The first rule of PAKE is: nobody ever wants to talk about PAKE. The second rule of PAKE is that this is a shame, because PAKE — which stands for Password Authenticated Key Exchange — is actually one of the most useful technologies that (almost) never gets used. It should be deployed everywhere, and yet it isn’t.

To understand why this is such a damn shame, let’s start by describing a very real problem.

Imagine I’m operating a server that has to store user passwords. The traditional way to do this is to hash each user password and store the result in a password database. There are many schools of thought on how to handle the hashing process; the most common recommendation these days is to use a memory-hard password hashing function like scrypt or argon2 (with a unique per-password salt), and then store only the hashed result. There are various arguments about which hash function to use, and whether it could help to also use some secret value (called “pepper“), but we’ll ignore these for the moment.

Regardless of the approach you take, all of these solutions have a single achilles heel:

When the user comes back to log into your website, they will still need to send over their (cleartext) password, since this is required in order for the server to do the check.

This requirement can lead to disaster if your server is ever persistently compromised, or if your developers make a simple mistake. For example, earlier this year Twitter asked all of its (330 million!) users to change their passwords — because it turned out that company had been logging cleartext (unhashed) passwords.

Now, the login problem doesn’t negate the advantage of password hashing in any way. But it does demand a better solution: one where the user’s password never has to go to the server in cleartext. The cryptographic tool that can give this to us is PAKE, and in particular a new protocol called OPAQUE, which I’ll get to at the end of this post.

### What’s a PAKE?

A PAKE protocol, first introduced by Bellovin and Merritt, is a special form of cryptographic key exchange protocol. Key exchange (or “key agreement”) protocols are designed to help two parties (call them a client and server) agree on a shared key, using public-key cryptography. The earliest key exchange protocols — like classical Diffie-Hellman — were unauthenticated, which made them vulnerable to man-in-the-middle attacks. The distinguishing feature of PAKE protocols is the client will authenticate herself to the server using a password. For obvious reasons, the password, or a hash of it, is assumed to be already known to the server, which is what allows for checking.

If this was all we required, PAKE protocols would be easy to build. What makes a PAKE truly useful is that it should also provide protection for the client’s password. A stronger version of this guarantee can be stated as follows: after a login attempt (valid, or invalid) both the client and server should learn only whether the client’s password matched the server’s expected value, and no additional information. This is a powerful guarantee. In fact, it’s not dissimilar to what we ask for from a zero knowledge proof.

Of course, the obvious problem with PAKE is that many people don’t want to run a “key exchange” protocol in the first place! They just want to verify that a user knows a password.

The great thing about PAKE is that the simpler “login only” use-case is easy to achieve. If I have a standard PAKE protocol that allows a client and server to agree on a shared key K if (and only if) the client knows the right password, then all we need add is a simple check that both parties have arrived at the same key. (This can be done, for example, by having the parties compute some cryptographic function with it and check the results.) So PAKE is useful even if all you’ve got in mind is password checking.

### SRP: The PAKE that Time Forgot

The PAKE concept seems like it provides an obvious security benefit when compared to the naive approach we use to log into servers today. And the techniques are old, in the sense that PAKEs have been known since way back in 1992! Despite this, they’ve seen from almost no adoption. What’s going on?

There are a few obvious reasons for this. The most obvious has to do with the limitations of the web: it’s much easier to put a password form onto a web page than it is to do fancy crypto in the browser. But this explanation isn’t sufficient. Even native applications rarely implement PAKE for their logins. Another potential explanation has to do with patents, though most of these are expired now. To me there are two likely reasons for the ongoing absence of PAKE: (1) there’s a lack of good PAKE implementations in useful languages, which makes it a hassle to use, and (2) cryptographers are bad at communicating the value of their work, so most people don’t know PAKE is even an option.

Even though I said PAKE isn’t deployed, there are some exceptions to the rule.

