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@ -32,150 +32,183 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
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复合域   的不可约多项式为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?Q%28%5Cbeta%29%3D%5Cbeta%5E%7B17%7D+%5Cbeta%5E3+1")
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<img src="assets/formula/4-light.svg#gh-light-mode-only">
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<img src="assets/formula/4-dark.svg#gh-dark-mode-only">
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</p>
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各项系数全部位于 。设复合域的标准基为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B_2%3D%5C%7B1%2C%5Cbeta%2C%5Cbeta%5E2%2C%5Cldots%2C%5Cbeta%5E%7B16%7D%5C%7D")
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<img src="assets/formula/5-light.svg#gh-light-mode-only">
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<img src="assets/formula/5-dark.svg#gh-dark-mode-only">
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</p>
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则位于复合域   上的元素 ![B-inlined] 可以用如下方式表达：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%28%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%29%5Cbeta%5Ej%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cquad%20%5Cquad%20%5Cquad%20a_%7Bj%2Ci%7D%5Cin%5Ctextrm%7BGF%7D%282%29")
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<img src="assets/formula/6-light.svg#gh-light-mode-only">
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<img src="assets/formula/6-dark.svg#gh-dark-mode-only">
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</p>
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---
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为了方便表述我们用255比特的大数 ![D-inlined] 来表示位于复合域   上的元素 ![B-inlined]。它们的对应关系为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cleftrightarrow%20D%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Ccdot%202%5E%7B15j+i%7D")
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<img src="assets/formula/7-light.svg#gh-light-mode-only">
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<img src="assets/formula/7-dark.svg#gh-dark-mode-only">
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</p>
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## 2. 复合域 ![GF2p15p17-inlined] 上的椭圆曲线
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曲线方程为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?y%5E2+xy%3Dx%5E3+161%20%5Cquad%20%5Cquad%20%5Cquad%20161%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29")
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<img src="assets/formula/8-light.svg#gh-light-mode-only">
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<img src="assets/formula/8-dark.svg#gh-dark-mode-only">
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</p>
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基点 ![G-inlined] 为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20G%26%3D%28G_x%2CG_y%29%20%5C%5C%20G_x%26%3D%5Ctextrm%7B0x56fdcbc6a27acee0cc2996e0096ae74feb1acf220a2341b898b549440297b8cc%7D%20%5Cquad%20G_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%5C%5C%20G_y%26%3D%5Ctextrm%7B0x20da32e8afc90b7cf0e76bde44496b4d0794054e6ea60f388682463132f931a7%7D%20%5Cquad%20G_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D")
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<img src="assets/formula/9-light.svg#gh-light-mode-only">
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<img src="assets/formula/9-dark.svg#gh-dark-mode-only">
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</p>
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基点 ![G-inlined] 的阶 ![n-inlined] 为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?n%3D%5Ctextrm%7B0x1026dd85081b82314691ced9bbec30547840e4bf72d8b5e0d258442bbcd31%7D%20%5Cquad%20n%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D")
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<img src="assets/formula/10-light.svg#gh-light-mode-only">
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<img src="assets/formula/10-dark.svg#gh-dark-mode-only">
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</p>
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## 3. 消息哈希算法
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设长度为 ![l-inlined] 的消息为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?M%3Dm_0m_1%20%5Cldots%20m_%7Bl-1%7D%20%5Cquad%20%5Cquad%20m_i%5Cin%5B0%2C%20256%29")
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<img src="assets/formula/11-light.svg#gh-light-mode-only">
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<img src="assets/formula/11-dark.svg#gh-dark-mode-only">
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</p>
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则消息 ![M-inlined] 的SHA1值为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28M%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5Cquad%20%5Cquad%20S_i%5Cin%5B0%2C%202%5E%7B32%7D%29")
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<img src="assets/formula/12-light.svg#gh-light-mode-only">
