# Any formal proof or reference that pseudorandom permutation can be used as pseudorandom function

Assume that a DRBG passes all statistical tests. We use that DRBG to shuffle(Fisher-Yates) an array that contains $$\{0,1,\ldots,2^n-1\}$$. Now get a pseudorandom permutation $$\{0,1\}^n\rightarrow \{0,1\}^n$$.

My question is, If I change $$i$$-th bit at the input then the probability of $$j$$-th bit being flipped is $$\frac{1}{2}$$. Can anyone provide any formal proof or any reference for the previous statement?

• You might want to have a look at the PRP-PRF switching lemma. – SEJPM Mar 14 at 14:46