  The task of privacy amplification, in which Alice holds some partially secret
information with respect to an adversary Eve and wishes to distill it until it
is completely secret, is known to be solvable almost optimally both in the
classical and quantum world. Unfortunately, when considering an adversary who
is only limited by non-signalling constraints such a statement cannot be made
in general. We here prove that under the natural assumptions of time-ordered
non-signalling system, which allow past subsystems to signal future subsystems
(using the device's memory for example), super-polynomial privacy amplification
by any hashing is impossible. This is in great relevance when considering
practical device independent key distribution protocols which assume a
super-quantum adversary.
