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The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures

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Abstract

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi-secret sharing scheme is measured by means of the complexity σ and the randomness τ. Informally, the complexity σ is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness τ is the ratio between the amount of information distributed to the set of users U = {1, ⋯, n} and the minimum of information corresponding to every key.

In this paper, we discuss σ and τ of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make σ and τ to be the minimum, respectively. That is, they are optimal.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Chun-ming Tang

  2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, China

    Chun-ming Tang

  3. State Key Laboratory of Information Security, Beijing, 100093, China

    Chun-ming Tang

  4. School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, 510006, China

    Shu-guang Dai

Authors
  1. Chun-ming Tang
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  2. Shu-guang Dai
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Corresponding author

Correspondence to Chun-ming Tang.

Additional information

Supported in part by the National Natural Science Foundation of China under Grant No. 11271003, the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No. 20134410110003, High Level Talents Project of Guangdong, Guangdong Provincial Natural Science Foundation under Grant No. S2012010009950, the Project of Department of Education of Guangdong Province under Grant No 2013KJCX0146, and the Natural Science Foundation of Bureau of Education of Guangzhou under Grant No. 2012A004.

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Tang, Cm., Dai, Sg. The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures. Acta Math. Appl. Sin. Engl. Ser. 30, 1073–1084 (2014). https://doi.org/10.1007/s10255-014-0431-7

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  • DOI: https://doi.org/10.1007/s10255-014-0431-7

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