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.
@InProceedings{cohen_et_al:LIPIcs.ITCS.2025.39, author = {Cohen, Edith and Kaplan, Haim and Mansour, Yishay and Moran, Shay and Nissim, Kobbi and Stemmer, Uri and Tsfadia, Eliad}, title = {{Data Reconstruction: When You See It and When You Don't}}, booktitle = {16th Innovations in Theoretical Computer Science Conference (ITCS 2025)}, pages = {39:1--39:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-361-4}, ISSN = {1868-8969}, year = {2025}, volume = {325}, editor = {Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.39}, URN = {urn:nbn:de:0030-drops-226674}, doi = {10.4230/LIPIcs.ITCS.2025.39}, annote = {Keywords: differential privacy, reconstruction} }
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