# Distinguishing two sets of pseudorandom values when their keys differ by one

Suppose we use a pseudorandom function $PRF$ and a random key $k$ to generate a set of pseudorandom values:

$\forall i, 1\leq i \leq n: w_i=PRF(k,i)$

Now, consider instead of picking a fresh key, we increment the key by one:$k'=k+1$. Then, we compute a set of pseudorandom values:

$\forall i, 1\leq i \leq n: q_i=PRF(k',i)$

Question: Are the set of $w_i$ values are computationally indistinguishable from the set of $q_i$ values?

• That would be dependent of the PRF. – Azarinak Mar 1 '16 at 19:31
• For any cryptographic PRF, I would hope that's true, but you'd have to analyze each PRF algorithm to be sure. – Mike Ounsworth Mar 1 '16 at 19:48

Question: Are the set of $w_i$ values are computationally indistinguishable from the set of $q_i$ values?
• Thank you for the answer. What if we set $k'=k+PRF(k'',i)$ where $k''$ is a random key. – user153465 Mar 6 '16 at 12:55