AES的S盒和逆S盒的代数表达式

Algebraic Expression for AES S-box and InvS-box

利用GF(28)域中元素自身为变量表示元素分量的代数方法求解S盒和逆S盒的代数表达式,同时解释了S盒代数表达式只有9项而逆S盒代数表达式有255项的原因,此外提出了有限域下多项式幂次运算的一种快速乘方算法,实验结果表明该算法比直接乘法运算效果好。

This paper presents an algebraic method that the component of the field element can be expressed by a simple polynomial with the element itself as the variable over GF（2^8）. The algebraic expressions of S-box and lnvS-box can be resolved and the reasons why S-box has only 9 items but lnvS-box has 255 items are explained with this method. In addition it proposes a quick power algorithm for polynomial over finite field. The experimental results indicate that the algorithm is better than direct multiplication.