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Explicit Non-malleable Codes from Bipartite Graphs

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Book cover Arithmetic of Finite Fields (WAIFI 2022)

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Abstract

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.

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Acknowledgements

The authors are grateful to Mr. Peter Rasmussen and Prof. Amit Sahai for their helpful comments to an earlier version of this paper. S. Satake has been supported by JSPS Grant-in-Aid for JSPS Fellows (Grant No. 20J00469) and JST ACT-X (Grant No. JPMJAX2109). Y. Gu has been supported by JSPS Grant-in-Aid for Early-Career Scientists (Grant No. 21K13830).

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Authors and Affiliations

  1. School of Interdisciplinary Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan

    Shohei Satake

  2. Faculty of Information Science and Electrical Engineering, Kyushu University, 744 Motooka Nishi-ku, Fukuoka, 819-0395, Japan

    Yujie Gu & Kouichi Sakurai

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  1. Shohei Satake
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  2. Yujie Gu
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Correspondence to Yujie Gu .

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Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Satake, S., Gu, Y., Sakurai, K. (2023). Explicit Non-malleable Codes from Bipartite Graphs. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_14

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_14

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