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<img src="assets/formula/12-dark.svg#gh-dark-mode-only">
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</p>
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其中  为SHA1算法输出时的5个状态值；将这5个状态值按照大端字节序依次输出，即为的SHA1哈希值 。
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WinRAR在做完SHA1计算后，采用大数 ![h-inlined] 作为ECC签名时消息的哈希：
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其中  为SHA1算法输出时的5个状态值；将这5个状态值按照大端字节序依次输出，即为的SHA1哈希值 。
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WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时消息的哈希：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?h%3D%28%5Csum_%7Bi%3D0%7D%5E%7B4%7DS_i%20%5Ccdot%202%5E%7B32i%7D%29+%5Ctextrm%7B0x1bd10xb4e33c7c0ffd8d43%7D%20%5Ccdot%202%5E%7B32*5%7D")
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<img src="assets/formula/15-light.svg#gh-light-mode-only">
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<img src="assets/formula/15-dark.svg#gh-dark-mode-only">
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</p>
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## 4. ECC签名算法
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设私钥为 ![k-inlined]，公钥为 ![P-inlined]，即：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
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<img src="assets/formula/16-light.svg#gh-light-mode-only">
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<img src="assets/formula/16-dark.svg#gh-dark-mode-only">
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</p>
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消息哈希为 ![h-inlined]，则签名  为：
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1. 生成随机数 ![Rnd-inlined]，满足 。
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消息哈希为 ![h-inlined]，则签名  为：
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1. 生成随机数 ![Rnd-inlined]，满足 。
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2. 计算 ![r-inlined]
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?r%3D%28%28Rnd%20%5Ccdot%20G%29_x+h%29%5C%20%5C%20Mod%5C%20%5C%20n">
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<img src="assets/formula/19-light.svg#gh-light-mode-only">
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<img src="assets/formula/19-dark.svg#gh-dark-mode-only">
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</p>
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其中  表示取  的X坐标，同时将X坐标从 ![GF2p15p17-inlined] 转换为大数。
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若  或者  则回到步骤1。
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其中  表示取  的 X 坐标，同时将 X 坐标从 !  转换为大数。
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若  或者  则回到步骤1。
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3. 计算 ![s-inlined]
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
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<img src="assets/formula/24-light.svg#gh-light-mode-only">
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<img src="assets/formula/24-dark.svg#gh-dark-mode-only">
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</p>
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若  则回到步骤1。
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4. 输出 。
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若  则回到步骤1。
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4. 输出 。
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## 5. WinRAR的私钥生成算法
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该算法会利用长度为 ![l-inlined] 的数据
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?T%3Dt_0t_1%20%5Cldots%20t_%7Bl-1%7D%20%5Cquad%20%5Cquad%20t_i%5Cin%5B0%2C256%29">
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<img src="assets/formula/26-light.svg#gh-light-mode-only">
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<img src="assets/formula/26-dark.svg#gh-dark-mode-only">
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</p>
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来生成私钥 ![k-inlined]。
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1. 设6个32位整数为 ，则有
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1. 设6个32位整数为 ，则有
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?g_j%3D%5Csum_%7Bi%3D0%7D%5E%7B3%7Dg_%7Bj%2Ci%7D%20%5Ccdot%202%5E%7B8i%7D%20%5Cquad%20%5Cquad%20g_%7Bj%2Ci%7D%5Cin%5B0%2C256%29">
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<img src="assets/formula/28-light.svg#gh-light-mode-only">
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<img src="assets/formula/28-dark.svg#gh-dark-mode-only">
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</p>
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2. 令 。
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2. 令 。
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3. 如果  则计算 ![T-inlined] 的SHA1值，并将状态值  赋值给 ：
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3. 如果  则计算 ![T-inlined] 的 SHA1 值，并将状态值  赋值给 ：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20%5Ctextrm%7BSHA%7D_1%28T%29%26%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5C%5C%20g_1%26%3DS_0%20%5C%5C%20g_2%26%3DS_1%20%5C%5C%20g_3%26%3DS_2%20%5C%5C%20g_4%26%3DS_3%20%5C%5C%20g_5%26%3DS_4%20%5C%5C%20%5Cend%7Baligned%7D">
