# Key Derivation Function (KDF): Can a key derived from KDF be considered as a secure key?

Consider a case where we have a master key MS that is used in pseudo-random function to generate a set of pseudo-random values. Then we use key derivation function to derive a key from each of pseudo-random values. Assume all the keys are long enough (in security context).

Question: In the above scenario can I use the keys derived from the pseudo-random values (or the derived keys) as a encryption key or a key for pseudo-random function?

In other words, is there any situation where we should not consider a derived key as an actual random key?

• let $f$ be pseudorandom function and $KDF$ be key derivation function. I have a truly random key, $k$. I generate $n$ pseudorandom values: $v_i=f(k,i), 1\leq i \leq n$. Then I generate $n$ keys: $k_i=KDF(v_i)$. hy cannot I consider $v_i$ as a valid key (in this case I do not need KDF anymore? Nov 24 '15 at 17:29