密码学中的若干组合构形研究

In this project, we investigate the combination structures in key management and authentication/secrecy system. Based on establishing the connections between perfect authentication/secrecy codes and authentication partially balanced perpendicular arrays, perfect authentication/secrecy codes with arbitration and secrecy perfect ordered restricted strong partially balanced designs, perfect authentication/secrecy codes with splitting and authentication strong partially perpendicular multi-arrays, and the optimal authentication/secrecy codes with splitting and authentication perpendicular multi-arrays, through the investigation in the constructions and existence of above designs we obtain some new infinite classes of authentication/secrecy codes. Our research in strong partially balanced t-designs mainly focuses on the study of partitionable strong partially balanced t-designs. We plan to develop some new construction methods in this kind of design, obtain some new infinite classes of partitionable strong partially balanced t-designs and expand the existence range of perfect threshold schemes of this knid. The designs to be investigated in this project are ones of the fundamental subjects in combinatorial design theory and belong tofrontier feilds of this area. The research and possible breakthrough in this area will not only have great influence on the development of combinatorial design theory itself, but also have a positive impact on cryptography and communication theory.

本项目主要研究密钥管理和保密认证系统的组合结构，在建立完善保密认证码和认证部分平衡直交阵列, 保密完善带仲裁认证码和保密完善有序的约束强部分平衡设计, 完善保密分裂认证码和认证强部分直交多元阵列, 以及最优保密分裂认证码和认证直交多元阵列之间的联系的基础上, 通过对上述设计的构造方法和存在性的研究得到若干新的保密认证系统. 强部分平衡t-设计的研究则主要着眼于可划分强部分平衡t-设计, 摸索一些构造该类设计的新方法，建立若干新的无穷类的存在性, 扩大该类完美门限方案的存在范围.本项目所研究的设计均是组合设计理论中的基本课题，研究的内容均属该方向的前沿领域. 对它们的研究并取得突破性的成果，不仅在组合设计理论自身发展上有重要价值，也将对密码学和通信理论产生积极的影响.

本项目主要研究了密钥管理和保密认证系统的组合结构，在建立完善保密认证码和认证部分平衡直交阵列,保密完善带仲裁认证码和保密完善有序的约束强部分平衡设计,完善保密分裂认证码和认证强部分直交多元阵列,以及最优保密分裂认证码和认证直交多元阵列之间的联系的基础上,通过对上述设计的构造方法和存在性的研究得到了若干新的保密认证系统.强部分平衡t-设计的研究则主要着眼于可划分强部分平衡t-设计,摸索了一些构造该类设计的新方法，建立了若干新的无穷类的存在性,扩大了该类完美门限方案的存在范围.本项目所研究的设计均是组合设计理论中的基本课题，研究的内容均属该方向的前沿领域.对它们的研究并取得突破性的成果，不仅在组合设计理论自身发展上有重要价值，也将对密码学和通信理论产生积极的影响