One of the remarkable ones is a 1998 protocol designed by Tom Wu [correction: not Tim Wu] and called “SRP”. Short for “Secure Remote Password“, this is a simple three-round PAKE with a few elegant features that were not found in the earliest works. Moreover, SRP has the distinction of being (as far as I know) the most widely-deployed PAKE protocol in the world. I cite two pieces of evidence for this claim:

1. SRP has been standardized as a TLS ciphersuite, and is actually implemented in libraries like OpenSSL, even though nobody seems to use it much.
2. Apple uses SRP extensively in their iCloud Key Vault.

This second fact by itself could make SRP one of the most widely used cryptographic protocols in the world, so vast is the number of devices that Apple ships. So this is nothing to sneer at.

Industry adoption of SRP is nice, but also kind of a bummer: mainly because while any PAKE adoption is cool, SRP itself isn’t the best PAKE we can deploy. I was planning to go into the weeds about why I feel so strongly about SRP, but it got longwinded and it distracted from the really nice protocol I actually want to talk about further below. If you’re still interested, I moved the discussion onto this page.

In lieu of those details, let me give a quick and dirty TL;DR on SRP:

1. SRP does some stuff “right”. For one thing, unlike early PAKEs it does not require you to store a raw password on the server (or, equivalently, a hash that could be used by a malicious client in place of the password). Instead, the server stores a “verifier” which is a one-way function of the password hash. This means a leak of the password database does not (immediately) allow the attacker to impersonate the user — unless they conduct further expensive dictionary attacks. (The technical name for this is “asymmetric” PAKE.)
2. Even better, the current version of SRP (v4 v6a) isn’t obviously broken!
3. However (and with no offense to the designers) the SRP protocol design is completely bonkers, and earlier versions have been broken several times — which is why we’re now at revision 6a. Plus the “security proof” in the original research paper doesn’t really prove anything meaningful.
4. SRP currently relies on integer (finite field) arithmetic, and for various reasons (see point 3 above) the construction is not obviously transferable to the elliptic curve setting. This requires more bandwidth and computation, and thus SRP can’t take advantage of the many efficiency improvements we’ve developed in settings like Curve25519.
5. SRP is vulnerable to pre-computation attacks, due to the fact that it hands over the user’s “salt” to any attacker who can start an SRP session. This means I can ask a server for your salt, and build a dictionary of potential password hashes even before the server is compromised.
6. Despite all these drawbacks, SRP is simple — and actually ships with working code. Plus there’s working code in OpenSSL that even integrates with TLS, which makes it relatively easy to adopt.

Out of all these points, the final one is almost certainly responsible for the (relatively) high degree of commercial success that SRP has seen when compared to other PAKE protocols. It’s not ideal, but it’s real. This is something for cryptographers to keep in mind.

### OPAQUE: The PAKE of a new generation

When I started thinking about PAKEs a few months ago, I couldn’t help but notice that most of the existing work was kind of crummy. It either had weird problems like SRP, or it required the user to store the password (or an effective password) on the server, or it revealed the salt to an attacker — allowing pre-computation attacks.

Then earlier this year, Jarecki, Krawczyk and Xu proposed a new protocol called OPAQUE. Opaque has a number of extremely nice advantages:

1. It can be implemented in any setting where Diffie-Hellman and discrete log (type) problems are hard. This means that, unlike SRP, it can be easily instantiated using efficient elliptic curves.
2. Even better: OPAQUE does not reveal the salt to the attacker. It solves this problem by using an efficient “oblivious PRF” to combine the salt with the password, in a way that ensures the client does not learn the salt and the server does not learn the password.
3. OPAQUE works with any password hashing function. Even better, since all the hashing work is done on the client, OPAQUE can actually take load off the server, freeing an online service up to use much strong security settings — for example, configuring scrypt with large RAM parameters.
4. In terms of number of messages and exponentiations, OPAQUE is not much different from SRP. But since it can be implemented in more efficient settings, it’s likely to be a lot more efficient.
5. Unlike SRP, OPAQUE has a reasonable security proof (in a very strong model).

