is actually just a guess. Apple could also outsource their key storage to a third-party provider, even though this would be dumb.
** A big caveat here is that some iCloud backup systems use convergent encryption, also known as “message locked encryption”. The idea in these systems is that file encryption keys are derived by hashing the file itself. Even if a cloud storage provider does not possess encryption keys, it might be able to test if a user has a copy of a specific file. This could be problematic. However, it’s not really clear from Apple’s documentation if this attack is feasible. (Thanks to RPW for pointing this out.)
If you’ve read this blog before, you know that secure messaging is one of my favorite topics. However, recently I’ve been a bit disappointed. My sadness comes from the fact that lately these systems have been getting too damned good. That is, I was starting to believe that most of the interesting problems had finally been solved.
If nothing else, today’s post helped disabuse me of that notion.
This result comes from a new paper by Rösler, Mainka and Schwenk from Ruhr-Universität Bochum (affectionately known as “RUB”). The RUB paper paper takes a close look at the problem of group messaging, and finds that while messengers may be doing fine with normal (pairwise) messaging, group messaging is still kind of a hack.
If all you want is the TL;DR, here’s the headline finding: due to flaws in both Signal and WhatsApp (which I single out because I use them), it’s theoretically possible forstrangers to add themselves to an encrypted group chat. However, the caveat is that these attacks are extremely difficult to pull off in practice, so nobody needs to panic. But both issues are very avoidable, and tend to undermine the logic of having an end-to-end encryption protocol in the first place. (Wired also has a good article.)
First, some background.
How do end-to-end encryption and group chats work?
In recent years we’ve seenplenty of evidence that centralized messaging servers aren’t a very good place to store confidential information. The good news is: we’re not stuck with them. One of the most promising advances in the area of secure communications has been the recentwidespread deployment of end-to-end (e2e) encrypted messaging protocols.
At a high level, e2e messaging protocols are simple: rather than sending plaintext to a server — where it can be stolen or read — the individual endpoints (typically smartphones) encrypt all of the data using keys that the server doesn’t possess. The server has a much more limited role, moving and storing only meaningless ciphertext. With plenty of caveats, this means a corrupt server shouldn’t be able to eavesdrop on the communications.
In pairwise communications (i.e., Alice communicates with only Bob) this encryption is conducted using a mix of public-key and symmetric key algorithms. One of the most popular mechanisms is the Signal protocol, which is used by Signal and WhatsApp (notable for having 1.3 billion users!) I won’t discuss the details of the Signal protocol here, except to say that it’s complicated, but it works pretty well.
A fly in the ointment is that the standard Signal protocol doesn’t work quite as well for group messaging, primarily because it’s not optimized for broadcasting messages to many users.
To handle that popular case, both WhatsApp and Signal use a small hack. It works like this: each group member generates a single “group key” that this member will use to encrypt all of her messages to everyone else in the group. When a new member joins, everyone who is already in the group needs to send a copy of their group key to the new member (using the normal Signal pairwise encryption protocol). This greatly simplifies the operation of group chats, while ensuring that they’re still end-to-end encrypted.
How do members know when to add a new user to their chat?
Here is where things get problematic.
From a UX perspective, the idea is that only one person actually initiates the adding of a new group member. This person is called the “administrator”. This administrator is the only human being who should actually do anything — yet, her one click must cause some automated action on the part of every other group members’ devices. That is, in response to the administrator’s trigger, all devices in the group chat must send their keys to this new group member.
(In Signal, every group member is an administrator. In WhatsApp it’s just a subset of the members.)
The trigger is implemented using a special kind of message called (unimaginatively) a “group management message”. When I, as an administrator, add Tom to a group, my phone sends a group management message to all the existing group members. This instructs them to send their keys to Tom — and to notify the members visually so that they know Tom is now part of the group. Obviously this should only happen if I reallydid add Tom, and not if some outsider (like that sneaky bastard Tom himself!) tries to add Tom.
And this is where things get problematic.
Ok, what’s the problem?
According to the RUB paper, both Signal and WhatsApp fail to properly authenticate group management messages.
The upshot is that, at least in theory, this makes it possible for an unauthorized person — not a group administrator, possibly not even a member of the group — to add someone to your group chat.
The issues here are slightly different between Signal and WhatsApp. To paraphrase Tolstoy, every working implementation is alike, but every broken one is broken in its own way. And WhatsApp’s implementation is somewhat worse than Signal. Here I’ll break them down.
