Data Reconstruction: When You See It and When You Don't

TL;DR

This paper explores the nuanced definition of reconstruction attacks, introduces Narcissus Resiliency as a new security paradigm, and links attack success to Kolmogorov complexity, advancing understanding of data protection.

Contribution

It proposes Narcissus Resiliency as a novel, self-referential security framework and connects reconstruction attacks to Kolmogorov complexity for better evaluation.

Findings

Narcissus Resiliency captures multiple existing security notions.

A link between reconstruction attacks and Kolmogorov complexity is established.

The framework offers a nuanced perspective on data protection.

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.