给出这个s盒 sbox = [0x3,0x7,0x2,0x4,0xf,0xd,0xb,0x1,0xa,0x8,0xc,0x3,0x0,0x9,0x7,0xa]的差分均匀性
时间: 2023-09-18 08:14:05 浏览: 66
差分均匀性是刻画一个S盒在输入比特和输出比特变化的关系中的性质,可以用差分分布表来描述。对于一个n比特的S盒,差分分布表是一个2^n * 2^n的矩阵,其中第i行j列的元素表示输入差分为i,输出差分为j的输入输出对数目。
对于这个S盒,差分分布表如下:
| i\j | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | a | b | c | d | e | f |
|-----|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 2 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 |
| 2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 |
| 3 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 0 | 0 |
| 5 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 2 | 0 |
| 6 | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 |
| 7 | 0 | 0 | 2 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 |
| 8 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 2 | 0 | 2 |
| 9 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 0 | 2 | 0 |
| a | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 2 | 0 | 0 |
| b | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 2 |
| c | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 2 |
| d | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 2 | 2 | 0 | 0 |
| e | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 2 |
| f | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 |
其中,每个元素的值表示该输入输出对出现的次数。差分均匀性定义为差分分布表中所有元素的绝对值之和除以输入输出对的总数,即
$U=\frac{1}{2^{2n}}\sum_{i=0}^{2^n-1}\sum_{j=0}^{2^n-1}|\text{Ddt}(i,j)|$
其中,Ddt(i,j)表示差分分布表中第i行j列的元素值。
对于这个S盒,输入输出比特数均为4比特,因此n=4。将差分分布表中所有元素的绝对值相加,得到
$U=2^{-8}\cdot 112=0.4375$
因此,这个S盒的差分均匀性为0.4375。