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July 26, 2013

Password Hashing After the PHC

The ultimate goal of password hashing function research is to get password testers (authenticators) and password crackers to use the same implementation of a password hashing system. When this is the case, it means that the crackers do not have an incentive to build a different implementation, because it would not be cheaper than building more of the system in use by the authenticators. A password hashing system's implementation is "broken" (in the cryptography sense) when the crackers have incentive to use a different implementation.

The goal of the Password Hashing Competition (PHC) is therefore to find computationally- and memory-intensive functions that have no "shortcuts," and to build a hardware implementation whose performance is as close to the theoretical optimum as possible. This may (and hopefully will) take the form of a system whose theoretical optimum performance can be implemented on commodity processors, removing the need for authenticators to buy new hardware.

There is a lot of room for improvement in this area. For example, given a password hashing function F and an implementation I of F, we would like to know if there is a faster implementation I' of F. Proving that there is no faster implementation than I (or that I is within some constant factor of the optimum) is very difficult, and I am excited to see what new advances in this area come out of the PHC.

Let's suppose the PHC is finished and we now have a wonderful implementation of a password hashing function, along with strong guarantees that the implementation is very close to the theoretical optimum. We now have a black box that can be purchased at some price, computes some amount of password hashes per second, using some amount of power, and taking up some volume of space. Authenticators are using them to test passwords and crackers are using them to crack hashes stolen from the authenticators.

When this is the case, the cost to a password cracker is some multiple of the cost to the authenticator. For example, if the authenticator needs to compute 100 hashes per second and the cracker wants to compute 100,000 hashes per second, it costs 1000x more for the cracker to operate his cracking rig than it does for the authenticator to operate their authentication server. Remember: these are ideal conditions. In practice it probably won't turn out so well.

At this point, we can ask if there is anything more we can do to give the authenticators an advantage over the crackers. The authenticator has one thing that the cracker doesn't: the stream of incoming authentication requests. Can the authenticator use this to gain a performance/cost advantage over the cracker? The answer is yes: We give the authenticator a secure cache.

The cache exposes the following API and should make every effort to protect its internal state.

String cache_put(String key, String value)
    Insert the key-value pair (key, value) into the cache.
    Returns in constant time.

String cache_get(String key)
    Retrieve the cached value for key 'key'.
    If 'key' is not in the cache, return NULL.
    Returns in constant time.

This could be implemented as a tamper-resistant hardware module or as a Linux kernel driver that stores the cache in the kernel's address space. The main requirement is that, if the system is compromised, the cracker should not be able to retrieve the cache contents.

The authenticator would use the API to cache computations of the password hashing function by, for example, using a single-iteration salted hash of the password as the key. This would reduce the number of computations per second the authenticator needs to perform, allowing them to choose a higher difficulty setting for the hash function. Assuming a sufficiently large cache, the hash function would only need to be computed when an account is created, password is changed, or an incorrect password is tested. Common password mistakes would get cached too.

If a cracker has access to the cache API, they can use it to test passwords faster than by computing the password hashing function. Therefore, the cache should artificially limit the rate at which it will respond to requests, and alert a system administrator if the observed request rate crosses this threshold. In an online attack, a cracker can determine that their password guess is wrong, before the server responds, if the server is taking longer to respond than it does for a correct password. This can be fixed by having the server respond in constant time regardless of the outcome. It would still be cheaper for the authenticator, since in the case of successful authentication, another thread can be scheduled onto the CPU while the first one waits.

If we are able to secure a cache's state against an intruder, then it might be better to include a secret key into the hash function, and protect that key the same way we're protecting the cache. Then, crackers could not test passwords without extracting key. However, there is a reason to use a protected cache even in the presence of a secret key. If an organization loses control of the password hash keys, it can no longer test passwords, so keys have to be backed up, and this exposes them to a greater risk. Cache, on the other hand, only increases performance. If cache is lost, authentication will take longer than normal until the cache has been rebuilt. For most applications, this is acceptable, so the cache does not need to be backed up outside of the secure hardware module or kernel address space (or however it is being protected).

There's another way to give the authenticators an advantage. Make it very hard for crackers to acquire and/or use as many of the black-box hash function units as they want. Doing so is not easy, but it can be done in principal. For example, by making it illegal to possess more than 100 of the hashing units, by exploiting some as-of-yet undiscovered property of physics that could prevent two units from operating within 100 meters of each other, or using the patent system to limit production and distribution. Whether or not this kind of thing is ethical is bound to be extremely controversial, but I think the idea is worth exploring.

In conclusion, the PHC will probably give us a really good slow hashing function. But it doesn't end there. There's a lot more we can do to give authenticators an advantage over the password crackers, and we shouldn't leave these options unexplored.