Expander Graphs Are Non-Malleable Codes

Authors Peter Michael Reichstein Rasmussen, Amit Sahai

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Author Details

Peter Michael Reichstein Rasmussen
  • Basic Algorithms Research Copenhagen, University of Copenhagen, Denmark
Amit Sahai
  • UCLA, Los Angeles, CA, USA


A significant effort was made to simplify our proof as much as possible, which eventually resulted in the approximately 2-page proof of our main result presented here; we thank Anders Aamand and Jakob Bæk Tejs Knudsen for suggestions and insights regarding the main theorem that helped simplify and improve the results presented. Furthermore, we thank Aayush Jain, Yuval Ishai, and Dakshita Khurana for early discussions regarding simple constructions of split-state non-malleable codes not based on expander graphs.

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Peter Michael Reichstein Rasmussen and Amit Sahai. Expander Graphs Are Non-Malleable Codes. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Any d-regular graph on n vertices with spectral expansion λ satisfying n = Ω(d³log(d)/λ) yields a O((λ^{3/2})/d)-non-malleable code for single-bit messages in the split-state model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
  • Mathematics of computing → Spectra of graphs
  • Non-Malleable Code
  • Expander Graph
  • Mixing Lemma


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