Authentication codes with secrecy are an interesting and important topic in cryptography. Their constructions can be classified into three categories: combinatorial, algebraic and geometric. However, the existing construction methods are mostly combinatorial. Since combinatorial designs satisfying certain requirements are very rare, the parameters of the authentication codes based on combinatorial designs are restricted to certain sets. Thus it is of great value to seek other construction methods....[ Read more ]

Authentication codes with secrecy are an interesting and important topic in cryptography. Their constructions can be classified into three categories: combinatorial, algebraic and geometric. However, the existing construction methods are mostly combinatorial. Since combinatorial designs satisfying certain requirements are very rare, the parameters of the authentication codes based on combinatorial designs are restricted to certain sets. Thus it is of great value to seek other construction methods.

In this thesis, we propose a series of construction methods of authentication codes with secrecy. Two of them are geometric, the others are algebraic. These constructions are flexible, and can be trimmed to meet different levels of secrecy and security requirements. They are also optimal or asymptotically optimal in the sense that they meet or asymptotically meet some information-theoretic and combinatorial bounds.