There’s even an Internet Draft proposal for OPAQUE, which you can read here. Unfortunately, at this point I’m not aware of any production quality implementations of the code (if you know of one, please link to it in the comments and I’ll update). (Update: There are several potential implementations listed in the comments — I haven’t looked closely enough to endorse any, but this is great!) But that should soon change.

The full OPAQUE protocol is given a little bit further below. In the rest of this section I’m going to go into the weeds on how OPAQUE works.

Problem 1: Keeping the salt secret. As I mentioned above, the main problem with earlier PAKEs is the need to transmit the salt from a server to a (so far unauthenticated) client. This enables an attacker to run pre-computation attacks, where they can build an offline dictionary based on this salt.

The challenge here is that the salt is typically fed into a hash function (like scrypt) along with the password. Intuitively someone has to compute that function. If it’s the server, then the server needs to see the password — which defeats the whole purpose. If it’s the client, then the client needs the salt.

In theory one could get around this problem by computing the password hashing function using secure two-party computation (2PC). In practice, solutions like this are almost certainly not going to be efficient — most notably because password hashing functions are designed to be complex and time consuming, which will basically explode the complexity of any 2PC system.

OPAQUE gets around this with the following clever trick. They leave the password hash on the client’s side, but they don’t feed it the stored salt. Instead, they use a special two-party protocol called an oblivious PRF to calculate a second salt (call it salt2) so that the client can use salt2 in the hash function — but does not learn the original salt.

The basic idea of such a function is that the server and client can jointly compute a function PRF(salt, password), where the server knows “salt” and the client knows “password”. Only the client learns the output of this function. Neither party learns anything about the other party’s input.

The gory details:

The actual implementation of the oblivious PRF relies on the idea that the client has the password $P$ and the server has the salt, which is expressed as a scalar value $s$. The output of the PRF function should be of the form $H(P)^s$, where $H:\{0,1\}^* \rightarrow {\mathcal G}$ is a special hash function that hashes passwords into elements of a cyclic (prime-order) group.

To compute this PRF requires a protocol between the client and server. In this protocol, the client first computes $H(P)$ and then “blinds” this password by selecting a random scalar value r, and blinding the result to obtain $C = H(P)^r$. At this point, the client can send the blinded value C over to the server, secure in the understanding that (in a prime-order group), the blinding by r hides all partial information about the underlying password.

The server, which has a salt value s, now further exponentiates this calue to obtain $R = C^s$ and sends the result R back to the client. If we write this out in detail, the result can be expressed as $R = H(P)^{rs}$. The client now computes the inverse of its own blinding value r and exponentiates one more time as follows: $R' = R^{r^{-1}} = H(P)^s$. This element $R'$, which consists of the hash of the password exponentiated by the salt, is the output of the desired PRF function.

A nice feature of this protocol is that, if the client enters the wrong password into the protocol, she should obtain a value that is very different from the actual value she wants. This guarantee comes from the fact that the hash function is likely to produce wildly different outputs for distinct passwords.

Problem 2: Proving that the client got the right key K. Of course, at this point, the client has derived a key K, but the server has no idea what it is. Nor does the server know whether it’s the right key.

The solution OPAQUE uses based an old idea due to Gentry, Mackenzie and Ramzan. When the user first registers with the server, she generates a strong public and private key for a secure agreement protocol (like HMQV), and encrypts the resulting private key under K, along with the server’s public key. The resulting authenticated ciphertext (and the public key) is stored in the password database.

C = Encrypt(K, client secret key | server’s public key)

When the client wishes to authenticate using the OPAQUE protocol, the server sends it the stored ciphertext C. If the client entered the right password into the first phase, she can derive K, and now decrypt this ciphertext. Otherwise it’s useless. Using the embedded secret key, she can now run a standard authenticated key agreement protocol to complete the handshake. (The server verifies the clients’ inputs against its copy of the client’s public key, and the client does similarly.)