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<img src="assets/formula/33-light.svg#gh-light-mode-only">
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<img src="assets/formula/33-dark.svg#gh-dark-mode-only">
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</p>
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否则，即  时，令：
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否则，即  时，令：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20g_1%26%3D%5Ctextrm%7B0xeb3eb781%7D%20%5C%5C%20g_2%26%3D%5Ctextrm%7B0x50265329%7D%20%5C%5C%20g_3%26%3D%5Ctextrm%7B0xdc5ef4a3%7D%20%5C%5C%20g_4%26%3D%5Ctextrm%7B0x6847b9d5%7D%20%5C%5C%20g_5%26%3D%5Ctextrm%7B0xcde43b4c%7D%20%5C%5C%20%5Cend%7Baligned%7D">
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<img src="assets/formula/35-light.svg#gh-light-mode-only">
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<img src="assets/formula/35-dark.svg#gh-dark-mode-only">
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</p>
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4. 把  作为计数器，自增1。
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4. 把  作为计数器，自增1。
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计算SHA1值：
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计算 SHA1 值：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28g_%7B0%2C0%7D%7C%7Cg_%7B0%2C1%7D%7C%7Cg_%7B0%2C2%7D%7C%7Cg_%7B0%2C3%7D%7C%7Cg_%7B1%2C0%7D%7C%7Cg_%7B1%2C1%7D%7C%7C%5Cldots%7C%7Cg_%7B5%2C0%7D%7C%7Cg_%7B5%2C1%7D%7C%7Cg_%7B5%2C2%7D%7C%7Cg_%7B5%2C3%7D%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4">
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<img src="assets/formula/37-light.svg#gh-light-mode-only">
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<img src="assets/formula/37-dark.svg#gh-dark-mode-only">
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</p>
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取  的低16位并记为 。
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取  的低16位并记为 。
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5. 步骤4再重复14次。
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6. 重复执行完后会得到 ，则输出私钥
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6. 重复执行完后会得到 ，则输出私钥
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?k%3D%5Csum_%7Bi%3D1%7D%5E%7B15%7Dk_i%20%5Ccdot%202%5E%7B16i%7D">
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<img src="assets/formula/41-light.svg#gh-light-mode-only">
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<img src="assets/formula/41-dark.svg#gh-dark-mode-only">
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</p>
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## 6. WinRAR的公钥和私钥
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@ -183,106 +216,121 @@ WinRAR在做完SHA1计算后，采用大数 ![h-inlined] 作为ECC签名时消
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WinRAR的私钥 ![k-inlined] 为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?k%3D%5Ctextrm%7B0x59fe6abcca90bdb95f0105271fa85fb9f11f467450c1ae9044b7fd61d65e%7D%20%5Cquad%20%5Cquad%20k%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D">
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<img src="assets/formula/42-light.svg#gh-light-mode-only">
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<img src="assets/formula/42-dark.svg#gh-dark-mode-only">
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</p>
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该私钥是通过算法5生成的，其中数据 ![T-inlined] 的长度为0。
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公钥 ![P-inlined] 为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20P%26%3D%28P_x%2CP_y%29%20%5C%5C%20P_x%26%3D%5Ctextrm%7B0x3861220ed9b36c9753df09a159dfb148135d495db3af8373425ee9a28884ba1a%7D%20%5Cquad%20P_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5C%5C%20P_y%26%3D%5Ctextrm%7B0x12b64e62db43a56114554b0cbd573379338cea9124c8443c4f50e6c8b013ec20%7D%20%5Cquad%20P_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D">
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<img src="assets/formula/43-light.svg#gh-light-mode-only">
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<img src="assets/formula/43-dark.svg#gh-dark-mode-only">
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</p>
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## 7. 授权文件"rarreg.key"的生成
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授权文件的生成需要两个参数：
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1. 用户名的ANSI字符串，不包括null-terminator；记为
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1. 用户名的 ANSI 字符串，不包括 null-terminator；记为
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?U%3Du_0u_1%20%5Cldots%20u_%7Bl-1%7D">
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<img src="assets/formula/44-light.svg#gh-light-mode-only">
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<img src="assets/formula/44-dark.svg#gh-dark-mode-only">
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</p>
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2. 授权类型的ANSI字符串，不包括null-terminator；记为
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2. 授权类型的 ANSI 字符串，不包括 null-terminator；记为
