Can a attacker compute a hash from another hash of the same plaintext (both using different salt)? Imagine two PBKDF2-SHA-512 hashes of the same password are generated. Each has individual salt. If an attacker had one hash and the salt of both hashes, would he be able to compute the missing hash or would he gain a significant advantage guessing it?

My situation:
A user inputs a password that should be used for AES encryption. The password is hashed once to get a AES Key. Then a second hash of the password the user entered is generated with a different salt than the first one and is sent to the server together with the salts of both hashes. Can a attacker who hijacked the server, calculate the hash that is used as AES key?
Imagine two PBKDF2-SHA-512 hashes of the same password are generated. Each has individual salt. If an attacker had one hash and the salt of both hashes, would he be able to compute the missing hash or would he gain a significant advantage guessing it?


No. The idea of a hash is that it is impossible to reverse a hash. You can of course guess the hash then both outputs can be calculated, but having two different salts will not give any advantage to an attacker.



Note however that by performing PBKDF2 twice you are giving some advantage to an attacker, who only need to perform PBKDF2 once to verify correctness of a guess. Basically your advantage compared to the attacker is reduced by a single bit.

This is why you could also use PBKDF2 once and then create two values using a KBKDF such as HKDF(-expand) twice with two different labels. KBKDF's such as HKDF do not perform key strengthening so the work factor implied by PBKDF2 doesn't need to be performed twice on the server.