确定RijndaelS盒布尔函数的等价方法

Method to determine equivalent Boolean function of Rijndael S-box

针对Rijindael S盒输出分量函数等价方法的复杂度随搜索空间增大急剧升高的问题,利用有限域中元素分量与迹函数间的关系,从迹函数的角度研究Rijndael S盒输出分量函数,证明了Rijndael S盒输出比特的分量函数间存在着线性等价关系.与Joanne Fuller方法相比,该方法简单且复杂度低,不受搜索的函数空间限制;同时根据有限域中元素分量函数之间的等价关系,发现其元素分量函数代数表达式的系数全不相等且不为0或1.

The equivalence of element coordinates of advanced encryption standard （AES） S-box is very complicated because of using the local structural properties and equivalent classes. The bit coordinates of Rijndael S-box from the point of trace function was studied, indicatint that the bit coordinates of Rijndael S-box is equivalent. Comparison with Joanne Fuller＇s method, this method is very simple without the limitation of the space of searched functions. It is also discovered that none of the coefficients of element coordinate functions is equal and is 0 or 1.