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基于通用访问结构的秘密共享的一般性结论 被引量：1

General Results on Secret Sharing Based on General Access Structure
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摘要 目前对于秘密共享的研究主要集中在具备完善性的访问结构上,且所包含的访问集个数较少;关于份额界的研究主要是以被研究对象服从均匀分布为假设前提,并以份额所需比特位数作为界的度量,从而导致研究成果具有局限性.基于通用访问结构,给出了包含任意多个访问集、适用于完善性与非完善性访问结构的基于信息论的一般性结论,是当前相关研究成果的一般化总结,并可作为更深层次研究的基础和工具.同时,以份额的信息熵作为界的度量,给出了适用于所有份额的通用界和只适用于特定份额的通用界,这些结论同样是对相关研究成果的一般化总结,且均适用于任意概率分布,其中某些界要比许多已知研究结果具有更好的紧致性. For secret sharing, current researches mainly focus on perfect access structures with a very limited number of access subsets, where each subset is either a qualified set or a forbidden set and no semi-access subset exists, as well as on the share＇s bounds under a uniform distribution, where the number of the bits required by a share is used as the measurement of the bounds. Therefore, the research results are inevitably limited to some extent. Based on general access structures, some generalized information-theoretic results that are suitable for both perfect and non-perfect access structures with an unlimited number of access subsets identified by qualified, forbidden or semi-access are presented in this paper. These results are the general conclusions of many current related works and can be used as the basis for further researches. Meantime, using the information entropy of a share as the measurement of the bounds, some generalized bounds that are suitable for all shares and bounds that are suitable only for particular shares are given too. The bounds are also the generalization of many current related results under arbitrary probability distributions. Some of the bounds are tighter than those well-known ones. Additionally, with the help of the above new generalized results, some potential results can be easily deduced and the proof for many well-known results can be easier and more concise.
作者 张海波 王小非 黄友澎
机构地区 武汉数字工程研究所
出处 《计算机研究与发展》 EI CSCD 北大核心 2010年第2期207-215,共9页 Journal of Computer Research and Development
基金 国家"八六三"高技术研究发展计划基金项目(2007AA01Z464)~~
关键词 秘密共享 份额 通用访问结构 完善秘密共享 非完善秘密共享 secret sharing share general access structure perfect secret sharing non-perfect secret sharing
分类号 TP309 [自动化与计算机技术—计算机系统结构] TP393.08 [自动化与计算机技术—计算机应用技术]
  • 相关文献

参考文献26

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共引文献9

同被引文献12

  • 1李慧贤,程春田,庞辽军.一个基于细胞自动机的多秘密共享方案[J].系统工程理论与实践,2006,26(6):113-116. 被引量：1
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  • 6He J, Dawson E. Multi-secret sharing scheme based on one- way function [J]. Electronics Letters, 1995, 31(2) : 93-95.
  • 7Chen T H, Wu C S. Ef{icient multi-secret image sharing based on Boolean operations [J]. Signal Processing, 2011, 91(1): 90-97.
  • 8Das A, Adhikari A. An efficient multi-use multi-secret sharing scheme based on hash function [J]. Applied Mathematics Letters, 2010, 23(9): 993-996.
  • 9Dehkordi M H, Mashhadi S. New efficient and practical verifiable multi-secret sharing schemes [J]. Information Sciences, 2008, 178(9): 2262-2274.
  • 10Lin H Y, Yeh Y S. Dynamic multi-secret sharing scheme [J]. International Journal of Contemporary Mathematical Sciences, 2008, 3(1): 37-42.

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计算机研究与发展
2010年 第2期

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