Putting it all together. All of these different steps can be merged together into a single protocol that has the same number of rounds as SRP. Leaving aside the key verification steps, it looks like the protocol above. Basically, just two messages: one from the client and one returned to the server.

The final aspect of the OPAQUE work is that it includes a strong security proof that shows the resulting protocol can be proven secure under the 1-more discrete logarithm assumption in the random oracle model, which is a (well, relatively) standard assumption that appears to hold in the settings we work with.

### In conclusion

So in summary, we have this neat technology that could make the process of using passwords much easier, and could allow us to do it in a much more efficient way — with larger hashing parameters, and more work done by the client? Why isn’t this everywhere?

Maybe in the next few years it will be.

# Is Apple’s Cloud Key Vault a crypto backdoor?

TL;DR: No, it isn’t. If that’s all you wanted to know, you can stop reading.

Still, as you can see there’s been some talk on Twitter about the subject, and I’m afraid it could lead to a misunderstanding. That would be too bad, since Apple’s new technology is kind of a neat experiment.

So while I promise that this blog is not going to become all-Apple-all-the-time, I figured I’d take a minute to explain what I’m talking about. This post is loosely based on an explanation of Apple’s new escrow technology that Ivan Krstic gave at BlackHat. You should read the original for the fascinating details.

### What is Cloud Key Vault (and what is iCloud Keychain)?

A few years ago Apple quietly introduced a new service called iCloud Keychain. This service is designed to allow you to back up your passwords and secret keys to the cloud. Now, if backing up your sensitive passwords gives you the willies, you aren’t crazy. Since these probably include things like bank and email passwords, you really want these to be kept extremely secure.

And — at least going by past experience — security is not where iCloud shines:

The problem here is that passwords need to be secured at a much higher assurance level than most types of data backup. But how can Apple ensure this? We can’t simply upload our secret passwords the way we upload photos of our kids. That would create a number of risks, including:

1. The risk that someone will guess, reset or brute-force your iCloud password. Password resets are a particular problem. Unfortunately these seem necessary for normal iCloud usage, since people do forget their passwords. But that’s a huge risk when you’re talking about someone’s entire password collection.
2. The risk that someone will break into Apple’s infrastructure. Even if Apple gets their front-end brute-forcing protections right (and removes password resets), the password vaults themselves are a huge target. You want to make sure that even someone who hacks Apple can’t get them out of the system.
3. The risk that a government will compel Apple to produce data. Maybe you’re thinking of the U.S. government here. But that’s myopic: Apple stores iCloud data all over the world.

So clearly Apple needs a better way to protect these passwords. How do to it?

### Why not just encrypt the passwords?

It is certainly possible for an Apple device to encrypt your password vault before sending it to iCloud. The problem here is that Apple doesn’t necessarily have a strong encryption key to do this with. Remember that the point of a backup is to survive the loss of your device, and thus we can’t assume the existence of a strong recovery key stored on your phone.

This leaves us with basically one option: a user password. This could be either the user’s iCloud password or their device passcode. Unfortunately for the typical user, these tend to be lousy. They may be strong enough to use as a login password — in a system that allows only a very limited number of login attempts. But the kinds of passwords typical users choose to enter on mobile devices are rarely strong enough to stand up to an offline dictionary attack, which is the real threat when using passwords as encryption keys.

(Even using a strong memory-hard password hash like scrypt — with crazy huge parameters — probably won’t save a user who chooses a crappy password. Blame phone manufacturers for making it painful to type in complicated passwords by forcing you to type them so often.)

### So what’s Apple to do?

So Apple finds itself in a situation where they can’t trust the user to pick a strong password. They can’t trust their own infrastructure. And they can’t trust themselves. That’s a problem. Fundamentally, computer security requires some degree of trust — someone has to be reliable somewhere.

