Explicit Non-malleable Codes from Bipartite Graphs

Shohei Satake; Yujie Gu; Kouichi Sakurai

doi:10.1007/978-3-031-22944-2_14

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 proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers
Editors	Sihem Mesnager, Sihem Mesnager, Zhengchun Zhou
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	221-236
Number of pages	16
ISBN (Print)	9783031229435
DOIs	https://doi.org/10.1007/978-3-031-22944-2_14
State	Published - 2023
Externally published	Yes
Event	9th International Workshop on the Arithmetic of Finite Fields, WAIFI 2022 - Chengdu, China Duration: 29 Aug 2022 → 2 Sep 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13638 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International Workshop on the Arithmetic of Finite Fields, WAIFI 2022
Country/Territory	China
City	Chengdu
Period	29/08/22 → 2/09/22

Keywords

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

Access to Document

10.1007/978-3-031-22944-2_14

Cite this

Satake, S., Gu, Y., & Sakurai, K. (2023). Explicit Non-malleable Codes from Bipartite Graphs. In S. Mesnager, S. Mesnager, & Z. Zhou (Eds.), Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers (pp. 221-236). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13638 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-22944-2_14

Satake, Shohei ; Gu, Yujie ; Sakurai, Kouichi. / Explicit Non-malleable Codes from Bipartite Graphs. Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers. editor / Sihem Mesnager ; Sihem Mesnager ; Zhengchun Zhou. Springer Science and Business Media Deutschland GmbH, 2023. pp. 221-236 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

keywords = "Biregular graph, Expander graph, Non-malleable code, Split-state model",

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Satake, S, Gu, Y & Sakurai, K 2023, Explicit Non-malleable Codes from Bipartite Graphs. in S Mesnager, S Mesnager & Z Zhou (eds), Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13638 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 221-236, 9th International Workshop on the Arithmetic of Finite Fields, WAIFI 2022, Chengdu, China, 29/08/22. https://doi.org/10.1007/978-3-031-22944-2_14

Explicit Non-malleable Codes from Bipartite Graphs. / Satake, Shohei; Gu, Yujie; Sakurai, Kouichi.
Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers. ed. / Sihem Mesnager; Sihem Mesnager; Zhengchun Zhou. Springer Science and Business Media Deutschland GmbH, 2023. p. 221-236 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13638 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Satake S, Gu Y, Sakurai K. Explicit Non-malleable Codes from Bipartite Graphs. In Mesnager S, Mesnager S, Zhou Z, editors, Arithmetic of Finite Fields - 9th International Workshop, WAIFI 2022, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2023. p. 221-236. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-22944-2_14