# Reconstructing face from randomised embedding

It is fairly agreed in literature that from a given face-embedding (that is a vector of features values) it is possible, with a good amount of effort, to reconstruct the original face, (See here for instance) assuming to have access to the embedding extractor.

Now, for concreteness, let's say that I've a 2000 long embedding of floats. I randomly rearrange the 2000 entries of the vector in one the $$2000!$$ permutations. The random rearrangement is specific to the owner of the face.

Is it still possible to recover the original face?

(A brute force attack is clearly excluded, as $$2000! \approx 10^{5735}$$)