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A construction for optimal c-splitting authentication and secrecy codes

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Abstract

Authentication and secrecy codes which provide both secrecy and authentication have been intensively studied in the case where there is no splitting; however the results concerning the case where there is splitting are far fewer. In this paper, we focus on the case with c-splitting, and obtain a bound on the number of encoding rules required in order to obtain maximum levels of security. A c-splitting authentication and secrecy code is called optimal if it obtains maximum levels of security and has the minimum number of encoding rules. We define a new design, called an authentication perpendicular multi-array, and prove that the existence of authentication perpendicular multi-arrays implies the existence of optimal c-splitting authentication and secrecy codes. Further, we study the constructions and existence of authentication perpendicular multi-arrays, and then obtain two new infinite classes of optimal c-splitting authentication and secrecy codes.

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Acknowledgements

The research of Mingchao Li was supported by the National Natural Science Foundation of China under Grant No. 11501161 and the Natural Science Foundation of Hebei Province under Grant No. A2016402164. The research of Miao Liang was 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. The research of Beiliang Du was supported by the National Natural Science Foundation of China under Grant No. 11571251.

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Authors and Affiliations

  1. Department of Mathematics, Hebei University of Engineering, Handan, 056038, People’s Republic of China

    Mingchao Li

  2. Department of Mathematics and Physics, Suzhou Vocational University, Suzhou, 215104, People’s Republic of China

    Miao Liang

  3. Department of Mathematics, Soochow University, Suzhou, 215006, People’s Republic of China

    Beiliang Du & Jingyuan Chen

Authors
  1. Mingchao Li
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  2. Miao Liang
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  3. Beiliang Du
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  4. Jingyuan Chen
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Correspondence to Miao Liang.

Additional information

Communicated by C. Blundo.

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Li, M., Liang, M., Du, B. et al. A construction for optimal c-splitting authentication and secrecy codes. Des. Codes Cryptogr. 86, 1739–1755 (2018). https://doi.org/10.1007/s10623-017-0421-x

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  • DOI: https://doi.org/10.1007/s10623-017-0421-x

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