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A Verifiable multi-secret sharing scheme Based on Hermite Interpolation

Journal of Mathematics and System Science 2014年第9期4卷 587-592页

作者： Tomoko Adachi Chie Okazaki Department of Information Sciences Toho University 274-8510 Japan Kowa Electric Industry CO LTD

A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one key, that is, a multi-secret sharing scheme has p （〉_ 2） keys. Dealer distribute shares of keys among n participants. Gathering t （〈 n） participants, keys can be reconstructed. Yang et al. （2004） gave a scheme of a （t, n） multi-secret sharing based on Lagrange＇s interpolation. Zhao et al. （2007） gave a scheme of a （t, n） verifiable multi-secret sharing based on Lagrange＇s interpolation. Recently, Adachi and Okazaki give a scheme of a （t, n） multi-secret sharing based on Hermite interpolation, in the case ofp 〈 t. In this paper, we give a scheme ofa （t, n） verifiable multi-secret sharing based on Hermite interpolation.

关键词： Verifiable secret sharing scheme multi-secret sharing scheme Hermite interpolation

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The Complexity and Randomness of Linear multi-secret sharing schemes with Non-threshold Structures

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 1073-1084页

作者： Chun-ming Tang Shu-guang DAI School of Mathematics and Information Science Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University State Key Laboratory of Information Security School of Information Science and Technology Sun Yat-Sen University

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 a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness 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 a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.

关键词： secret sharing multi-secret sharing scheme non-threshold multi-access structure linear code complexity randomness

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Linear multi-secret sharing schemes

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Science in China(Series F) 2005年第1期48卷 125-136页

作者： XlAOLiangliang LIUMulan AcademyofMathematicsandSystemSciencesandKeyLaboratoryofMathematicsMechanization ChineseAcademyofSciencesBeijing100080China

In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access structures by using linear multi-secret sharing schemes is shown. Furthermore, the concept of optimal linear multi-secret sharing scheme is presented and the several schemes are proved to be optimal.

关键词： multi-secret sharing scheme linear multi-secret sharing scheme monotone span program optimal linear multi-secret sharing scheme.

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