Implementation of arithmetic operation of finite field GF(2n)

Finite field GF(2ⁿ) is an indispensable mathematical tool for some research fields such as information coding, cryptology and theory and application of network coding. Its arithmetic operation is the foundation of encoding information. Based on its formation, this paper discusses the principle and method of arithmetic operation of finite field GF(2ⁿ), and focuses on the inverse operation and division operation, then presents the concrete realization algorithm of arithmetic operation. This paper also analyzes the mechanism of implementing inverse operation with extended Euclidean algorithm. Based on Gauss elimination, an algorithm to implement division operation is proposed, the implementing process of arithmetic operation and the results of simulation calculations are provided.