DES加密算法

DES加密算法

简要说明

对称加密算法;
加密块大小: 64位;
密钥长度: 64位(加密算法只用了其中的56位, 另8位可作为校验位使用);
输出密文长度: 64位;
加密迭代次数: 16轮;

算法流程

算法步骤

相关矩阵常量见附录;

Key Schedule计算

记有64位长密钥 $K E Y$ , 置换 $P C 1_{C}$ / $P C 1_{D}$ / $P C 2$ , 及每一轮迭代的循环左移函数 $L S$ . 通过 $P C 1_{C}$ 和 $P C 1_{D}$ 置换选择得到28位长的 $C_{0}$ 和 $D_{0}$ , 那么第 $i$ 轮的加密密钥 $K_{i}$ 计算步骤如下( $i = [0, 16)$ ):

$C_{i + 1} = C_{i} ⋘ L S [i]$ , $D_{i + 1} = D_{i} ⋘ L S [i]$ ;
$K^{'} = C_{i + 1} ≪ 28 | D_{i + 1}$ ;
$P C 2 : K^{'} \to K_{i + 1}$

加密

记有64位输入输入 $I n p u t$ , 初始置换 $I P$ 和其逆 $I P^{- 1}$ , feistel函数 $f$ , 每一轮迭代的加密密钥集 $K$ . 通过初始置换 $I P$ 映射得到 $L R$ , $L R = L_{0} ≪ 32 | R_{0}$ . 那么第 $i$ 轮加密过程可描述如下( $i = [0, 15]$ ):

$L_{i + 1} = R_{i}$ ;
$R_{i + 1} = L_{i} \oplus f (R_{i}, K_{i + 1})$ ;

通过以上迭代16轮后, 得到 $L_{16}$ 和 $R_{16}$ , 组合得到预输出 $R L = R_{16} ≪ 32 | L_{16}$ , 再通过 $I P^{- 1}$ 置换得到输出数据 $O u t p u t$ .

Feistel函数

记有从32位扩展到48位映射矩阵 $E$ 和压缩映射矩阵 $S_{i}$ , 及置换 $P$ . 对于32位的输入 $R$ 和48位长的密钥 $K$ , $f$ 计算过程如下:

$E : R \to R^{'}$ ;
$t = K \oplus R^{'}$ ;
将 $t$ 按每6位一组, 共8组, 每组记为 $t_{i}$ ( $i = [0, 7]$ ). 将 $t_{i}$ 的第0位和第5位组合在一起的十进制数记为 $m$ , 将 $t_{i}$ 中间的4位组合在一起记为 $n$ . 例 $t_{i} = 011011$ , 那么 $m = 01 = 2$ , $n = 1101 = 13$ ;
$S : t_{i} \to t_{i}^{^{'}}$ , 映射方式是 $t_{i}^{^{'}} = S [m * 16 + n]$ , $t_{i}^{^{'}}$ 是4位的;
将 $t_{0}^{^{'}} \dots t_{7}^{^{'}}$ 拼接组合在一起得到 $t_{0}^{^{'}} t_{1}^{^{'}} \dots t_{7}^{^{'}}$ 得到32位长的数据, 记为 $d$ ;
$P : d \to d^{'}$ 置换得到f的输出;

字节序: 大端序;
$⋘$ : 循环左移;
$≪$ : 逻辑左移;
$\oplus$ : 二进制加模2;
$p : S^{'} \to S$ : 通过映射(置换) $p$ , 从集 $S^{'}$ 映射到 $S$ . 本文中, 如无特别说明, 就是将 $S^{'}$ 的第 $p [i]$ 位放在 $S$ 的第 $i$ 位;

TDEA

TDEA三重DES加密: 通过三组密钥 $[K 1, K 2, K 3]$ 重复三次加密解密. 即加密过程: 用密钥 $K 1$ DES加密, $K 2$ DES解密, $K 3$ DES加密; 解密是其逆过程; 描述如下:

\begin{aligned} I n p u t \to D E S (E_{K 1}) \to D E S (D_{K 2}) \to D E S (E_{K 3}) \to O u t p u t \\ I n p u t \to D E S (D_{K 3}) \to D E S (E_{K 2}) \to D E S (D_{K 1}) \to O u t p u t \end{aligned}

标准中 $[K 1, K 2, K 3]$ 有如下三种可能:

$K 1 \neq K 2 \neq K 3$ ;
$K 1 \neq K 2, K 3 = K 1$ ;
$K 1 = K 2 = K 3$ ;

