Abstract: The algorithm of AES is restated on exponential domain to reveal its properties. The unique nonlinear operation of AES, i.e., the inverse of multiplication becomes linear. However, the linear operation XOR induces a nonlinear operation ∨ on exponential domain. Moreover,the operation ∨ is represented by star-dual operation and addition modulo 255,the law of star-dual operation is obtained, and the randomness of ∨-operation and star-dual operation is limited and put into a subset including nine elements. A new framework is given for advanced cryptanalysis.