完善秘密共享体制的存取结构研究

Secret sharing is one important branch of modern cryptography and one important research field of information security. It plays a key role in safely preserving, transmitting and legally using the important information and the secret data. This project is going to study key problems of access structures in the research on the perfect classic and quantum secret sharing scheme. First, for the construction of ideal access structures of classic secret sharing schemes, through investigating the weight enumerators of certain linear codes, the conditions whether several types of linear codes are minimal are studied so as to make it easier to determine the ideal access structures; As for non-ideal access structure, according to graph theory and classical information theory, the method of computing optimal information rates for graph access structures of 5 to 9 participants will be generalized to the case of n participants. Then more general statement as well as the related algorithm can be proved. And second, in the field of quantum cryptography, based on hypergraph theory and quantum information theory, this project will derive optimal information rates of quantum access structures with more than four players. On the other hand, more general results such as the characterization of ideal quantum access structures will be studied. Research results will enrich the theory of access structures of secret sharing schemes, and lay a theoretical foundation for its application in cryptography.

秘密共享是现代密码学领域一个非常重要的分支，它在信息和秘密数据的安全保存、传输及合法利用上都起着关键的作用。本项目拟研究完善的经典和量子秘密共享体制中有关存取结构的关键问题。 首先，针对线性码上经典秘密共享体制的理想存取结构的构造问题，拟通过研究线性码的重量算子来确定码的极小性，从而获取极小线性码上秘密共享体制的理想存取结构；其次，对于经典秘密共享体制的非理想的图存取结构的最优信息率计算问题，基于图理论及经典信息论，将现有的含5至9个参与者的图存取结构信息率计算方法推广至n个参与者时的情况，得出信息率上下界值一般性结论，设计图存取结构的最优信息率的计算算法。最后，针对量子存取结构信息率的计算问题，基于超图理论及量子信息论，计算4人以上的量子存取结构最优信息率，并对理想的量子存取结构进行初步刻画。研究成果将丰富秘密共享体制的存取结构的理论体系，并为其在密码学中的应用奠定理论基础。

秘密共享是现代密码学领域一个非常重要的分支，它在信息和秘密数据的安全保存、传输及合法利用上都起着关键的作用。本项目拟研究完善的经典和量子秘密共享体制中存取结构及其方案构造的一些关键问题。本项目针对线性码上经典秘密共享体制的理想存取结构的构造及应用做了以下研究。首先，针对线性码上理想访问结构难以构造的问题，拟通过研究有限域上多种类型码的重量算子，寻求这些码中极小码字的分布规律，获取较多的理想访问结构；其次，建立访问控制策略中用户属性集与理想访问结构中授权集的对应关系，利用线性码上访问结构的理想性、多样性，构造具有一般属性集的高效安全的属性基签密方案。最后，研究了具有较好性质的量子秘密共享方案的构建，并给出了详细的安全性证明。