由Kam和Davida所提出完全性的觀念，相信是抓住了替代箱複雜性的直覺概念。而為了更進一步加強完全性的觀念，Hwang和Ho提出了雙向完全性的觀點，使替代箱的品質更趨完美。在本論文中，我們提出能建造具有中間值多數性雙向完全性替代箱的一些演算法。而我們也知道，一完全性的替代箱，它的多數性大於零，故求多數性上限值的演算法也在本論文被提出。

The concept of completeness introduced by Kam and Davida is believed to have captured the intuitive notion of complexity of substitution boxes. In order to strengthen completeness concept further, Hwang and Ho presented a modification called two-way completeness. Substitution boxes having this new prop- erty possesses improved performance in general. In this thesis , we provide some algorithms which construct two-way complete substitution boxes with medium multiplicities. An upper bound on multiplicity is also derived.