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README.HOW_DOES_IT_WORK.zh-CN.md
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@ -19,7 +19,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
</p>
则位于基域 ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![A-inlined] 可以用如下方式表达：
则位于基域 ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![A](assets/formula/AA-inlined-light.svg#gh-light-mode-only)![A](assets/formula/AA-inlined-dark.svg#gh-dark-mode-only) 可以用如下方式表达：
<p align="center">
<img src="assets/formula/3-light.svg#gh-light-mode-only">
@ -45,7 +45,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
</p>
则位于复合域 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![B-inlined] 可以用如下方式表达：
则位于复合域 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![B](assets/formula/BB-inlined-light.svg#gh-light-mode-only)![B](assets/formula/BB-inlined-dark.svg#gh-dark-mode-only) 可以用如下方式表达：
<p align="center">
<img src="assets/formula/6-light.svg#gh-light-mode-only">
@ -55,7 +55,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
---
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](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![B-inlined]。它们的对应关系为：
为了方便表述我们用255比特的大数 ![D](assets/formula/DD-inlined-light.svg#gh-light-mode-only)![D](assets/formula/DD-inlined-dark.svg#gh-dark-mode-only) 来表示位于复合域 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 上的元素 ![B](assets/formula/BB-inlined-light.svg#gh-light-mode-only)![B](assets/formula/BB-inlined-dark.svg#gh-dark-mode-only)。它们的对应关系为：
<p align="center">
<img src="assets/formula/7-light.svg#gh-light-mode-only">
@ -73,7 +73,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
</p>
基点 ![G-inlined] 为：
基点 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 为：
<p align="center">
<img src="assets/formula/9-light.svg#gh-light-mode-only">
@ -81,7 +81,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
</p>
基点 ![G-inlined] 的阶 ![n-inlined] 为：
基点 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 的阶 ![n](assets/formula/n-inlined-light.svg#gh-light-mode-only)![n](assets/formula/n-inlined-dark.svg#gh-dark-mode-only) 为：
<p align="center">
<img src="assets/formula/10-light.svg#gh-light-mode-only">
@ -91,7 +91,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
## 3. 消息哈希算法
设长度为 ![l-inlined] 的消息为：
设长度为 ![l](assets/formula/l-inlined-light.svg#gh-light-mode-only)![l](assets/formula/l-inlined-dark.svg#gh-dark-mode-only) 的消息为：
<p align="center">
<img src="assets/formula/11-light.svg#gh-light-mode-only">
@ -99,7 +99,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
</p>
则消息 ![M-inlined] 的SHA1值为：
则消息 ![M](assets/formula/MM-inlined-light.svg#gh-light-mode-only)![M](assets/formula/MM-inlined-dark.svg#gh-dark-mode-only) 的 SHA1 值为：
<p align="center">
<img src="assets/formula/12-light.svg#gh-light-mode-only">
@ -109,7 +109,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
其中 ![s0,4](assets/formula/13-light.svg#gh-light-mode-only)![s0,4](assets/formula/13-dark.svg#gh-dark-mode-only) 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 ![SHA1M](assets/formula/14-light.svg#gh-light-mode-only)![SHA1M](assets/formula/14-dark.svg#gh-dark-mode-only)。
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：
WinRAR 在做完 SHA1 计算后，采用大数 ![h](assets/formula/h-inlined-light.svg#gh-light-mode-only)![h](assets/formula/h-inlined-dark.svg#gh-dark-mode-only) 作为 ECC 签名时消息的哈希：
<p align="center">
