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source/_posts/2021-10-05-sm3.md

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+---
+layout: post
+title:  "SM3密码杂凑算法"
+date: 2021-10-05 23:59:12
+categories: [算法]
+excerpt_separator: <!--more-->
+---
+SM3密码杂凑算法
+<!--more-->
+
+## 1. 填充
+
+    假设消息m 的长度为l 比特。首先将比特“1”添加到消息的末尾,再添加k 个“0”,k是满足l + 1 + k ≡ 448mod512 的最小的非负整数。然后再添加一个64位比特串,该比特串是长度l的二进制表示。
+
+其中将bit转byte有$448bit = 56byte$，$512bit = 64byte$。
+$l + 1 + k \equiv 448 mod 512$ 等于 $l + 1 + k \equiv 56 mod 64$
+若$a \equiv b \mod p$，则对于任意的c，都有$(a + c) \equiv (b + c) \mod p$。
+$$k \equiv (56 - 1 - l) \mod 64 \qquad 0 \le k \le 63$$
+
+```go
+// 填充go语言实现
+// 1 byte end marker :: 0-63 padding bytes :: 8 byte length
+tmp := [1 + 63 + 8]byte{0x80}
+pad := (55 - len) % 64                          // calculate number of padding bytes
+binary.BigEndian.PutUint64(tmp[1+pad:], len<<3) // append length in bits
+Write(tmp[:1+pad+8])
+```
+
+## 2. 迭代过程
+
+将填充后的消息m′按512比特进行分组:m′ = B(0)B (1)· · · B(n−1)。
+
+```go
+for i := 0; i <= len(p)-BlockSize; i += BlockSize {
+    // eliminate bounds checks on p
+    q := p[i:]
+    q = q[:BlockSize:BlockSize]
+}
+```
+
+## 3. 消息扩展
+
+* a) 将消息分组B(i)划分为16个字W0, W1, · · ·, W15。
+```go
+for j := 0; j < 16; j++ {
+    w0[j] = binary.BigEndian.Uint32(q[4*j : 4*(j+1)])
+}
+```
+
+* b)
+$
+FOR \quad j=16 \quad TO \quad 67 \\
+\qquad W_j ← P1(W_{j−16} ⊕ W_{j−9} ⊕ (W_{j−3} ≪ 15)) ⊕ (W_{j−13} ≪ 7) ⊕ W_{j−6} \\
+ENDFOR
+$
+```go
+for j := 16; j < 68; j++ {
+    w0[j] = P1(w0[j-16]^w0[j-9]^bits.RotateLeft32(w0[j-3], 15)) ^ bits.RotateLeft32(w0[j-13], 7) ^ w0[j-6]
+}
+```
+
+* c)
+$
+FOR \quad j=0 \quad TO \quad 63 \\
+\qquad W'_j = W_j ⊕ W_{j+4} \\
+ENDFOR
+$
+
+```go
+for j := 0; j < 64; j++ {
+    w1[j] = w0[j] ^ w0[j+4]
+}
+```
+
+## 4. 压缩函数
+
+```go
+A, B, C, D, E, F, G, H := a, b, c, d, e, f, g, h
+for j := 0; j < 16; j++ {
+    SS1 := bits.RotateLeft32(bits.RotateLeft32(A, 12)+E+bits.RotateLeft32(0x79cc4519, j), 7)
+    SS2 := SS1 ^ bits.RotateLeft32(A, 12)
+    TT1 := FF0(A, B, C) + D + SS2 + w1[j]
+    TT2 := GG0(E, F, G) + H + SS1 + w0[j]
+    D = C
+    C = bits.RotateLeft32(B, 9)
+    B = A
+    A = TT1
+    H = G
+    G = bits.RotateLeft32(F, 19)
+    F = E
+    E = P0(TT2)
+}
+for j := 16; j < 64; j++ {
+    SS1 := bits.RotateLeft32(bits.RotateLeft32(A, 12)+E+bits.RotateLeft32(0x7a879d8a, j), 7)
+    SS2 := SS1 ^ bits.RotateLeft32(A, 12)
+    TT1 := FF1(A, B, C) + D + SS2 + w1[j]
+    TT2 := GG1(E, F, G) + H + SS1 + w0[j]
+    D = C
+    C = bits.RotateLeft32(B, 9)
+    B = A
+    A = TT1
+    H = G
+    G = bits.RotateLeft32(F, 19)
+    F = E
+    E = P0(TT2)
+}
+a, b, c, d, e, f, g, h = a^A, b^B, c^C, d^D, e^E, f^F, g^G, h^H
+```