模2~n加与模2加相对结合律相容程度的分析

Analysis on the consistent degree of addition modulo 2~n with XOR for associative law

模2n加和模2加是密码算法设计中经常使用的两个编码环节,二者对于结合律的相容程度是指改变二者形成的混合等式中两个变量的运算顺序所造成的误差大小。本文研究了模2n加与模2加相对于结合律的相容程度,给出了在改变[(xy)+z]mod 2n的运算顺序时,产生的噪声函数ξ(x,y,z)=[(xy)+nz][x(y+nz)]在各点取值的概率分布规律,以及对噪声函数所有取值点的概率值平方求和的计算公式。这些结论在区分攻击中有一定的应用价值。

Addition modulo 2n and XOR addition are two code links which are often used in cipher algorithms,the consistent degree of the two links means the difference degree when the computing sequence is changed in the equation including the two links.The difference function between addition modulo 2n and XOR addition corresponding to associative law is studied.When the computing sequence of [（xy）＋z] mod 2n is changed,the computation formulae of the probability distribution of the difference function ξ（x,y,z）=[（xy）＋nz][x（y＋nz）] is given,and the square sum of the probability is given too.The results presented are useful for some distinguishing attack.