常量表

/// 初始置换IP  
const DES_IP: [u8; 64] = [
58, 50, 42, 34, 26, 18, 10, 2,
60, 52, 44, 36, 28, 20, 12, 4,
62, 54, 46, 38, 30, 22, 14, 6,
64, 56, 48, 40, 32, 24, 16, 8,
57, 49, 41, 33, 25, 17, 9, 1,
59, 51, 43, 35, 27, 19, 11, 3,
61, 53, 45, 37, 29, 21, 13, 5,
63, 55, 47, 39, 31, 23, 15, 7,
];

/// 逆初始置换IIP  
const DES_IIP: [u8; 64] = [
40, 8, 48, 16, 56, 24, 64, 32,
39, 7, 47, 15, 55, 23, 63, 31,
38, 6, 46, 14, 54, 22, 62, 30,
37, 5, 45, 13, 53, 21, 61, 29,
36, 4, 44, 12, 52, 20, 60, 28,
35, 3, 43, 11, 51, 19, 59, 27,
34, 2, 42, 10, 50, 18, 58, 26,
33, 1, 41, 9, 49, 17, 57, 25,
];

/// feistel函数使用的相关映射表  
/// 32位长度数据映射到48位长数据的位映射表  
const DES_E: [u8; 48] = [
32, 1, 2, 3, 4, 5,
4, 5, 6, 7, 8, 9,
8, 9, 10, 11, 12, 13,
12, 13, 14, 15, 16, 17,
16, 17, 18, 19, 20, 21,
20, 21, 22, 23, 24, 25,
24, 25, 26, 27, 28, 29,
28, 29, 30, 31, 32, 1,
];

/// 48位长数据映射到32位长数据的映射表, Si将第i个6位数据映射到4位长数据  
const DES_S1: [u8; 64] = [
14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7,
0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8,
4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0,
15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13,
];

const DES_S2: [u8; 64] = [
15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10,
3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5,
0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15,
13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9,
];

const DES_S3: [u8; 64] = [
10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8,
13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1,
13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7,
1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12,
];

const DES_S4: [u8; 64] = [
7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15,
13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9,
10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4,
3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14,
];

const DES_S5: [u8; 64] = [
2, 12, 4, 1, 7, 10, 11, 6, 8, 5, 3, 15, 13, 0, 14, 9,
14, 11, 2, 12, 4, 7, 13, 1, 5, 0, 15, 10, 3, 9, 8, 6,
4, 2, 1, 11, 10, 13, 7, 8, 15, 9, 12, 5, 6, 3, 0, 14,
11, 8, 12, 7, 1, 14, 2, 13, 6, 15, 0, 9, 10, 4, 5, 3,
];

const DES_S6: [u8; 64] = [
12, 1, 10, 15, 9, 2, 6, 8, 0, 13, 3, 4, 14, 7, 5, 11,
10, 15, 4, 2, 7, 12, 9, 5, 6, 1, 13, 14, 0, 11, 3, 8,
9, 14, 15, 5, 2, 8, 12, 3, 7, 0, 4, 10, 1, 13, 11, 6,
4, 3, 2, 12, 9, 5, 15, 10, 11, 14, 1, 7, 6, 0, 8, 13,
];

const DES_S7: [u8; 64] = [
4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1,
13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6,
1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2,
6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12,
];

const DES_S8: [u8; 64] = [
13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7,
1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2,
7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8,
2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11,
];

/// feistel使用的置换函数  
const DES_P: [u8; 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,
];

/// key schedule密钥调度表计算使用到的映射表  
const DES_PC1_C: [u8; 28] = [
57, 49, 41, 33, 25, 17, 9,
1, 58, 50, 42, 34, 26, 18,
10, 2, 59, 51, 43, 35, 27,
19, 11, 3, 60, 52, 44, 36,
];  

const DES_PC1_D: [u8; 28] = [
63, 55, 47, 39, 31, 23, 15,
7, 62, 54, 46, 38, 30, 22,
14, 6, 61, 53, 45, 37, 29,
21, 13, 5, 28, 20, 12, 4,
];  

const DES_PC2: [u8; 48] = [
14, 17, 11, 24, 1, 5,
3, 28, 15, 6, 21, 10,
23, 19, 12, 4, 26, 8,
16, 7, 27, 20, 13, 2,
41, 52, 31, 37, 47, 55,
30, 40, 51, 45, 33, 48,
44, 49, 39, 56, 34, 53,
46, 42, 50, 36, 29, 32,
];

/// 每轮密钥计算的左移位数  
const DES_LS: [u8; 16] = [
1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1,
];