Data Reconstruction: When You See It and When You Don't
Edith Cohen, Haim Kaplan, Yishay Mansour, Shay Moran, Kobbi Nissim, Uri Stemmer, Eliad Tsfadia
TL;DR
This work tackles the problem of defining reconstruction attacks, arguing that no single universal definition suffices and proposing a sandwich strategy built around two questions about protection and attack indications. It introduces Narcissus resiliency, a self-referential security paradigm that compares an attacker's success on real data to its success when blind to the data, thereby avoiding fixed baselines and aligning with cryptographic and privacy notions such as DP and MI. The paper also formalizes extraction from outputs via Kolmogorov complexity, showing that Narcissus resiliency prevents non-trivial extraction and relating this framework to well-known concepts like one-way functions and encryption, while discussing practical verification and limitations. Through expressiveness results, it demonstrates how MI and predicate singling out fit as specific instantiations of Narcissus resiliency, and it surveys related works in memorization, DP, and legal privacy concepts. Overall, Narcissus resiliency offers a unified, adaptable lens for reasoning about reconstruction attacks and the protection they require, with clear implications for designing and auditing privacy-preserving mechanisms.
Abstract
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.