| 乘性单调张成方案 |
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| 作者姓名： | 张志芳 |
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| 作者单位： | 中国科学院数学与系统科学研究院，北京，100080. E-mail: zfz@amss.ac.cn |
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| 摘 要： | 乘性单调张成方案（或乘性的线性密钥共享体制）是设计安全多方计算协议的一个重要 工具。本文给出了一个单调张成方案（或线性密钥共享体制）具有乘性的充分必要条件，即通过判断 一个线性方程组是否有解可以确定一个单调张成方案是否具有乘性。作为例子，我们研究了Shamir的 门限密钥共享体制以及带权重的门限密钥共享体制，指出了它们具有乘性时所应具备的条件。
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| 关 键 词： | 乘性单调张成方案 线性密钥共享体制 安全多方计算 |
Multiplicative Monotone Span Programs |
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| Authors: | ZHANG Zhi-Fang |
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| Institution: | Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | Multiplicative monotone span program (or multiplicative linear secret sharing scheme) is a important tool for building a multi-party computation protocol。In this paper, we give a necessary and su±cient condition for a monotone span program (or linear secret sharing scheme) to be multiplica- tive，i.e., we can decide whether a monotone span program is multiplicative by judging if a system of linear equations is solvable. As examples, we study Shamir’s threshold secret sharing scheme and the extended threshold scheme with weights, pointing out when they are multiplicative, respectively. |
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