  We revisit the fundamental question of formally defining what constitutes a
reconstruction attack. While often clear from the context, our exploration
reveals that a precise definition is much more nuanced than it appears, to the
extent that a single all-encompassing definition may not exist. Thus, we employ
a different strategy and aim to "sandwich" the concept of reconstruction
attacks by addressing two complementing questions: (i) What conditions
guarantee that a given system is protected against such attacks? (ii) Under
what circumstances does a given attack clearly indicate that a system is not
protected? More specifically,
  * We introduce a new definitional paradigm -- Narcissus Resiliency -- to
formulate a security definition for protection against reconstruction attacks.
This paradigm has a self-referential nature that enables it to circumvent
shortcomings of previously studied notions of security. Furthermore, as a
side-effect, we demonstrate that Narcissus resiliency captures as special cases
multiple well-studied concepts including differential privacy and other
security notions of one-way functions and encryption schemes.
  * We formulate a link between reconstruction attacks and Kolmogorov
complexity. This allows us to put forward a criterion for evaluating when such
attacks are convincingly successful.
