伽罗华域(Galois Field)

基本概念

有限域(Finite Field)

A finite field is a finite set on which the four operations multiplication, addition, subtraction and division (excluding division by zero) are defined, satisfying the rules of arithmetic known as the field axioms.
The simplest examples of finite fields are the fields of prime order: for each prime number p, the field GF(p)of order (that is, size) p may be constructed as the integers modulo p.

只包含有限个元素的域称为有限域。
在该域上定了了加减乘除四种操作。

GF(p)

元素个数为p的有限域一般记为GF(p)
GF代表伽罗华域，Galois Field

模运算

模运算

GF(2)

GF(8)

GF(256)

References:

https://wenku.baidu.com/view/2193ce590029bd64793e2c39.html?from=search
https://en.wikipedia.org/wiki/Finite_field