Can I use a key-derivation-function as the hash function H in SRP?

Question

In the Secure Remote Password Protocol, the verifier must be stored on the server. In the case of a server compromise, an attacker could obtain these verifiers. If nobody reused passwords, this wouldn't be a big deal (as the users' data is probably also compromised). However since people do reuse passwords it seems a good idea to make offline attacks against the password file difficult.

SRP is based off of a cryptographic hash H; part of the cost of an offline attack would be calculating H, so using an expensive hash for this step seems good. However, I am unsure of the suitability of tunably expensive hashing mechanisms (e.g. PBKDF2, bcrypt, scrypt) for this.

Answer 1

Yes, you can and use a slow hashing function when constructing the verifier. I would recommend using PBKDF2, as it is designed for this purpose.

In fact, Wikipedia says:

$v$ is the host's password verifier, $v = g^x$, $x = H(s,p)$. Using of functions like PBKDF2 instead of $H$ for password hashing is highly recommended.

Thus, you could use $x=\text{PBKDF2}(s,p)$. Alternatively, you could pre-hash the password with PBKDF2, then use the result as your $p$.

Answer 2

1. There is no reason why you can't, i.e. why H() used for hashing passwords and for the rest of protocol should be the same.

2. The only thing you pay for that is the speed. Password hash is only generated on the client while you usually want to spare server's CPU time, client's is less important.