Apple’s solution is clever: they decided to make something more trustworthy than themselves. To create a new trust anchor, Apple purchased a bunch of fancy devices called Hardware Security Modules, or HSMs. These are sophisticated, tamper-resistant specialized computers that store and operate with cryptographic keys, while preventing even malicious users from extracting them. The high-end HSMs Apple uses also allow the owner to include custom programming.

Rather than trusting Apple, your phone encrypts its secrets under a hardcoded 2048-bit RSA public key that belongs to Apple’s HSM. It also encrypts a function of your device passcode, and sends the resulting encrypted blob to iCloud. Critically, only the HSM has a copy of the corresponding RSA decryption key, thus only the HSM can actually view any of this information. Apple’s network sees only an encrypted blob of data, which is essentially useless.

When a user wishes to recover their secrets, they authenticate themselves directly to the HSM. This is done using a user’s “iCloud Security Code” (iCSC), which is almost always your device passcode — something most people remember after typing it every day. This authentication is done using the Secure Remote Password protocol, ensuring that Apple (outside of the HSM) never sees any function of your password.

Now, I said that device passcodes are lousy secrets. That’s true when we’re talking about using them as encryption keys — since offline decryption attacks allow the attacker to make an unlimited number of attempts. However, with the assistance of an HSM, Apple can implement a common-sense countermeasure to such attacks: they limit you to a fixed number of login attempts. This is roughly the same protection that Apple implements on the devices themselves.

 The encrypted contents of the data sent to the HSM (source).

The upshot of all these ideas is that — provided that the HSM works as designed, and that it can’t be reprogrammed — even Apple can’t access your stored data except by logging in with a correct passcode. And they only get a limited number of attempts to guess correctly, after which the account locks.

This rules out both malicious insiders and government access, with one big caveat.

### What stops Apple from just reprogramming its HSM?

This is probably the biggest weakness of the system, and the part that’s driving the “backdoor’ concerns above. You see, the HSMs Apple uses are programmable. This means that — as long as Apple still has the code signing keys — the company can potentially update the custom code it includes onto the HSM to do all sort sorts of things.

These things might include: programming the HSM to output decrypted escrow keys. Or disabling the maximum login attempt counting mechanism. Or even inserting a program that runs a brute-force dictionary attack on the HSM itself. This would allow Apple to brute-force your passcode and/or recover your passwords.

Fortunately Apple has thought about this problem and taken steps to deal with it. Note that on HSMs like the one Apple is using, the code signing keys live on a special set of admin smartcards. To remove these keys as a concern, once Apple is done programming the HSM, they run these cards through a process that they call a “physical one-way hash function”.

If that sounds complicated, here’s Ivan’s slightly simpler explanation.

So, with the code signing keys destroyed, updating the HSM to allow nefarious actions should not be possible. Pretty much the only action Apple can take is to  wipe the HSM, which would destroy the HSM’s RSA secret keys and thus all of the encrypted records it’s responsible for. To make sure all admin cards are destroyed, the company has developed a complex ceremony for controlling the cards prior to their destruction. This mostly involves people making assertions that they haven’t made copies of the code signing key — which isn’t quite foolproof. But overall it’s pretty impressive.

The downside for Apple, of course, is that there had better not be a bug in any of their programming. Because right now there’s nothing they can do to fix it — except to wipe all of their HSMs and start over.

### Couldn’t we use this idea to implement real crypto backdoors?

A key assertion I’ve heard is that if Apple can do this, then surely they can do something similar to escrow your keys for law enforcement. But looking at the system shows isn’t true at all.

To be sure, Apple’s reliance on a Hardware Security Module indicates a great deal of faith in a single hardware/software solution for storing many keys. Only time will tell if that faith is really justified. To be honest, I think it’s an overly-strong assumption. But iCloud Keychain is opt-in, so individuals can decide for themselves whether or not to take the risk. That wouldn’t be true of a mandatory law enforcement backdoor.

