There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class ℱ? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: - Functions that change d/2 symbols, where d is the distance of the code; - Functions where each input symbol affects only a single output symbol; - Functions where each of the n output bits is a function of n-log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes ℱ via reductions to the assumption that a distributional problem is hard for ℱ, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P ⊈ NC.
@InProceedings{ball_et_al:LIPIcs.ITCS.2020.80, author = {Ball, Marshall and Dachman-Soled, Dana and Kulkarni, Mukul and Malkin, Tal}, title = {{Limits to Non-Malleability}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {80:1--80:32}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-134-4}, ISSN = {1868-8969}, year = {2020}, volume = {151}, editor = {Vidick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.80}, URN = {urn:nbn:de:0030-drops-117657}, doi = {10.4230/LIPIcs.ITCS.2020.80}, annote = {Keywords: non-malleable codes, black-box impossibility, tamper-resilient cryptogtaphy, average-case hardness} }
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