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Limits to Non-Malleability

Authors Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, Tal Malkin

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Marshall Ball
  • Columbia University, New York City, NY, USA
Dana Dachman-Soled
  • University of Maryland, College Park, MD, USA
Mukul Kulkarni
  • University of Massachusetts Amherst, MA, USA
Tal Malkin
  • Columbia University, New York City, NY, USA

Funding

The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either express or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
  • Ball, Marshall: M. Ball is supported by an IBM Research PhD Fellowship. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006.
  • Dachman-Soled, Dana: This work is supported in part by NSF grants #CNS-1933033, #CNS-1840893, #CNS-1453045 (CAREER), by a research partnership award from Cisco and by financial assistance award 70NANB15H328 from the U.S. Department of Commerce, National Institute of Standards and Technology.
  • Malkin, Tal: This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006.

Cite AsGet BibTex

Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin. Limits to Non-Malleability. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 80:1-80:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ITCS.2020.80

Abstract

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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Security and privacy → Mathematical foundations of cryptography
  • Security and privacy → Cryptography
Keywords
  • non-malleable codes
  • black-box impossibility
  • tamper-resilient cryptogtaphy
  • average-case hardness

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