<img src="assets/formula/15-light.svg#gh-light-mode-only">
@ -118,7 +118,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
## 4. ECC签名算法
设私钥为 ![k-inlined]，公钥为 ![P-inlined]，即：
设私钥为 ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only)，公钥为 ![P](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only)，即：
<p align="center">
<img src="assets/formula/16-light.svg#gh-light-mode-only">
@ -126,11 +126,11 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
</p>
消息哈希为 ![h-inlined]，则签名 ![(r,s)](assets/formula/17-light.svg#gh-light-mode-only)![(r,s)](assets/formula/17-dark.svg#gh-dark-mode-only) 为：
消息哈希为 ![h](assets/formula/h-inlined-light.svg#gh-light-mode-only)![h](assets/formula/h-inlined-dark.svg#gh-dark-mode-only)，则签名 ![(r,s)](assets/formula/17-light.svg#gh-light-mode-only)![(r,s)](assets/formula/17-dark.svg#gh-dark-mode-only) 为：
1. 生成随机数 ![Rnd-inlined]，满足 ![RND](assets/formula/18-light.svg#gh-light-mode-only)![RND](assets/formula/18-dark.svg#gh-dark-mode-only)。
1. 生成随机数 ![Rnd](assets/formula/Rnd-inlined-light.svg#gh-light-mode-only)![Rnd](assets/formula/Rnd-inlined-dark.svg#gh-dark-mode-only)，满足 ![RND](assets/formula/18-light.svg#gh-light-mode-only)![RND](assets/formula/18-dark.svg#gh-dark-mode-only)。
2. 计算 ![r-inlined]
2. 计算 ![r](assets/formula/r-inlined-light.svg#gh-light-mode-only)![r](assets/formula/r-inlined-dark.svg#gh-dark-mode-only)
<p align="center">
<img src="assets/formula/19-light.svg#gh-light-mode-only">
@ -142,7 +142,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
若 ![r=0](assets/formula/22-light.svg#gh-light-mode-only)![r=0](assets/formula/22-dark.svg#gh-dark-mode-only) 或者 ![rRnd](assets/formula/23-light.svg#gh-light-mode-only)![rRnd](assets/formula/23-dark.svg#gh-dark-mode-only) 则回到步骤1。
3. 计算 ![s-inlined]
3. 计算 ![s](assets/formula/s-inlined-light.svg#gh-light-mode-only)![s](assets/formula/s-inlined-dark.svg#gh-dark-mode-only)
<p align="center">
<img src="assets/formula/24-light.svg#gh-light-mode-only">
@ -156,7 +156,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
## 5. WinRAR的私钥生成算法
该算法会利用长度为 ![l-inlined] 的数据
该算法会利用长度为 ![l](assets/formula/l-inlined-light.svg#gh-light-mode-only)![l](assets/formula/l-inlined-dark.svg#gh-dark-mode-only) 的数据
<p align="center">
<img src="assets/formula/26-light.svg#gh-light-mode-only">
@ -164,7 +164,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
</p>
来生成私钥 ![k-inlined]。
来生成私钥 ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only)。
1. 设6个32位整数为 ![g0-5](assets/formula/27-light.svg#gh-light-mode-only)![g0-5](assets/formula/27-dark.svg#gh-dark-mode-only)，则有
@ -175,7 +175,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
2. 令 ![g0=0](assets/formula/29-light.svg#gh-light-mode-only)![g0=0](assets/formula/29-dark.svg#gh-dark-mode-only)。
3. 如果 ![l!=0](assets/formula/30-light.svg#gh-light-mode-only)![l!=0](assets/formula/30-dark.svg#gh-dark-mode-only) 则计算 ![T-inlined] 的 SHA1 值，并将状态值 ![Si](assets/formula/31-light.svg#gh-light-mode-only)![Si](assets/formula/31-dark.svg#gh-dark-mode-only) 赋值给 ![gi+1](assets/formula/32-light.svg#gh-light-mode-only)![gi+1](assets/formula/32-dark.svg#gh-dark-mode-only)：
3. 如果 ![l!=0](assets/formula/30-light.svg#gh-light-mode-only)![l!=0](assets/formula/30-dark.svg#gh-dark-mode-only) 则计算 ![TT](assets/formula/TT-inlined-light.svg#gh-light-mode-only)![T](assets/formula/TT-inlined-dark.svg#gh-dark-mode-only) 的 SHA1 值，并将状态值 ![Si](assets/formula/31-light.svg#gh-light-mode-only)![Si](assets/formula/31-dark.svg#gh-dark-mode-only) 赋值给 ![gi+1](assets/formula/32-light.svg#gh-light-mode-only)![gi+1](assets/formula/32-dark.svg#gh-dark-mode-only)：
