Explicit Non-malleable Codes from Bipartite Graphs

Shohei Satake, Yujie Gu*, Kouichi Sakurai

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Non-malleable codes are introduced to protect the communication against adversarial tampering of data, as a relaxation of the error-correcting codes and error-detecting codes. To explicitly construct non-malleable codes is a central and challenging problem which has drawn considerable attention and been extensively studied in the past few years. Recently, Rasmussen and Sahai built an interesting connection between non-malleable codes and (non-bipartite) expander graphs, which is the first explicit construction of non-malleable codes based on graph theory other than the typically exploited extractors. So far, there is no other graph-based construction for non-malleable codes yet. In this paper, we aim to explore more connections between non-malleable codes and graph theory. Specifically, we first extend the Rasmussen-Sahai construction to bipartite expander graphs. Accordingly, we establish several explicit constructions for non-malleable codes based on Lubotzky-Phillips-Sarnak Ramanujan graphs and generalized quadrangles, respectively. It is shown that the resulting codes can either work for a more flexible split-state model or have better code rate in comparison with the existing results.

Original languageEnglish
Title of host publicationArithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers
EditorsSihem Mesnager, Sihem Mesnager, Zhengchun Zhou
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9783031229435
StatePublished - 2023
Externally publishedYes
Event9th International Workshop on the Arithmetic of Finite Fields, WAIFI 2022 - Chengdu, China
Duration: 29 Aug 20222 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13638 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Workshop on the Arithmetic of Finite Fields, WAIFI 2022


  • Biregular graph
  • Expander graph
  • Non-malleable code
  • Split-state model


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