Limits to Non-Malleability

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



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Author Details

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

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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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