With the development of mix-net, the basic properties of mix-net cannot satisfy all the requirements of people. The verifiable mix-net raised in response to the proper time and conditions. In this paper, we study the problem of simultaneously achieving several security properties, for mix-nets and verifiability mix-nets. More precisely, under different assumptions and requirements, verifiability ... [Show full abstract] mix-nets have more extra security properties than mix-nets. The basic properties of mix-nets contain correctness, privacy, robustness, availability and efficient. The extra properties of verifiability mix-nets contain universal verifiability, unconditional anonymous, receipt-freeness. This paper summarizes all of the security properties, and defines them explicitly and systematically.