A Study on a Method for Computing the Powers and Inverses in GF($2^m$)

GF($2^m$) 상의 누승 및 역원을 구하는 방법에 관한 연구

This paper presents a method for computing the powers and inverse of an element in GF($2^m$). This method is based on the squaring algorithm $A^2=\sum\limits_{i=0}^{2m-2}P_i$, where $Pi={\alpha}_{i/2}$ if i is even, Pi=0 otherwise, derived from the multiplication algorithm for two elements in GF($2^m$). The powers and inverses in GF($2^m$) for m=2, 3, 4,5 were obtained using computer program, and used in circuit realization of Galois switching function. The squaring and inverse generating circuits are also shown.