But the argument that Apple has enabled a law enforcement backdoor seems to miss what Apple has actually done. Instead of building a system that allows the company to recover your secret information, Apple has devoted enormous resources to locking themselves out. Only customers can access their own information. In other words, Apple has decided that the only way they can hold this information is if they don’t even trust themselves with it.

That’s radically different from what would be required to build a mandatory key escrow system for law enforcement. In fact, one of the big objections to such a backdoor — which my co-authors and I recently outlined in a report — is the danger that any of the numerous actors in such a system could misuse it. By eliminating themselves from the equation, Apple has effectively neutralized that concern.

### If Apple can secure your passwords this way, then why don’t they do the same for your backed up photos, videos, and documents?

That’s a good question. Maybe you should ask them?

# Neat research ideas that went nowhere: Preventing offline dictionary attacks with CAPTCHAs

Once in a while I come across a research paper that’s so off the beaten path and so obviously applicable to a real problem, that I know it’s going to sink like a stone and never be heard from again.

Today I’d like to talk about an idea that was introduced back in CRYPTO 2006, but doesn’t seem to have gotten any real traction out in the real world since. (If I’m wrong and someone is using it, feel free to email me. I’d be happy to eat my words and hear more.)

This particular idea comes from a 2006 paper by Ran Canetti, Shai Halevi and Michael Steiner,* and it addresses a very real problem that we have with deployed encryption schemes: namely, they tend to rely on passwords. This means that even if you use strong cryptography, all of your data is vulnerable to someone with a password dictionary and a lot of computing power.

### Password-Based Encryption (and why we hate it)

To explain how Canetti, Halevi and Steiner propose to deal with this, I need to give a little bit of background on password-based encryption.

First of all of all, no matter what Dan Brown says, we’ve gotten pretty good at building encryption schemes that stand up against very motivated adversaries. If you’re using a modern scheme and are properly generating/storing your secret keys, then it’s awfully unlikely that a third party is going to decrypt your data — even if that party is a government agency.** (I’m leaving aside the wrench factor).

Unfortunately, the previous paragraph embeds one major assumption that makes it inapplicable to the way that many people secure their data. You see, in a cryptographer’s imagination, everyone encrypts with a strong, random 128+ bit secret key, which they memorize and never write down.

But in real life, people mostly prefer to use their cat’s name.

The use of passwords to derive encryption keys is a lot more common than it should be. It’s depressingly common in many applications where people really need security. Passwords are the default authorization method for many fancy encrypting hard-drives and WDE packages. Windows just loves to encrypt things under your login credentials. (Many of these tools also support hardware tokens and TPM, but these are such a drag that most people don’t bother.)

To your attacker, this is a feature not a bug. If a key is derived from dictionary words, or some predictable mutation of dictionary words, then it can be guessed. All it takes is time and  computing power. Moreover, since password guessing is embarrassingly parallel, it’s just the kind of enterprise that you can throw a data center or five at. (Ever wondered why the state of Maryland uses so much electricity?)

So far I haven’t said anything you didn’t already know. But just for fun, let’s quickly talk about what we currently do to prevent dictionary attacks. There are basically three approaches:

1. Use some trusted, on-line server (or tamper-resistant hardware) to assist with the key derivation process. If done correctly, the server/hardware can shut off an attacker after a few invalid guesses, assuming that it isn’t also compromised. Unfortunately, this solution assumes that the server or hardware will be available when you need your data. That isn’t always possible.
2. Use key stretching, which increases the time required to convert a password into a cryptographic key. This can slow down a dictionary attack, but it just slows it down. Moreover, it’s pretty ineffective against an attacker with specialized hardware.
3. Use salt, which is hardly worth mentioning since if you aren’t salting your passwords then you’re crazy. Unfortunately all this does is prevent pre-computation. It does nothing against normal dictionary attacks.

