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On (tL)-fold perfect authentication and secrecy codes with arbitration

  • Miao LiangEmail author
  • Lijun Ji
Article
  • 18 Downloads

Abstract

An authentication code with arbitration is t-fold perfect if the numbers of decoding rules and encoding rules meet the information-theoretic lower bounds with equality. A code has perfect L-fold secrecy if observing a set of \(L'\le L\) messages in the channel gives no information to the opponent regarding the \(L'\) source states. In this paper, we investigate (tL)-fold perfect authentication and secrecy codes with arbitration which provide both t-fold perfect and perfect L-fold secrecy. We define a new design, L-secrecy perfect ordered restricted strong partially balanced t-design, which is used to construct a (tL)-fold perfect authentication and secrecy code with arbitration. We also obtain some infinite classes of (t, 1)-fold perfect authentication and secrecy codes with arbitration, especially for \(t>2\).

Keywords

t-Fold perfect authentication codes with arbitration Perfect L-fold secrecy codes Orthogonal arrays Restricted strong partially balanced t-designs 

Mathematics Subject Classification

05B05 94A62 

Notes

Acknowledgements

The research of Miao Liang is supported by the National Natural Science Foundation of China under Grant Nos. 11301370 and 11571251, the China Postdoctoral Science Foundation under Grant No. 2016M601873, and sponsored by Qing Lan Project of Jiangsu Province and Suzhou Vocational University. The research of Lijun Ji is supported by the National Natural Science Foundation of China under Grant Nos. 11871363 and 11431003.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouPeople’s Republic of China
  2. 2.Department of Mathematics and PhysicsSuzhou Vocational UniversitySuzhouPeople’s Republic of China

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