<p align="center">
<img src="assets/formula/33-light.svg#gh-light-mode-only">
@ -213,7 +213,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h-inlined] 作为 ECC 签名时
## 6. WinRAR的公钥和私钥
WinRAR的私钥 ![k-inlined] 为：
WinRAR 的私钥 ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only) 为：
<p align="center">
<img src="assets/formula/42-light.svg#gh-light-mode-only">
@ -221,9 +221,9 @@ WinRAR的私钥 ![k-inlined] 为：
</p>
该私钥是通过算法5生成的，其中数据 ![T-inlined] 的长度为0。
该私钥是通过算法5生成的，其中数据 ![T](assets/formula/TT-inlined-light.svg#gh-light-mode-only)![T](assets/formula/TT-inlined-dark.svg#gh-dark-mode-only) 的长度为0。
公钥 ![P-inlined] 为：
公钥 ![P](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only) 为：
<p align="center">
<img src="assets/formula/43-light.svg#gh-light-mode-only">
@ -251,29 +251,29 @@ WinRAR的私钥 ![k-inlined] 为：
`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 ![ku](assets/formula/46-light.svg#gh-light-mode-only)![ku](assets/formula/46-dark.svg#gh-dark-mode-only) 以及公钥 ![pu](assets/formula/47-light.svg#gh-light-mode-only)![pu](assets/formula/47-dark.svg#gh-dark-mode-only)，并将公钥 ![pu](assets/formula/47-light.svg#gh-light-mode-only)![pu](assets/formula/47-dark.svg#gh-dark-mode-only) 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 ![U](assets/formula/UU-inlined-light.svg#gh-light-mode-only)![U](assets/formula/UU-inlined-dark.svg#gh-dark-mode-only) 通过算法5计算出私钥 ![ku](assets/formula/46-light.svg#gh-light-mode-only)![ku](assets/formula/46-dark.svg#gh-dark-mode-only) 以及公钥 ![pu](assets/formula/47-light.svg#gh-light-mode-only)![pu](assets/formula/47-dark.svg#gh-dark-mode-only)，并将公钥 ![pu](assets/formula/47-light.svg#gh-light-mode-only)![pu](assets/formula/47-dark.svg#gh-dark-mode-only) 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](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only)。
![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](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) 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
2. 令字符串 ![Data3](assets/formula/Data3-inlined-light.svg#gh-light-mode-only)![Data3](assets/formula/Data3-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<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 ![kdata3](assets/formula/49-light.svg#gh-light-mode-only)![kdata3](assets/formula/49-dark.svg#gh-dark-mode-only) 以及公钥 ![pdata3](assets/formula/50-light.svg#gh-light-mode-only)![pdata3](assets/formula/50-dark.svg#gh-dark-mode-only)，并将公钥 ![pdata3](assets/formula/50-light.svg#gh-light-mode-only)![pdata3](assets/formula/50-dark.svg#gh-dark-mode-only) 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](assets/formula/Data3-inlined-light.svg#gh-light-mode-only)![Data3](assets/formula/Data3-inlined-dark.svg#gh-dark-mode-only) 通过算法5计算出私钥 ![kdata3](assets/formula/49-light.svg#gh-light-mode-only)![kdata3](assets/formula/49-dark.svg#gh-dark-mode-only) 以及公钥 ![pdata3](assets/formula/50-light.svg#gh-light-mode-only)![pdata3](assets/formula/50-dark.svg#gh-dark-mode-only)，并将公钥 ![pdata3](assets/formula/50-light.svg#gh-light-mode-only)![pdata3](assets/formula/50-dark.svg#gh-dark-mode-only) 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](assets/formula/Data0-inlined-light.svg#gh-light-mode-only)![Data0](assets/formula/Data0-inlined-dark.svg#gh-dark-mode-only)。