### The human touch

In a perfect world, the online solution (1) above would probably be the best way to go. Unfortunately, we don’t live in a perfect world, and this may not be compatible with people’s requirements.

While it’s not possible to prevent dictionary attacks in an offline system, we may be able to slow them down. To do this, we have to make the decryption process much more resource-intensive. Unfortunately, it’s hard to win this game through computation alone, at least not in a world full of FPGAs and elastic compute clouds.

 Not this sort of brains. (XKCD).

What Canetti, Halevi and Steiner realized is that there’s one resource that the adversary might not have in abundance: human brains.

What if we could mandate some sort of human interaction each time a user tries to decrypt a file? This shouldn’t be too burdensome for the legitimate decryptor, since presumably he’s human, and moreover he only needs to try once.

But a password cracker needs to try millions of passwords. Requiring a human interaction for each attempt should throw a serious wrench into the process.

### Using Human Puzzles to stop dictionary attacks

Fortunately we already have a whole class of technologies that differentiate human beings from computers. Generally, these are known as Reverse Turing Tests (RTTs). Canetti, Halevi and Steiner propose to use RTTs to construct “human puzzles”. At a high level, the idea is pretty simple.

In every PBE scheme, a password must first be converted into a key. Normally you do this by hashing the password and some salt via a standard key derivation function (e.g., PBKDF2). Usually this is where you’d stop. The output of this function, which we’ll call K, would be the key used to encrypt and decrypt.

However, now we’re going to take things one step further. The first key will be further processed by converting it into a puzzle that only a human can solve. When a human solves this puzzle, they create a new key that, ideally, a computer all by itself should not be able to recover. The process should be reliable — it needs to produce the same result every time it’s run, possibly across many different users.

Once you get past the theoretical stuff, the concrete example that Canetti, Halevi and Steiner propose is to use CAPTCHAs to implement human puzzles.

### CAPTCHAs: don’t you love them?

In their example, the process of deriving an encryption key from a password now looks like this:

1. First hash the password with some random salt r to derive a first key K. Now break this into a bunch of small chunks, each (for example) about 20 bits long.
2. Use each of these 20-bit chunks to index into a huge table containing 2^20 (about 1 million) distinct CAPTCHA images. Each CAPTCHA contains a hard-to-read string with at least 20 bits of entropy in it. This string could be a bunch of numbers, or some randomly-selected dictionary words.
3. Give each CAPTCHA to the human user to solve. Collect the results.
4. Hash all of the user’s responses together with another salt s to derive a final decryption key.

If we instantiate the hash function with, say, PBKDF2 and a 160-bit output, then this requires the legitimate user to solve 8 puzzles the first time they encrypt, and every subsequent time they decrypt.

### In summary

Now maybe CAPTCHAs aren’t your thing. Maybe you don’t like the idea of storing 4GB worth of files just to ship someone an encrypted ZIP file. That’s fine. One of the neatest open problems in the paper is to find new sorts of human puzzles. In general, a human puzzle is any function that converts some input (say a 20-bit string) into an output, such that only a human being can do the transformation.

These don’t need to rely on bulky, stored CAPTCHAs. Hypothetically you could come up with a human puzzle that dynamically generates instances without a big stored database. For example, your puzzle might be based on recognizing human expressions, or inkblots. It just has to be reliable.

And that’s why I think this is such a neat paper. Whether or not this particular idea changes the world, it’s a new idea, it tries to solve a hard practical problem that most people have given up on, and it inspires some new ideas.

The crypto publishing game rarely produces papers with that particular combination. Just for that, I’d love to see it go somewhere.

Notes:

* Ran Canetti, Shai Halevi and Michael Steiner. 2006. Mitigating Dictionary Attacks on Password-Protected Local Storage. In CRYPTO ’06.

** Leaving aside what we all know the NSA’s got in its basement.