常见对称加密算法的扩散层(P盒)及其密码学指标

扩散层作为对称加密算法中的线性部件，它提供了算法必需的雪崩效应，它使得输出的一个比特依赖于输入的多个比特，让输出的密文数据更加随机，从而增加了算法抵抗破解的能力。

本文列出了常见加密算法的P盒各项密码指标，以供各位参考。

（1）汉明重量

对于向量X=(x1,x2,.....,xn)∈(F)，x1,x2,.....,xn中非零元的个数称为向量X的汉明重量，记为W(X)。

（2）差分分支数

线性变换θ的差分分支数定义为：

（3）线性分支数

线性变换θ的线性分支数定义为：

      （4）差分分支数和线性分支数

任意的线性变换θ一般都能够用有限域上的矩阵M进行刻画，若将线性变换θ：(F)→(F)表示成矩阵形式θ(X)=M•X，那么差分分支数和线性分支数可以分别表示为：

DES的扩散层：比特置换

BYTE DES_PBOX[32] =

{

16,7,20,21,29,12,28,17,1,15,23,26,5,18,31,10,2,8,24,14,32,27,3,9,19,13,30,6,22,11,4,25

}；

AES的扩散层：MDS矩阵(差分分支数和线性分支数都为5)

{

M[4][4]={{0x02,0x03,0x01,0x01},{0x01,0x02,0x03,0x01},{0x01,0x01,0x02,0x03},{0x03,0x01,0x01,0x02}}；

MInv[4][4]={{0x0e,0x0b,0x0d,0x09},{0x09,0x0e,0x0b,0x0d},{0x0d,0x09,0x0e,0x0b},{0x0b,0x0d,0x09,0x0e}}；

}

Serpent的扩散层：异或和移位

Serpent_PBOX：(X0,X1,X2,X3)→(Y0,Y1,Y2,Y3)

{

X0=X0<<<13

X2=X2<<<3

X1=X1⊕X0⊕X2

X3=X3⊕X2⊕(X0<<3)

X1=X1<<<1

X3=X3<<<7

X0=X0⊕X1⊕X3

X2=X2⊕X3⊕(X1<<7)

X0=X0<<<5

X2=X2<<<22

Y0=X0 Y1=X1 Y2=X2 Y3=X3

}；

ARIA的扩散层：MDBL矩阵(差分分支数和线性分支数都为8)

ARIA_PBOX(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15)→(y0,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)

{

y0 = x3⊕x4⊕x6⊕x8⊕x9⊕x13⊕x14;

y1 = x2⊕x5⊕x7⊕x8⊕x9⊕x12⊕x15;

y2 = x1⊕x4⊕x6⊕x10⊕x11⊕x12⊕x15;

y3 = x0⊕x5⊕x7⊕x10⊕x11⊕x13⊕x14;

y4 = x0⊕x2⊕x5⊕x8⊕x11⊕x14⊕x15;

y5 = x1⊕x3⊕x4⊕x9⊕x10⊕x14⊕x15;

y6 = x0⊕x2⊕x7⊕x9⊕x10⊕x12⊕x13;

y7 = x1⊕x3⊕x6⊕x8⊕x11⊕x12⊕x13;

y8 = x0⊕x1⊕x4⊕x7⊕x10⊕x13⊕x15;

y9 = x0⊕x1⊕x5⊕x6⊕x11⊕x12⊕x14;

y10 = x2⊕x3⊕x5⊕x6⊕x8⊕x13⊕x15;

y11 = x2⊕x3⊕x4⊕x7⊕x9⊕x12⊕x14;

y12 = x1⊕x2⊕x6⊕x7⊕x9⊕x11⊕x12;

y13 = x0⊕x3⊕x6⊕x7⊕x8⊕x10⊕x13;

y14 = x0⊕x3⊕x4⊕x5⊕x9⊕x11⊕x14;

y15 = x1⊕x2⊕x4⊕x5⊕x8⊕x10⊕x15;

}；

SM4的扩散层：异或和循环移位(差分分支数和线性分支数都为5)

SM4_PBOX：Y→Z

{

Z=L(Y)=Y⊕(Y<<<2)⊕(Y<<<10)⊕(Y<<<18)⊕(Y<<<24)

}；

CLEFIA的扩散层：MDS矩阵(差分分支数和线性分支数都为5)

{

M0[4][4]={{0x01,0x02,0x04,0x06},{0x02,0x01,0x06,0x04},{0x04,0x06,0x01,0x02},{0x06,0x04,0x02,0x01}}；

M1[4][4]={{0x01,0x08,0x02,0x0a},{0x08,0x01,0x0a,0x02},{0x02,0x0a,0x01,0x08},{0x0a,0x02,0x08,0x01}}；

}

Camellia的扩散层：MDBL矩阵(差分分支数和线性分支数都为5)

(x0,x1,x2,x3,x4,x5,x6,x7)→(y0,y1,y2,y3,y4,y5,y6,y7)

