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Algebraic manipulation detection codes via highly nonlinear functions

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Abstract

In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly nonlinear functions. Systematic AMD codes with new parameters can be generated from known highly nonlinear functions. Especially, several infinite classes of optimal systematic AMD codes, some with asymptotically optimal tag size, can be constructed. On the other hand, systematic AMD codes are used to construct highly nonlinear functions. The known construction by Cramer et al. (2008) for systematic AMD codes turns out to be based on a special kind of functions with high nonlinearity.

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Acknowledgments

The authors are very grateful to the reviewers for their comments and suggestions that improved the presentation and quality of this paper.

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  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba, 305-8573, Japan

    Minfeng Shao & Ying Miao

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  1. Minfeng Shao
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  2. Ying Miao
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Correspondence to Minfeng Shao.

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This research is supported by JSPS Grant-in-Aid for Scientific Research (B) under Grant No. 18H01133.

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Shao, M., Miao, Y. Algebraic manipulation detection codes via highly nonlinear functions. Cryptogr. Commun. 13, 53–69 (2021). https://doi.org/10.1007/s12095-020-00453-z

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