DES加密算法
簡要說明
- 對稱加密算法;
- 加密塊大小: 64位;
- 密鑰長度: 64位(加密算法只用了其中的56位, 另8位可作為校驗位使用);
- 輸出密文長度: 64位;
- 加密迭代次數: 16輪;
算法流程
graph TD; id1(輸入) --> id2(初始置換L0R0); id2 --> id3_1(R0); id3_0 --> rotate1((異或)); f1(f) --> rotate1; k1(K1) --> f1; id3_1 --> f1; id2 --> id3_0(L0); id3_1 --> l1(L1); rotate1 --> r1(R1); k2(K2) --> f2(f); r1 --> f2; f2 --> rotate2((異或)); l1 --> rotate2; rotate2 --> r2(R2); r1 --> l2(L2); r2 -.-> fn(f); kn(kn) -.-> fn(f); fn -.-> rotaten((異或)); l2 -.-> rotaten; rotaten -.-> r15(R15); r2 -.-> l15(L15); r15 --> l16(L16); l15 --> rotate16((異或)); k16(K16) --> rotate16; rotate16 --> r16(R16); l16 --> r16l16(R16L16); r16 --> r16l16; r16l16 --> preout(逆初始置換); preout --> output(輸出);
算法步驟
- 相關矩陣常量見附錄;
Key Schedule計算
記有64位長密鑰\(KEY\), 置換\(PC1_C\)/\(PC1_D\)/\(PC2\), 及每一輪迭代的循環左移函數\(LS\). 通過\(PC1_C\)和\(PC1_D\)置換選擇得到28位長的\(C_0\)和\(D_0\), 那么第\(i\)輪的加密密鑰\(K_i\)計算步驟如下(\(i=[0, 16)\)):
- \(C_{i+1} = C_i \lll LS[i]\), \(D_{i+1} = D_i \lll LS[i]\);
- \(K' = C_{i+1} \ll 28 \quad | \quad D_{i+1}\);
- \(PC2: K' \rightarrow K_{i+1}\)
加密
記有64位輸入輸入\(Input\), 初始置換\(IP\)和其逆\(IP^{-1}\), feistel函數\(f\), 每一輪迭代的加密密鑰集\(K\). 通過初始置換\(IP\)映射得到\(LR\), \(LR = L_0 \ll 32 \quad | \quad R_0\). 那么第\(i\)輪加密過程可描述如下(\(i=[0,15]\)):
- \(L_{i+1} = R_{i}\);
- \(R_{i+1} = L_{i} \oplus f(R_{i}, K_{i+1})\);
通過以上迭代16輪后, 得到\(L_{16}\)和\(R_{16}\), 組合得到預輸出\(RL = R_{16} \ll 32 \quad | \quad L_{16}\), 再通過\(IP^{-1}\)置換得到輸出數據\(Output\).
Feistel函數
記有從32位擴展到48位映射矩陣\(E\)和壓縮映射矩陣\(S_i\), 及置換\(P\). 對於32位的輸入\(R\)和48位長的密鑰\(K\), \(f\)計算過程如下:
- \(E: R \rightarrow R'\);
- \(t = K \oplus R'\);
- 將\(t\)按每6位一組, 共8組, 每組記為\(t_i\)(\(i=[0,7]\)). 將\(t_i\)的第0位和第5位組合在一起的十進制數記為\(m\), 將\(t_i\)中間的4位組合在一起記為\(n\). 例\(t_i=011011\), 那么\(m=01=2\), \(n=1101=13\);
- \(S: t_i \rightarrow t_{i}^{'}\), 映射方式是\(t_{i}^{'}=S[m*16+n]\), \(t_{i}^{'}\)是4位的;
- 將\(t_{0}^{'} \cdots t_{7}^{'}\)拼接組合在一起得到\(t_{0}^{'}t_{1}^{'}\dots t_{7}^{'}\)得到32位長的數據, 記為\(d\);
- \(P: d \rightarrow d'\)置換得到f的輸出;
解密
解密是加密的逆過程, 步驟略;
附錄
符號說明
- 字節序: 大端序;
- \(\lll\): 循環左移;
- \(\ll\): 邏輯左移;
- \(\oplus\): 二進制加模2;
- \(p: S' \rightarrow S\): 通過映射(置換)\(p\), 從集\(S'\)映射到\(S\). 本文中, 如無特別說明, 就是將\(S'\)的第\(p[i]\)位放在\(S\)的第\(i\)位;
TDEA
TDEA三重DES加密: 通過三組密鑰\([K1, K2, K3]\)重復三次加密解密. 即加密過程: 用密鑰\(K1\)DES加密, \(K2\)DES解密, \(K3\)DES加密; 解密是其逆過程; 描述如下:
\[\begin{aligned} Input \rightarrow DES(E_{K1}) \rightarrow DES(D_{K2}) \rightarrow DES(E_{K3}) \rightarrow Output \\ \quad Input \rightarrow DES(D_{K3}) \rightarrow DES(E_{K2}) \rightarrow DES(D_{K1}) \rightarrow Output \end{aligned} \]
標准中\([K1, K2, K3]\)有如下三種可能:
- \(K1 \neq K2 \neq K3\);
- \(K1 \neq K2, K3 = K1\);
- \(K1 = K2 = K3\);
常量表
/// 初始置換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,
];
/// 逆初始置換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函數使用的相關映射表
/// 32位長度數據映射到48位長數據的位映射表
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位長數據映射到32位長數據的映射表, Si將第i個6位數據映射到4位長數據
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使用的置換函數
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密鑰調度表計算使用到的映射表
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,
];
/// 每輪密鑰計算的左移位數
const DES_LS: [u8; 16] = [
1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1,
];
參考資料
- FIPS 46-3;