Signal. Signal takes a pragmatic (and reasonable) approach to group management. In Signal, every group member is considered an administrator — which means that any member can add a new member. Thus if I’m a member of a group, I can add a new member by sending a group management message to every other member. These messages are sent encrypted via the normal (pairwise) Signal protocol.
The group management message contains the “group ID” (a long, unpredictable number), along with the identity of the person I’m adding. Because messages are sent using the Signal (pairwise) protocol, they should be implicitly authenticated as coming from me — because authenticity is a property that the pairwise Signal protocol already offers. So far, this all sounds pretty good.
The problem that the RUB researchers discovered through testing, is that while the Signal protocol does authenticate that the group management comes from me, it doesn’t actually check that I am a member of the group — and thus authorized to add the new user!
In short, if this finding is correct, it turns out that any random Signal user in the world can you send a message of the form “Add Mallory to the Group 8374294372934722942947”, and (if you happen to belong to that group) your app will go ahead and try to do it.
The good news is that in Signal the attack is very difficult to execute. The reason is that in order to add someone to your group, I need to know the group ID. Since the group ID is a random 128-bit number (and is never revealed to non-group-members or even the server**) that pretty much blocks the attack. The main exception to this is former group members, who already know the group ID — and can now add themselves back to the group with impunity.
(And for the record, while the group ID may block the attack, it really seems like a lucky break — like falling out of a building and landing on a street awning. There’s no reason the app should process group management messages from random strangers.)
So that’s the good news. The bad news is that WhatsApp is a bit worse.
WhatsApp. WhatsApp uses a slightly different approach for its group chat. Unlike Signal, the WhatsApp server plays a significant role in group management, which means that it determines who is an administrator and thus authorized to send group management messages.
Additionally, group management messages are not end-to-end encrypted or signed. They’re sent to and from the WhatsApp server using transport encryption, but not the actual Signal protocol.
When an administrator wishes to add a member to a group, it sends a message to the server identifying the group and the member to add. The server then checks that the user is authorized to administer that group, and (if so), it sends a message to every member of the group indicating that they should add that user.
The flaw here is obvious: since the group management messages are not signed by the administrator, a malicious WhatsApp server can add any user it wants into the group. This means the privacy of your end-to-end encrypted group chat is only guaranteed if you actually trust the WhatsApp server.
This undermines the entire purpose of end-to-end encryption.
But this is silly. Don’t we trust the WhatsApp server? And what about visual notifications?
One perfectly reasonable response is that exploiting this vulnerability requires a compromise of the WhatsApp server (or legal compulsion, perhaps). This seems fairly unlikely.
And yet, the entire point of end-to-end encryption is to remove the server from the trusted computing base. We haven’t entirely achieved this yet, thanks to things like key servers. But we are making progress. This bug is a step back, and it’s one a sophisticated attacker potentially could exploit.
A second obvious objection to these issues is that adding a new group member results in a visual notification to each group member. However, it’s not entirely clear that these messages are very effective. In general they’re relatively easy to miss. So these are meaningful bugs, and things that should be fixed.
How do you fix this?
The great thing about these bugs is that they’re both eminently fixable.
The RUB paper points out some obvious countermeasures. In Signal, just make sure that the group management messages come from a legitimate member of the group. In WhatsApp, make sure that the group management messages are signed by an administrator.*
Obviously fixes like this are a bit complex to roll out, but none of these should be killers.
Is there anything else in the paper?
Oh yes, there’s quite a bit more. But none of it is quite as dramatic. For one thing, it’s possible for attackers to block message acknowledgements in group chats, which means that different group members could potentially see very different versions of the chat. There are also several cases where forward secrecy can be interrupted. There’s also some nice analysis of Threema, if you’re interested.
I need a lesson. What’s the moral of this story?
The biggest lesson is that protocol specifications are never enough. Both WhatsApp and Signal (to an extent) have detailed protocol specifications that talk quite a bit about the cryptography used in their systems. And yet the issues reported in the RUB paper not obvious from reading these summaries. I certainly didn’t know about them.
In practice, these problems were only found through testing.
So the main lesson here is: test, test, test. This is a strong argument in favor of open-source applications and frameworks that can interact with private-garden services like Signal and WhatsApp. It lets us see what the systems are getting right and getting wrong.
