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计算机工程

• 安全技术 • 上一篇    下一篇

基于特权数组的向量空间秘密共享方案

刘荣香1,2,赖 红2,张 威3   

  1. (1. 青岛理工大学通信与电子工程学院,山东 青岛 266520;2. 北京邮电大学理学院,北京 100876;3. 黄岛边防检查站技术科,山东 青岛 266555)
  • 收稿日期:2012-11-14 出版日期:2014-01-15 发布日期:2014-01-13
  • 作者简介:刘荣香(1977-),女,讲师、博士研究生,主研方向:网络安全;赖 红,博士研究生;张 威,助理工程师
  • 基金资助:
    国家自然科学基金资助项目(50275061)

Vector Space Secret Sharing Scheme Based on Privileged Array

LIU Rong-xiang本 1,2, LAI Hong 2, ZHANG Wei 3   

  1. (1. School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, China; 2. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; 3. Technique Department, Huangdao Frontier Inspection Station, Qingdao 266555, China)
  • Received:2012-11-14 Online:2014-01-15 Published:2014-01-13

摘要: 基于Shamir秘密共享方案中的特权数组提出一个新的秘密共享方案。研究Shamir秘密共享方案中允许迹、非允许迹及特权数组的概念,分析非门限的Shamir秘密共享方案,并将允许迹、非允许迹和特权数组等概念推广到Brickell向量空间秘密共享体制中。该方案解决了Brickell方案中 函数的构造难题和Spiez S等人提出的公开问题,即任意长度特权数组的求解问题(Finite Fields and Their Applications, 2011, No.4)。分析结果表明,该方案基于向量空间秘密共享体制所构造,具有线性性,因此计算量较小。同时在秘密重构阶段,参与者可以相互验证彼此秘密份额的真实性,具有防欺诈功能。

关键词: Shamir秘密共享方案, Brickell秘密共享体制, 允许迹, 非允许迹, 特权数组, 防欺诈

Abstract: Based on privileged arrays in Shamir secret sharing schemes, a novel ideal secret sharing scheme is proposed. By researching the new concepts of admissible tracks, non-admissible tracks and privileged arrays on Shamir secret sharing schemes, this paper analyzes non-threshold Shamir schemes. Furthermore, these concepts are extended to Brickell secret sharing scheme based on vector space. This new scheme solves two questions: the difficulty the construction of function in Brickell scheme, and the algorithm to find privileged arrays of any length if such arrays exist. This scheme, on the basis of Brickell scheme, is linear, which has a low computational cost. Meanwhile, the participants can verify their shares with each other, which provids cheat-proof property of the scheme.

Key words: Shamir secret sharing scheme, Brickell secret sharing system, admissible track, non-admissible track, privileged array, cheat-proof

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