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?L%3Dl_0l_1%20%5Cldots%20l_%7Bl-1%7D">
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<img src="assets/formula/45-light.svg#gh-light-mode-only">
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<img src="assets/formula/45-dark.svg#gh-dark-mode-only">
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</p>
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`rarreg.key` 的生成算法如下：
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1. 使用用户名 ![UU-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照SM2压缩公钥格式以Hex字符串（ASCII编码）的形式输出。得到的Hex字符串记为临时值 ![Temp-inlined]。
|
||||
1. 使用用户名 ![UU-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照 SM2 压缩公钥格式以Hex字符串（ASCII编码)的形式输出。得到的 Hex 字符串记为临时值 ![Temp-inlined]。
|
||||
|
||||
![Temp-inlined] 的长度应该为64；若长度不足，则在前面补字符`'0'`，直到长度为64。
|
||||
![Temp-inlined] 的长度应该为64；若长度不足，则在前面补字符 `'0'`，直到长度为64。
|
||||
|
||||
2. 令字符串 ![Data3-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E3%3D%5Ctexttt%7B%2260%22%7D%7C%7CTemp_0%7C%7CTemp_1%7C%7C%5Cldots%7C%7CTemp_%7B47%7D">
|
||||
<img src="assets/formula/48-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/48-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
3. 使用 ![Data3-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照SM2压缩公钥格式以Hex字符串（ASCII编码）的形式输出。得到的Hex字符串记为 ![Data0-inlined]。
|
||||
3. 使用 ![Data3-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照 SM2 压缩公钥格式以 Hex 字符串（ASCII编码)的形式输出。得到的Hex字符串记为 ![Data0-inlined]。
|
||||
|
||||
![Data0-inlined] 的长度应该为64；若长度不足，则在前面补字符`'0'`，直到长度为64。
|
||||
|
||||
4. 令字符串 ![UID-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?UID%3DTemp_%7B48%7D%7C%7CTemp_%7B49%7D%7C%7C%5Cldots%7C%7CTemp_%7B63%7D%7C%7CData%5E0_0%7C%7CData%5E0_1%7C%7CData%5E0_2%7C%7CData%5E0_3">
|
||||
<img src="assets/formula/51-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/51-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
5. 对授权类型 ![LL-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
5. 对授权类型 ![LL-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
|
||||
6. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
6. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
|
||||
若长度不满60，则在前面补字符`'0'`，直到长度为60。
|
||||
若长度不满60，则在前面补字符 `'0'`，直到长度为60。
|
||||
|
||||
7. 令字符串 ![Data1-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E1%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_L%7D%7C%7CSZ%5E%7Br_L%7D">
|
||||
<img src="assets/formula/57-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/57-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
8. 令字符串 ![Temp-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Temp%3DU%7C%7CData%5E0">
|
||||
<img src="assets/formula/58-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/58-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
对 ![Temp-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
|
||||
9. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
对 ![Temp-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
|
||||
9. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
|
||||
若长度不满60，则在前面补字符`'0'`，直到长度为60。
|
||||
|
||||
10. 令字符串 ![Data2-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E2%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_%7BTemp%7D%7D%7C%7CSZ%5E%7Br_%7BTemp%7D%7D">
|
||||
<img src="assets/formula/64-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/64-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
11. 对
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?L%7C%7CU%7C%7CData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3">
|
||||
<img src="assets/formula/65-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/65-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
计算CRC32值，最终校验和为CRC32值的反。将校验和以10进制形式输出，若长度不满10，则在前面补字符`'0'`，直到长度为10，记为 。
|
||||
|
||||
计算 CRC32 值，最终校验和为 CRC32 值的反。将校验和以10进制形式输出，若长度不满10，则在前面补字符 `'0'`，直到长度为10，记为 。
|
||||
|
||||
12. 令字符串 ![Data-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cinline%20Data%3DData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3%7C%7CSZ%5E%7Bchecksum%7D">
|
||||
<img src="assets/formula/67-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/67-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
13. 格式化输出。
|
||||
|
||||
* 固定文件头`"RAR registration data"`，占一行。
|
||||
* 固定文件头 `"RAR registration data"`，占一行。
|
||||
|
||||
* 用户名，占一行。
|
||||
|
||||
|
|
@ -291,7 +339,8 @@ WinRAR的私钥 ![k-inlined] 为：
|
|||
* UID，占一行：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctexttt%7B%22UID%3D%22%7D%7C%7CUID">
|
||||
<img src="assets/formula/68-light.svg#gh-light-mode-only">
|
||||
<img src="assets/formula/68-dark.svg#gh-dark-mode-only">
|
||||
</p>
|
||||
|
||||
|
||||
* 将 ![Data-inlined] 按照每行54个字符输出。
|
||||
|
|
|
|||
96
assets/formula/10-dark.svg
Normal file
96
assets/formula/10-dark.svg
Normal file
|
|
@ -0,0 +1,96 @@
|
|||
<?xml version='1.0' encoding='UTF-8'?>
|
||||
<!-- Generated by CodeCogs with dvisvgm 2.9.1 -->
|
||||
<svg fill="#fff" version='1.1' xmlns='http://www.w3.org/2000/svg' xmlns:xlink='http://www.w3.org/1999/xlink' width='491.530226pt' height='10.050949pt' viewBox='-.239051 -.242965 491.530226 10.050949'>
|
||||
<defs>
|
||||
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