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首页> 外文期刊>SIAM Journal on Discrete Mathematics >ON SECRET SHARING WITH NONLINEAR PRODUCT RECONSTRUCTION
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ON SECRET SHARING WITH NONLINEAR PRODUCT RECONSTRUCTION

机译：非线性产品重构的秘密共享

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摘要

Multiplicative linear secret sharing is a fundamental notion in the area of secure multiparty computation and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that the product of two secrets is obtained as a linear function of the vector consisting of the coordinatewise product of two respective share-vectors. This paper focuses on the following foundational question, which is novel to the best of our knowledge. Suppose we abandon the latter linearity condition and instead require that this product is obtained by some, not-necessarily-linear "product reconstruction function." Is the resulting notion equivalent to multiplicative linear secret sharing? We show the (perhaps somewhat counterintuitive) result that this relaxed notion is strictly more general. Concretely, fix a finite field F-q as the base field over which linear secret sharing is considered. Then we show there exists an (exotic) linear secret sharing scheme with an unbounded number of players n such that it has t-privacy with t = Omega(n) and such that it does admit a product reconstruction function, yet this function is necessarily nonlinear. In addition, we determine the minimum number of players for which those exotic schemes exist. Our proof is based on combinatorial arguments involving quadratic forms. It extends to similar separation results for important variations, such as strongly multiplicative secret sharing.
机译：乘法线性秘密共享是安全多方计算领域中的基本概念，并且自从最近以来，在两方密码学领域中也是一个基本概念。简而言之，该概念保证了将两个秘密的乘积作为向量的线性函数而获得，该向量由两个相应的份额向量的坐标乘积组成。本文关注以下基本问题，据我们所知，这是一个新颖的问题。假设我们放弃了后者的线性条件，而是要求通过某些非必要的线性“乘积重建函数”获得乘积。得到的概念是否等同于乘法线性秘密共享？我们显示（也许有些违反直觉）的结果表明，这种宽松的概念严格地更笼统。具体而言，将有限域F-q固定为考虑线性秘密共享的基础域。然后，我们证明存在一个（外来的）线性秘密共享方案，其中参与者的数量不受限制，因此它具有t = Omega（n）的t隐私，并且确实具有产品重构功能，但是该功能必不可少非线性的此外，我们确定了那些具有异国情调的计划的最小玩家数量。我们的证明基于涉及二次形式的组合论证。对于重要的变化，例如强乘法秘密共享，它扩展到相似的分离结果。

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  • 来源
    《SIAM Journal on Discrete Mathematics》 |2015年第2期|1114-1131|共18页
  • 作者

    Cascudo Ignacio; Cramer Ronald; Mirandola Diego; Padro Carles; Xing Chaoping;

  • 作者单位

    Aarhus Univ, DK-8200 Aarhus, Denmark;

    Leiden Univ, CWI Amsterdam, NL-2300 RA Leiden, Netherlands|Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands;

    Leiden Univ, CWI Amsterdam, NL-2300 RA Leiden, Netherlands|Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands|Univ Bordeaux, Inst Math Bordeaux, UMR 5251, Bordeaux, France;

    Univ Politecn Cataluna, Matemat Aplicada, Barcelona, Spain;

    Nanyang Technol Univ, Div Math Sci, Singapore 639798, Singapore;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    (arithmetic) secret sharing;

    机译：（算术）秘密共享;

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