The second lesson — and a very old one — is that cryptography is only half the battle. There’s no point in building the most secure encryption protocol in the world if someone can simply instruct your client to send your keys to Mallory. The greatest lesson of all time is that real cryptosystems are always broken this way — and almost never through the fancy cryptographic attacks we love to write about.
* The challenge here is that since WhatsApp itself determines who the administrators are, this isn’t quite so simple. But at very least you can ensure that someone in the group was responsible for the addition.
** According to the paper, the Signal group IDs are always sent encrypted between group members and are never revealed to the Signal server. Indeed, group chat messages look exactly like pairwise chats, as far as the server is concerned. This means only current or former group members should know the group ID.
Yesterday, David Benjamin posted a pretty esoteric note on the IETF’s TLS mailing list. At a superficial level, the post describes some seizure-inducingly boring flaws in older Canon printers. To most people that was a complete snooze. To me and some of my colleagues, however, it was like that scene in X-Files where Mulder and Scully finally learn that aliens are real.
Those fossilized printers confirmed a theory we’d developed in 2014, but had been unable to prove: namely, the existence of a specific feature in RSA’s BSAFE TLS library called “Extended Random” — one that we believe to be evidence of a concerted effort by the NSA to backdoor U.S. cryptographic technology.
Before I get to the details, I want to caveat this post in two different ways. First, I’ve written about the topic of cryptographic backdoors way too much. In 2013, the Snowden revelations revealed the existence of a campaign to sabotage U.S. encryption systems. Since that time, cryptographers have spent thousands of hours identifying, documenting, and trying to convince people to care about these backdoors. We’re tired and we want to do more useful things.
The second caveat covers a problem with any discussion of cryptographic backdoors. Specifically, you never really get absolute proof. There’s always some innocent or coincidental explanation that could sort of fit the evidence — maybe it was all a stupid mistake. So you look for patterns of unlikely coincidences, and use Occam’s razor a lot. You don’t get a Snowden every day.
With all that said, let’s talk about Extended Random, and what this tells us about the NSA. First some background.
Dual_EC_DRBG and RSA BSAFE
To understand the context of this discovery, you need to know about a standard called Dual EC DRBG. This was a proposed random number generator that the NSA developed in the early 2000s. It was standardized by NIST in 2007, and later deployed in some important cryptographic products — though we didn’t know it at the time.
Dual EC has a major problem, which is that it likely contains a backdoor. This was pointed out in 2007 by Shumow and Ferguson, and effectively confirmed by the Snowden leaks in 2013. Drama ensued. NIST responded by pulling the standard. (For an explainer on the Dual EC backdoor, see here.)
Somewhere around this time the world learned that RSA Security had made Dual EC the default random number generator in their popular cryptographic library, which was called BSAFE. RSA hadn’t exactly kept this a secret, but it was such a bonkers thing to do that nobody (in the cryptographic community) had known. So for years RSA shipped their library with this crazy algorithm, which made its way into all sorts of commercial devices.
The RSA drama didn’t quite end there, however. In late 2013, Reuters reported that RSA had taken $10 million to backdoor their software. RSA sort of denies this. Or something. It’s not really clear.
Regardless of the intention, it’s known that RSA BSAFE did incorporate Dual EC. This could have been an innocent decision, of course, since Dual EC was a NIST standard. To shed some light on that question, in 2014 my colleagues and I decided to reverse-engineer the BSAFE library to see if it the alleged backdoor in Dual EC was actually exploitable by an attacker like the NSA. We figured that specific engineering decisions made by the library designers could be informative in tipping the scales one way or the other.
It turns out they were.
In the course of reverse engineering the Java version of BSAFE, we discovered a funny inclusion. Specifically, we found that BSAFE supports a non-standard extension to the TLS protocol called “Extended Random”.
The Extended Random extension is an IETF Draft proposed by an NSA employee named Margaret Salter (at some point the head of NSA’s Information Assurance Directorate, which worked on “defensive” crypto for DoD) along with Eric Rescorla as a contractor. (Eric was very clearly hired to develop a decent proposal that wouldn’t hurt TLS, and would primarily be used on government machines. The NSA did not share their motivations with him.)
It’s important to note that Extended Random by itself does not introduce any cryptographic vulnerabilities. All it does is increase the amount of random data (“nonces”) used in a TLS protocol connection. This shouldn’t hurt TLS at all, and besides it was largely intended for U.S. government machines.
