Home > Security > Phidelius: Constructing Asymmetric Keypairs From Mere Passwords For Fun and PAKE

Phidelius: Constructing Asymmetric Keypairs From Mere Passwords For Fun and PAKE

TL;DR: New toy.

$ phidelius
Phidelius 1.0: Entropy Spoofing Engine
Author: Dan Kaminsky / dan@doxpara.com
Description: This code replaces most sources of an application's entropy with
a psuedorandom stream seeded from a password, a file, or a generated
sequence. This causes most cryptographic key generators (ssh-keygen,
openssl, etc) to emit apparently strong keys with a presumably memorable
backdoor. For many protocols this creates PAKE (Password Authenticated
Key Exchange) semantics without the server updating any code or even
being aware of the password stored client side. However, the cost of
blinding the server is increased exposure to offline brute force
attacks by a MITM, a risk only partially mitigatable by time/memory
hard crack resistance.
Example: phidelius -p "ax-op-nm-qw-yi" -e "ssh-keygen -f id_dsa"

Passwords are a problem. They’re constantly being lost, forgotten, and stolen. Something like 50% of compromises are associated with their loss. Somewhere along the way, websites started thinking l33tsp33k was a security technology to be enforced upon users.

So what we’re about to talk about in this post — and, in fact, what’s in the code I’m about to finally drop — is by no means a good idea. It may perhaps be an interesting idea, however.

So! First discussed in my Black Ops of 2011 talk, I’m finally releasing Phidelius 1.0. Phidelius allows a client armed with nothing but a password to generate predictable RSA/DSA/ECC keypairs that can then be used, unmodified, against real world applications such as SSH, SSL, IPsec, PGP, and even BitCoin (though I haven’t quite figured out that particular invocation yet — it’s pretty cool, you could send money to the bearer of a photograph).

Now, why would you do this? There’s been a longstanding question as to how can a server support passwords, without necessarily learning those passwords. The standard exhortations against storing unhashed passwords mean nothing against this problem; even if the server is storing hashed values, it’s still receiving them in plain text. There are hash-based challenge response protocols (“please give me the password hashed with this random value”) but they require the server to then store the password (or a password equivalent) so they can recognize valid responses.

There’s been a third class of solutions, belonging to the PAKE (Password Authenticated Key Exchange) family. These solutions generally come down to “password authenticated Diffie-Helman”. For various reasons, not least of which have been patents, these approaches haven’t gotten far. Phidelius basically “solves” PAKE, by totally cheating. Rather than authenticating an otherwise random exchange, the keypair itself is nothing but an encoding of the password. The server doesn’t even have to know. (If you are a dev, your ears just perked up. Solutions that require only one side to patch are infinitely easier to deploy.) How can this work?

Well, what was the one bug that affected asymmetric key generation universally, corrupting RSA, DSA, and ECC equally? Of course, the Debian Random Number Generator flaw. See, asymmetric keys of all sorts are all essentially built the same way. A pile of bits is drawn from some ostensibly random source (/dev/random, CryptGenRandom, etc). These bits are then accepted, massaged, or rejected, until they meet the required form for a keypair of the appropriate algorithm.

Under the Debian RNG bug, only a rather small subset of bit patterns could be drawn, so the same keys would be generated over and over. Phidelius just makes predictable key generation a feature: We know how to turn a password into a stream of random numbers. We call that “seeding a pseudorandom number generator”. So, we just make the output of a PRNG the input to /dev/random, /dev/urandom, a couple of OpenSSL functions, and some other miscellaneous noise, and — poof — same password in, same keypair out, as so:

# phidelius -p "ax-op-nm-qw-yi" -e "ssh-keygen -f $RANDOM -N ''"
...The key fingerprint is:
# phidelius -p "ax-op-nm-qw-yi" -e "ssh-keygen -f $RANDOM -N ''"
The key fingerprint is:

Now, as I mentioned earlier, it’s not necessarily a particularly good idea to use this technique, and not just because passwords themselves are inherently messy. The biggest weakness of the Phidelius approach is that the public keys it generates are also backdoored with the password. The problem here is subtle. It’s not interesting that the server can brute force the public key back to the password. This is *always* the case, even in properly beautiful protocols like SRP. (In fact, Phidelius uses the PRNG from scrypt, a time and memory hard algorithm, to make brute forcing not only hard, but probably harder than any traditional PAKE algorithm can achieve.)

What’s interesting is that public keys are supposed to be public. So, most protocols expose them at least to MITM’s, and sometimes even publish the things. Yes, there’s quite a bit of effort put into suppressing brute force attacks, but this is a scheme that really threatens you with them.

It also doesn’t help that salting Phidelius-derived keys is pretty tricky. The fact that the exact same password creates the exact same keypair isn’t necessarily ideal. The best trick I’ve found is to embed parameters for the private key in the larger context afforded to most public keys, i.e. the certificate. You’d retrieve the public key, mix in the randomized salt and some useful parameters (like, say, options for scrypt), and reconstruct the private key. This requires quite a bit of infrastructure though.

And finally, of course, this is a rather fragile solution. The precise bit-for-bit use of entropy isn’t standardized; all bits are supposed to be equal. So you’re not just generating a key with ssh-keygen, you’re generating from ssh-keygen 5.3, possibly as emitted from a particular compiler. A proper implementation would have to standardize all this.

So, there are caveats. But this is interesting, and I look forward to seeing how people play with it.

(Oh, why Phidelius? It’s a spell from Harry Potter, which properly understood is the story of the epic consequences of losing one’s password.)

Edit: Forgot! Tom Ritter saw my talk at Black Hat, and posted that he’d actually worked out how to do this sort of password-to-keypair construction for PGP keys. It’s actually a bit tricky. You can see his code here.

Categories: Security
  1. Henning Rogge
    January 28, 2012 at 8:14 am

    Whats about using the username and a server challenge as additional entropy? This way brute forcing the certificate would be both server and username specific.

    Registration would go this way:
    1) Client gives Server the requested username
    2) Server responds with a random challenge
    3) Client generates a public/private key with Hash(username|password|challenge) as entropy and sends the public key to the server
    4) Server stores the database entry “Username, public key, challenge”

    Login would be little bit different:
    1) Client gives Server his username
    2) Server responds with the stored challenge
    3) Client use Hash(username|password|challenge) to create the public/private key and logs in with it

    This could even work out with some kind of “device-id” that the client stores locally and puts into each of the entropy hashes. This way the key would be bound to a certain device.

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