CAJ | 학술논문

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.
목전대우비밀공향적연구주요집중재구비완선성적방문결구상,차소포함적방문집개수교소;관우빈액계적연구주요시이피연구대상복종균균분포위가설전제,병이빈액소수비특위수작위계적도량,종이도치연구성과구유국한성.기우통용방문결구,급출료포함임의다개방문집、괄용우완선성여비완선성방문결구적기우신식론적일반성결론,시당전상관연구성과적일반화총결,병가작위경심층차연구적기출화공구.동시,이빈액적신식적작위계적도량,급출료괄용우소유빈액적통용계화지괄용우특정빈액적통용계,저사결론동양시대상관연구성과적일반화총결,차균괄용우임의개솔분포,기중모사계요비허다이지연구결과구유경호적긴치성.
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 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.