![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。
![Data0](assets/formula/Data0-inlined-light.svg#gh-light-mode-only)![Data0](assets/formula/Data0-inlined-dark.svg#gh-dark-mode-only) 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
4. 令字符串 ![UID](assets/formula/UID-inlined-light.svg#gh-light-mode-only)![UID](assets/formula/UID-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<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 ![(rl,sl)](assets/formula/52-light.svg#gh-light-mode-only)![(rl,sl)](assets/formula/52-dark.svg#gh-dark-mode-only)，其中私钥见第6节。
5. 对授权类型 ![L](assets/formula/LL-inlined-light.svg#gh-light-mode-only)![L](assets/formulaLL-inlined-dark.svg#gh-dark-mode-only) 使用算法4得到签名 ![(rl,sl)](assets/formula/52-light.svg#gh-light-mode-only)![(rl,sl)](assets/formula/52-dark.svg#gh-dark-mode-only)，其中私钥见第6节。
要求 ![rl](assets/formula/53-light.svg#gh-light-mode-only)![rl](assets/formula/53-dark.svg#gh-dark-mode-only) 和 ![sl](assets/formula/54-light.svg#gh-light-mode-only)![sl](assets/formula/54-dark.svg#gh-dark-mode-only) 的长度都不得超过240比特，否则重复该步骤。
@ -281,14 +281,14 @@ WinRAR的私钥 ![k-inlined] 为：
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
7. 令字符串 ![Data1](assets/formula/Data1-inlined-light.svg#gh-light-mode-only)![Data1](assets/formula/Data1-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<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
8. 令字符串 ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<img src="assets/formula/58-light.svg#gh-light-mode-only">
@ -296,7 +296,7 @@ WinRAR的私钥 ![k-inlined] 为：
</p>
对 ![Temp-inlined] 使用算法4得到签名 ![(rTemp,sTemp)](assets/formula/59-light.svg#gh-light-mode-only)![(rTemp,sTemp)](assets/formula/59-dark.svg#gh-dark-mode-only)，其中私钥见第6节。
对 ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) 使用算法4得到签名 ![(rTemp,sTemp)](assets/formula/59-light.svg#gh-light-mode-only)![(rTemp,sTemp)](assets/formula/59-dark.svg#gh-dark-mode-only)，其中私钥见第6节。
要求 ![rTemp](assets/formula/60-light.svg#gh-light-mode-only)![rTemp](assets/formula/60-dark.svg#gh-dark-mode-only) 和 ![sTemp](assets/formula/61-light.svg#gh-light-mode-only)![sTemp](assets/formula/61-dark.svg#gh-dark-mode-only) 的长度都不得超过240比特，否则重复该步骤。
@ -304,7 +304,7 @@ WinRAR的私钥 ![k-inlined] 为：
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
10. 令字符串 ![Data2](assets/formula/Data2-inlined-light.svg#gh-light-mode-only)![Data2](assets/formula/Data2-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<img src="assets/formula/64-light.svg#gh-light-mode-only">
@ -318,10 +318,9 @@ WinRAR的私钥 ![k-inlined] 为：
<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 ![SZchecksum](assets/formula/66-light.svg#gh-light-mode-only)![SZchecksum](assets/formula/66-dark.svg#gh-dark-mode-only)。
12. 令字符串 ![Data-inlined]为
12. 令字符串 ![Data](assets/formula/Data-inlined-light.svg#gh-light-mode-only)![Data](assets/formula/Data-inlined-dark.svg#gh-dark-mode-only) 为
<p align="center">
<img src="assets/formula/67-light.svg#gh-light-mode-only">
@ -343,4 +342,4 @@ WinRAR的私钥 ![k-inlined] 为：
<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。
* 将 ![Data](assets/formula/Data-inlined-light.svg#gh-light-mode-only)![Data](assets/formula/Data-inlined-dark.svg#gh-dark-mode-only) 按照每行54个字符输出。

10
assets/formula/AA-inlined-dark.svg Normal file
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@ -0,0 +1,10 @@
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