{

y0=x0⊕x2⊕x3⊕x5⊕x6⊕x7

y1=x0⊕x1⊕x3⊕x4⊕x6⊕x7

y2=x0⊕x1⊕x2⊕x4⊕x5⊕x7

y3=x1⊕x2⊕x3⊕x4⊕x5⊕x6

y4=x0⊕x1⊕x5⊕x6⊕x7

y5=x1⊕x2⊕x4⊕x6⊕x7

y6=x2⊕x3⊕x4⊕x5⊕x7

y7=x0⊕x3⊕x4⊕x5⊕x6

}

Present的扩散层：比特置换

BYTE Present_PBOX[64] =

{

0,16,32,48,1,17,33,49,2,18,34,50,3,19,35,51,

4,20,36,52,5,21,37,53,6,22,38,54,7,23,39,55,

8,24,40,56,9,25,41,57,10,26,42,58,11,27,43,59,

12,28,44,60,13,29,45,61,14,30,46,62,15,31,47,63

}

GIFT的扩散层：比特置换

BYTE GIFT_PBOX[64] =

{

0,17,34,51,48,1,18,35,32,49,2,19,16,33,50,3,

4,21,38,55,52,5,22,39,36,53,6,23,20,37,54,7,

8,25,42,59,56,9,26,43,40,57,10,27,24,41,58,11,

12,29,46,63,60,13,30,47,44,61,14,31,28,45,62,15

}

LBlock的扩散层：半字节置换

(x0,x1,x2,x3,x4,x5,x6,x7)→(y0,y1,y2,y3,y4,y5,y6,y7)

{

(y0,y1,y2,y3,y4,y5,y6,y7)=(x1,x3,x0,x2,x5,x7,x4,x6);

}

MIBS的扩散层：MDBL矩阵(差分分支数和线性分支数都为5)

MIBS_PBOX：(x0,x1,x2,x3,x4,x5,x6,x7)→(y0,y1,y2,y3,y4,y5,y6,y7)

{

y0=x0⊕x1⊕x3⊕x4⊕x6⊕x7

y1=x1⊕x2⊕x3⊕x4⊕x5⊕x6

y2=x0⊕x1⊕x2⊕x4⊕x5⊕x7

y3=x1⊕x2⊕x3⊕x6⊕x7

y4=x0⊕x2⊕x3⊕x4⊕x7

y5=x0⊕x1⊕x3⊕x4⊕x5

y6=x0⊕x1⊕x2⊕x5⊕x6

y7=x0⊕x2⊕x3⊕x5⊕x6⊕x7

}

KLEIN的扩散层：MDS矩阵(差分分支数和线性分支数都为5)

{

M[4][4]={{0x02,0x03,0x01,0x01},{0x01,0x02,0x03,0x01},{0x01,0x01,0x02,0x03},{0x03,0x01,0x01,0x02}}；

MInv[4][4]={{0x0e,0x0b,0x0d,0x09},{0x09,0x0e,0x0b,0x0d},{0x0d,0x09,0x0e,0x0b},{0x0b,0x0d,0x09,0x0e}}；

}

LED的扩散层：对合MDS矩阵(差分分支数和线性分支数都为5)

{

M[4][4]={{0x04,0x01,0x02,0x02},{0x08,0x06,0x05,0x06},{0x0b,0x0e,0x0a,0x09},{0x02,0x02,0x0f,0x0b}}；

MInv[4][4]={{0x04,0x01,0x02,0x02},{0x08,0x06,0x05,0x06},{0x0b,0x0e,0x0a,0x09},{0x02,0x02,0x0f,0x0b}}；

}

Midori的扩散层：Near-MDS矩阵(差分分支数和线性分支数都为4)

{

M[4][4]={{0,1,1,1},{1,0,1,1},{1,1,0,1},{1,1,1,0}}；

}

FeW：异或和循环移位(差分分支数和线性分支数都为5)

FeW_PBOX：Y→Z

{

Z=L1(Y)=Y⊕(Y<<<1)⊕(Y<<<5)⊕(Y<<<9)⊕(Y<<<12)

Z=L2(Y)=Y⊕(Y<<<4)⊕(Y<<<7)⊕(Y<<<11)⊕(Y<<<15)

}；

ESF的扩散层：比特置换

BYTE ESF_PBOX[32] =

{

0,8,16,24,1,9,17,25,2,10,18,26,3,11,19,27

4,12,20,28,5,13,21,29,6,14,22,30,7,15,23,31

}

AC的扩散层：异或和移位

AC_PBOX：(X0,X1,X2,X3)→(Y0,Y1,Y2,Y3)

{

X1=X1⊕(X3<<<7)

X0=X0⊕(X2<<<1)

X3=X3⊕(X0<<<5)

X2=X2⊕(X1<<<8)

X1=X1⊕(X3<<<8)

Swap(X3,X2)

Swap(X1,X0)

X1=X1⊕(X3<<<8)

X2=X2⊕(X1<<<8)

X3=X3⊕(X0<<<5)

X0=X0⊕(X2<<<1)

X1=X1⊕(X3<<<7)

Y0=X0 Y1=X1 Y2=X2 Y3=X3

}

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