winrar-keygen

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README.HOW_DOES_IT_WORK.zh-CN.md.bak

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

[GF2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%29
[GF2p15-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%5E%7B15%7D%29
[GF2p15p17-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29
[A-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20A
[B-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20B
[D-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20D
[G-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20G
[M-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20M
[P-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20P
[h-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20h
[k-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20k
[l-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20l
[n-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20n
[r-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20r
[s-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20s
[T-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20T
[UU-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20U
[LL-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20L
[Rnd-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd
[Temp-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Temp
[UID-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20UID
[Data-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data
[Data0-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E0
[Data1-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E1
[Data2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E2
[Data3-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E3

# "rarreg.key"是如何生成的？

WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使用的签名算法是中国 SM2 数字签名算法的变体。与各种标准 ECDSA 不同的是，WinRAR 使用的椭圆曲线是一个基于复合域 ![GF2p15p17-inlined] 上的曲线。

## 1. 复合域 ![GF2p15p17-inlined]

基域 ![GF2p15-inlined] 采用标准基（多项式基）来表达，采用的不可约多项式为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?P%28%5Calpha%29%3D%5Calpha%5E%7B15%7D&plus;%5Calpha&plus;1">
</p>

各项系数全部位于 ![GF2-inlined]。设基域的标准基为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?B_1%3D%5C%7B1%2C%5Calpha%2C%5Calpha%5E2%2C%5Cldots%2C%5Calpha%5E%7B14%7D%5C%7D")
</p>

则位于基域 ![GF2p15-inlined] 上的元素 ![A-inlined] 可以用如下方式表达：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?A%3D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_i%5Calpha%5Ei%20%5Cquad%20%5Cquad%20%5Cquad%20a_i%5Cin%5Ctextrm%7BGF%7D%282%29")
</p>

---

复合域 ![GF2p15p17-inlined] 的不可约多项式为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?Q%28%5Cbeta%29%3D%5Cbeta%5E%7B17%7D&plus;%5Cbeta%5E3&plus;1")
</p>

各项系数全部位于 ![GF2p15-inlined]。设复合域的标准基为：

<p align="center">
    <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")
</p>

则位于复合域 ![GF2p15p17-inlined] 上的元素 ![B-inlined] 可以用如下方式表达：

<p align="center">
    <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")
</p>

---

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 ![GF2p15p17-inlined] 上的元素 ![B-inlined]。它们的对应关系为：

<p align="center">
    <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&plus;i%7D")
</p>

## 2. 复合域 ![GF2p15p17-inlined] 上的椭圆曲线

曲线方程为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?y%5E2&plus;xy%3Dx%5E3&plus;161%20%5Cquad%20%5Cquad%20%5Cquad%20161%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29")
</p>

基点 ![G-inlined] 为：

<p align="center">
    <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")
</p>

基点 ![G-inlined] 的阶 ![n-inlined] 为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?n%3D%5Ctextrm%7B0x1026dd85081b82314691ced9bbec30547840e4bf72d8b5e0d258442bbcd31%7D%20%5Cquad%20n%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D")
</p>

## 3. 消息哈希算法

设长度为 ![l-inlined] 的消息为：

<p align="center">
    <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")
</p>

则消息 ![M-inlined] 的SHA1值为：

<p align="center">
    <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")
</p>

其中 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_0%2CS_1%2CS_2%2CS_3%2CS_4) 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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BSHA%7D_1%28M%29)。

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：

<p align="center">
    <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&plus;%5Ctextrm%7B0x1bd10xb4e33c7c0ffd8d43%7D%20%5Ccdot%202%5E%7B32*5%7D")
</p>


## 4. ECC签名算法

设私钥为 ![k-inlined]，公钥为 ![P-inlined]，即：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
</p>

消息哈希为 ![h-inlined]，则签名 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r%2Cs%29) 为：

1. 生成随机数 ![Rnd-inlined]，满足 ![](http://latex.codecogs.com/svg.latex?%5Cinline%200%3CRnd%3Cn)。

2. 计算 ![r-inlined]

   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?r%3D%28%28Rnd%20%5Ccdot%20G%29_x&plus;h%29%5C%20%5C%20Mod%5C%20%5C%20n">
   </p>

   其中 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28Rnd%20%5Ccdot%20G%29_x) 表示取 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd%20%5Ccdot%20G) 的X坐标，同时将X坐标从 ![GF2p15p17-inlined] 转换为大数。

   若 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r%3D0) 或者 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r&plus;Rnd%3Dn) 则回到步骤1。