The only thing that’s interesting about Extended Random is what happens when that random data is generated using the Dual EC algorithm. Specifically, this extra data acts as “rocket fuel”, significantly increasing the efficiency of exploiting the Dual EC backdoor to decrypt TLS connections.
In short, if you’re an agency like the NSA that’s trying to use Dual EC as a backdoor to intercept communications, you’re muchbetter off with a system that uses both Dual EC DRBG and Extended Random. Since Extended Random was never standardized by the IETF, it shouldn’t be in any systems. In fact, to the best of our knowledge, BSAFE is the only system in the world that implements it.
In addition to Extended Random, we discovered a variety of features that, combined with the Dual EC backdoor, could make RSA BSAFE fairly easy to exploit. But Extended Random is by far the strangest and hardest to justify.
So where did this standard come from? For those who like technical mysteries, it turns out that Extended Random isn’t the only funny-smelling proposal the NSA made. It’s actually one of four failed IETF proposals made by NSA employees, or contractors who work closely with the NSA, all of which try to boost the amount of randomness in TLS. Thomas Ptacek has a mind-numbingly detailed discussion of these proposals and his view of their motivation in this post.
Oh my god I never thought spies could be so boring. What’s the new development?
Despite the fact that we found Extended Random in RSA BSAFE (a free version we downloaded from the Internet), a fly in the ointment was that it didn’t actually seem to be enabled. That is: the code was there but the switches to enable it were hard-coded to “off”.
This kind of put a wrench in our theory that RSA might have included Extended Random to make BSAFE connections more exploitable by the NSA. There might be some commercial version of BSAFE out there with this code active, but we were never able to find it or prove it existed. And even worse, it might appear only in some special “U.S. government only” version of BSAFE, which would tend to undermine the theory that there was something intentional about including this code — after all, why would the government spy on itself?
Which finally brings us to the news that appeared on the TLS mailing list the other day. It turns out that certain Canon printers are failing to respond properly to connections made using the new version of TLS (which is called 1.3), because they seem to have implemented an unauthorized TLS extension using the same number as an extension that TLS 1.3 needs in order to operate correctly. Here’s the relevant section of David’s post:
The web interface on some Canon printers breaks with 1.3-capable ClientHello messages. We have purchased one and confirmed this with a PIXMA MX492. User reports suggest that it also affects PIXMA MG3650 and MX495 models. It potentially affects a wide range of Canon printers.
These printers use the RSA BSAFE library to implement TLS and this library implements the extended_random extension and assigns it number 40. This collides with the key_share extension and causes 1.3-capable handshakes to fail.
So in short, this news appears to demonstrate that commercial (non-free) versions of RSA BSAFE did deploy the Extended Random extension, and made it active within third-party commercial products. Moreover, they deployed it specifically to machines — specifically off-the-shelf commercial printers — that don’t seem to be reserved for any kind of special government use.
(If these turn out to be special Department of Defense printers, I will eat my words.)
Ironically, the printers are now the only thing that still exhibits the features of this (now deprecated) version of BSAFE. This is not because the NSA was targeting printers. Whatever devices they were targeting are probably gone by now. It’s because printer firmware tends to be obsolete and yet highly persistent. It’s like a remote pool buried beneath the arctic circle that preserves software species that would otherwise vanish from the Internet.
Which brings us to the moral of the story: not only are cryptographic backdoors a terrible idea, but they totally screw up the assigned numbering system for future versions of your protocol.
Actually no, that’s a pretty useless moral. Instead, let’s just say that you can deploy a cryptographic backdoor, but it’s awfully hard to control where it will end up.
(Warning: nerdy inside-baseball academic blog post follows. If you’re looking for exciting crypto blogging, try back in a couple of days.)
If there’s one thing that academic computer scientists love (or love to hate), it’s comparing themselves to other academics. We don’t do what we do for the big money, after all. We do it — in large part — because we’re curious and want to do good science. (Also there’s sometimes free food.) But then there’s a problem: who’s going to tell is if we’re doing good science?
To a scientist, the solution seems obvious. We just need metrics. And boy, do we get them. Modern scientists can visit Google Scholar to get all sorts of information about their citation count, neatly summarized with an “H-index” or an “i10-index”. These metrics aren’t great, but they’re a good way to pass an afternoon filled with self-doubt, if that’s your sort of thing.
But what if we want to do something more? What if we want to compare institutions as well as individual authors? And even better, what if we could break those institutions down into individual subfields? You could do this painfully on Google Scholar, perhaps. Or you could put your faith in the abominable and apparently wholly made-up U.S. News rankings, as many academics (unfortunately) do.
