本项目主要研究带约束的强部分平衡t-设计, 正交阵列和认证直交表的构造方法和存在性, 用它们建立达到信息论下界或组合论下界的带仲裁的认证码和分裂认证码. 带约束的强部分平衡t-设计的研究主要围绕专著《消息认证码》中提出的研究问题进行, 特别是建立t>2的带序的完善带严格约束的强部分平衡t-设计的构造方法, 解决t>2的t-阶完善非Cartesion带仲裁认证码的存在问题. 正交阵列和认证直交表的研究则主要着眼于多元正交阵列和多元认证直交表这两类设计, 建立多元正交阵列和多元认证直交表的构造方法和存在性, 得到新的t-阶最优Cartesion分裂认证码和t-阶最优非Cartesion分裂认证码. 本项目所研究的内容涉及组合设计理论的基本课题且属该方向的前沿领域, 对它们的研究并取得突破性进展, 不仅在组合设计理论自身发展上有重要价值, 也将对信息安全理论产生积极的影响.

In this project, we will research the constructions and existence of restricted strong partially balanced t-designs，orthogonal arrays and authentication perpendicular arrays, and use them to construct authentication codes with arbitration and splitting authentication codes which achieve the information-theoretic bounds or the combinatorial bounds. Concerning the research of restricted strong partially balanced t-designs, we will work around the open problem presented in the monograph <<Message Authentication Codes>>, especially to establish the constructions of ordered perfect strict restricted strong partially balanced t-designs for t>2, solve the existence of t-fold perfect Non-Cartesion authentication codes with arbitration for t>2. Concerning the research of orthogonal arrays and authentication perpendicular arrays, we will pay attention to orthogonal multi-arrays and authentication perpendicular multi-arrays, establish the constructions and existence of orthogonal multi-arrays and authentication perpendicular multi-arrays, and give new t-fold optimal Cartesion splitting authentication codes and t-fold optimal Non-Cartesion splitting authentication codes. This project involves basic subjects of combinatorial design theory and belongs to frontier feilds of this area, researching them and making breakthrough progress, not only have important value in its own development of combinatorial design theory, but also have a positive impact on information security theory.