3. 计算 ![s-inlined]

   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
   </p>

   若 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s%3D0) 则回到步骤1。

4. 输出 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r%2Cs%29)。

## 5. WinRAR的私钥生成算法

该算法会利用长度为 ![l-inlined] 的数据 

<p align="center">
    <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">
</p>

来生成私钥 ![k-inlined]。

1. 设6个32位整数为 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%2Cg_1%2Cg_2%2Cg_3%2Cg_4%2Cg_5)，则有

   <p align="center">
       <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">
   </p>

2. 令 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%3D0)。

3. 如果 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%5Cneq%200) 则计算 ![T-inlined] 的SHA1值，并将状态值 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_i) 赋值给 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_%7Bi&plus;1%7D)：

   <p align="center">
       <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">
   </p>

   否则，即 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%3D0) 时，令：

   <p align="center">
       <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">
   </p>

4. 把 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0) 作为计数器，自增1。

   计算SHA1值：

   <p align="center">
       <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">
   </p>

   取 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_0) 的低16位并记为 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_%7Bg_0%7D)。

5. 步骤4再重复14次。

6. 重复执行完后会得到 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_1%2Ck_2%2Ck_3%2C%5Cldots%2Ck_%7B15%7D)，则输出私钥

   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?k%3D%5Csum_%7Bi%3D1%7D%5E%7B15%7Dk_i%20%5Ccdot%202%5E%7B16i%7D">
   </p>

## 6. WinRAR的公钥和私钥

WinRAR的私钥 ![k-inlined] 为：

<p align="center">
    <img src="http://latex.codecogs.com/svg.latex?k%3D%5Ctextrm%7B0x59fe6abcca90bdb95f0105271fa85fb9f11f467450c1ae9044b7fd61d65e%7D%20%5Cquad%20%5Cquad%20k%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D">
</p>

该私钥是通过算法5生成的，其中数据 ![T-inlined] 的长度为0。

公钥 ![P-inlined] 为：

<p align="center">
    <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">
</p>

## 7. 授权文件"rarreg.key"的生成

授权文件的生成需要两个参数：

1. 用户名的ANSI字符串，不包括null-terminator；记为 

   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?U%3Du_0u_1%20%5Cldots%20u_%7Bl-1%7D">
   </p>

2. 授权类型的ANSI字符串，不包括null-terminator；记为

   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?L%3Dl_0l_1%20%5Cldots%20l_%7Bl-1%7D">
   </p>

`rarreg.key` 的生成算法如下：

1. 使用用户名 ![UU-inlined] 通过算法5计算出私钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_U) 以及公钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_U)，并将公钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_U) 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。

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">
   </p>

3. 使用 ![Data3-inlined] 通过算法5计算出私钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_%7BData%5E3%7D) 以及公钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_%7BData%5E3%7D)，并将公钥 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_%7BData%5E3%7D) 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">
   </p>

5. 对授权类型 ![LL-inlined] 使用算法4得到签名 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_L%2Cs_L%29)，其中私钥见第6节。

   要求 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_L) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_L) 的长度都不得超过240比特，否则重复该步骤。

6. 将 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_L) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_L) 以16进制形式输出（无`"0x"`前缀），分别记为 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_L%7D) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_L%7D)。

   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">
   </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">
   </p>

   对 ![Temp-inlined] 使用算法4得到签名 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_%7BTemp%7D%2Cs_%7BTemp%7D%29)，其中私钥见第6节。
   
   要求 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_%7BTemp%7D) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_%7BTemp%7D) 的长度都不得超过240比特，否则重复该步骤。

9. 将 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_%7BTemp%7D) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_%7BTemp%7D) 以16进制形式输出（无`"0x"`前缀），分别记为 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_%7BTemp%7D%7D) 和 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_%7BTemp%7D%7D)。

   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">
    </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">
    </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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bchecksum%7D)。

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">
    </p>

13. 格式化输出。

    * 固定文件头`"RAR registration data"`，占一行。

    * 用户名，占一行。

    * 授权类型，占一行。

    * UID，占一行：

      <p align="center">
        <img src="http://latex.codecogs.com/svg.latex?%5Ctexttt%7B%22UID%3D%22%7D%7C%7CUID">
      </p>

    * 将 ![Data-inlined] 按照每行54个字符输出。

README.HOW_DOES_IT_WORK.zh-CN.md.bak Unescape Escape

README.HOW_DOES_IT_WORK.zh-CN.md.bak