Alternatively, you could actually collect some data about what scientists are publishing, and work with that.
This is the approach of a new site called “Computer Science Rankings”. As best I can tell, CSRankings is largely an individual project, and doesn’t have the cachet (yet) of U.S. News. At the same time, it provides researchers and administrators with something they love: another way to compare themselves, and to compare different institutions. Moreover, it does so with realdata (rather than the Ouija board and blindfold that U.S. News uses). I can’t see it failing to catch on.
And that worries me, because the approach of CSRankings seems a bit arbitrary. And I’m worried about what sort of things it might cause us to do.
You see, people in our field take rankings very seriously. I know folks who have moved their families to the other side of the country over a two-point ranking difference in the U.S. News rankings — despite the fact that we all agree those are absurd. And this is before we consider the real impact on salaries, promotions, and awards of rankings (individual and institutional). People optimize their careers and publications to maximize these stats, not because they’re bad people, but because they’re (mostly) rational and that’s what rankings inspire rational people do.
To me this means we should think very carefully about what our rankings actually say.
Which brings me to the meat of my concerns with CSRankings. At a glance, the site is beautifully designed. It allows you to look at dozens of institutions, broken down by CS subfield. Within those subfields it ranks institutions by a simple metric: adjusted publication counts in top conferences by individual authors.
The calculation isn’t complicated. If you wrote a paper by yourself and had it published in one of the designated top conferences in your field, you’d get a single point. If you wrote a paper with a co-author, then you’d each get half a point. If you wrote a paper that doesn’t appear in a top conference, you get zero points. Your institution gets the sum-total of all the points its researchers receive.
If you believe that people are rational actors optimize for rankings, you might start to see the problem.
First off, what CSRankings is telling us is that we should ditch those pesky co-authors. If I could write a paper with one graduate student, but a second student also wants to participate, tough cookies. That’s the difference between getting 1/2 a point and 1/3 of a point. Sure, that additional student might improve the paper dramatically. They might also learn a thing or two. But on the other hand, they’ll hurt your rankings.
(Note: currently on CSRankings, graduate students at the same institution don’t get included in the institutional rankings. So including them on your papers will actually reduce your school’s rank.)
I hope it goes without saying that this could create bad incentives.
Second, in fields that mix systems and theory — like computer security — CSRankings is telling us that theory papers (which typically have fewer authors) should be privileged in the rankings over systems papers. This creates both a distortion in the metrics, and also an incentive (for authors who do both types of work) to stick with the one that produces higher rankings. That seems undesirable. But it could very well happen if we adopt these rankings uncritically.
Finally, there’s this focus on “top conferences”. One of our big problems in computer science is that we spend a lot of our time scrapping over a very limited number of slots in competitive conferences. This can be ok, but it’s unfortunate for researchers whose work doesn’t neatly fit into whatever areas those conference PCs find popular. And CSRankings gives zero credit for publishing anywhere but those top conferences, so you might as well forget about that.
(Of course, there’s a question about what a “top conference” even is. In Computer Security, where I work, CSRankings does not consider NDSS to be a top conference. That’s because only three conferences are permitted for each field. The fact that this number seems arbitrary really doesn’t help inspire a lot of confidence in the approach.)
So what can we do about this?
As much as I’d like to ditch rankings altogether, I realize that this probably isn’t going to happen. Nature abhors a vacuum, and if we don’t figure out a rankings system, someone else will. Hell, we’re already plagued by U.S. News, whose methodology appears to involve a popcorn machine and live tarantulas. Something, anything, has to be better than this.
And to be clear, CSRankings isn’t a bad effort. At a high level it’s really easy to use. Even the issues I mention above seem like things that could be addressed. More conferences could be added, using some kind of metric to scale point contributions. (This wouldn’t fix all the problems, but would at least mitigate the worst incentives.) Statistics could perhaps be updated to adjust for graduate students, and soften the blow of having co-authors. These things are not impossible.
And fixing this carefully seems really important. We got it wrong in trusting U.S. News. What I’d like is this time for computer scientists to actually sit down and think this one out before someone imposes a ranking system on top of us. What behaviors are we trying to incentivize for? Is it smaller author lists? Is it citation counts? Is it publishing only in a specific set of conferences?
I don’t know that anyone would agree uniformly that these should be our goals. So if they’re not, let’s figure out what they really are.