📙 Optimization README

2026-03-11 17:45:31 +00:00 · 2024-04-24 16:27:14 +08:00 · 2024-04-24 16:27:14 +08:00 · 9fd45c343b
commit 9fd45c343b
parent f514d1faa4
16 changed files with 63 additions and 675 deletions
--- a/README.md
+++ b/README.md
@ -12,7 +12,7 @@
  </a>
  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298" />
  <a href="https://github.com/bitcookies/winrar-keygen/actions">
-      <img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/action.yml/badge.svg" />
+      <img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/action_secrets.yml/badge.svg" />
  </a>
  <a href="https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE">
  	<img alt="License" src="https://img.shields.io/github/license/bitcookies/winrar-keygen.svg" />
@ -61,9 +61,17 @@ Use [Secrets](https://docs.github.com/en/actions/security-guides/encrypted-secre
 ![Fork](assets/fork-dark.png#gh-dark-mode-only)
-### 4.2 Creating Secrets
+### 4.2 Allow Fork repo to run Workflows
-Open your forked repository, and go to **Settings > Secrets > Actions > New repository secret**.
+Go back to the repo you just forked and click **Actions** to allow Workflows to run in your forked repo.
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 4.3 Creating Secrets
 After allowing Workflows, go to **Settings > Secrets and variables > Actions > New repository secret**.
 ![Secrets](assets/secrets-light.png#gh-light-mode-only)
@ -81,7 +89,7 @@ Once created, you will see:
 ![Secrets Repo](assets/secrets-repo-dark.png#gh-dark-mode-only)
-### 4.3 Run Workflow
+### 4.4 Run Workflow
 Go to **Actions** and select **WinRAR Keygen Secrets** to run Workflow manually.
@ -95,6 +103,10 @@ After running successfully, open the corresponding task and select **rarreg_file
 ![Download](assets/file-download-dark.png#gh-dark-mode-only)
 After extract `rarreg_file.zip`, you will get `rarreg.key`, just drag and drop it into WinRAR. You can also compress `rarreg.key` into `rarkey.rar` and double-click it to run it, and the license import will take place automatically.
 If you get an invalid key, please check [the specific solution](#7-invalid-key).
 </details>
 ## 5. Use Github Actions with Push
@ -114,7 +126,15 @@ Using push for key generation is very simple and convenient, but when there are
 If you've forked before and I've committed new code, but you don't know how to merge the new content into your repository, then you can delete the current fork and fork again.
-### 5.2 Modify info.json
+### 5.2 Allow Fork repo to run Workflows
 Go back to the repo you just forked and click **Actions** to allow Workflows to run in your forked repo.
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 5.3 Edit info.json
 Open your forked repository, and go to `keygen/info.json` and click on the edit button to edit the file.
@ -144,13 +164,7 @@ It is important to note that `test1` and `test2` are **ANSI-encoded string, spac
 Once you have finished making changes, click the **Commit changes** button and Github Actions will start automatically.
-If Github Actions does not start automatically, you will need to click on the Actions page to **allow this workflows to run**, then modify and commit `keygen/info.json` again.
+### 5.4 Download Key
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 5.3 Download Key
 Go to **Actions** and select **WinRAR Keygen** to see the status of the program.
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@ -12,7 +12,7 @@
  </a>
  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298" />
  <a href="https://github.com/bitcookies/winrar-keygen/actions">
-      <img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/action.yml/badge.svg" />
+      <img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/action_secrets.yml/badge.svg" />
  </a>
  <a href="https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE">
  	<img alt="License" src="https://img.shields.io/github/license/bitcookies/winrar-keygen.svg" />
@ -61,9 +61,17 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 ![Fork](assets/fork-dark.png#gh-dark-mode-only)
-### 4.2 创建 Secrets
+### 4.2 允许 Fork 代码运行 Workflows
-打开你 fork 后的仓库，进入 **Settings > Secrets > Actions > New repository secret** 来创建：
+返回到你刚刚 fork 完成的 repo，然后点击 **Actions** 去允许 Workflows 在你的 fork repo 中运行：
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 4.3 创建 Secrets
 允许 Workflows 后，进入 **Settings > Secrets and variables > Actions > New repository secret** 来创建 Secrets：
 ![Secrets](assets/secrets-light.png#gh-light-mode-only)
@ -81,9 +89,9 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 ![Secrets Repo](assets/secrets-repo-dark.png#gh-dark-mode-only)
-### 4.3 运行 Workflow
+### 4.4 运行 Workflow
-进入 **Actions** 并选择 **WinRAR Keygen Secrets** 来手动执行 Workflow：
+进入 **Actions** 并选择 **WinRAR Keygen Secrets  >  Run workflow > Run workflow ** 来手动执行 Workflow：
 ![Run](assets/run-workflow-light.png#gh-light-mode-only)
@ -95,6 +103,10 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 ![Download](assets/file-download-dark.png#gh-dark-mode-only)
 将 `rarreg_file.zip` 解压缩后会得到 `rarreg.key`，然后拖动导入 WinRAR 即可。你也可以将 `rarreg.key` 压缩成 `rarkey.rar`，然后双击运行，授权导入将会自动进行。
 如果你得到的是 key 是无效的，请查看 [解决方法](#7-无效的-Key)。
 </details>
 ## 5. 通过 Push 使用 Github Actions
@ -114,9 +126,17 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 如果你之前 fork 过，然后我提交了新的代码，但是你不懂得如何合并新内容到你的仓库，那你也可以删掉当前 fork 的仓库，然后重新 fork 一次。
-### 5.2 修改 info.json
+### 5.2 允许 Fork 代码运行 Workflows
-打开你 fork 后的仓库，进入 `keygen/info.json`，点击编辑按钮，对该文件进行编辑：
+返回到你刚刚 fork 完成的 repo，然后点击 Actions 去允许 Workflows 在你的 fork repo 中运行：
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 5.3 修改 info.json
 允许 Workflows 后，进入 `keygen/info.json`，点击编辑按钮，对该文件进行编辑：
 ![Edit](assets/edit-json-light.png#gh-light-mode-only)
@ -144,13 +164,7 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 修改完成之后，点击 **Commit changes** 按钮，Github Actions 会自动开始执行。
-如果 Github Actions 未自动开始，你需要先点击 Actions 页面 **允许此 workflows 运行**，然后再次修改并提交 `keygen/info.json` 。
+### 5.4 下载文件
 ![Workflow](assets/enable-workflows-light.png#gh-light-mode-only)
 ![Workflow](assets/enable-workflows-dark.png#gh-dark-mode-only)
 ### 5.3 下载文件
 进入 **Actions** 并选择 **WinRAR Keygen** 页面查看程序运行状况：
@ -166,7 +180,7 @@ WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](htt
 将 `rarreg_file.zip` 解压缩后会得到 `rarreg.key`，然后拖动导入 WinRAR 即可。你也可以将 `rarreg.key` 压缩成 `rarkey.rar`，然后双击运行，授权导入将会自动进行。
-如果你得到的是 key 是无效的，请查看 [解决方法](#7-无效的key)。
+如果你得到的是 key 是无效的，请查看 [解决方法](#7-无效的-Key)。
 </details>
--- a/assets/README.HOW_DOES_IT_WORK.md.bak
+++ b/assets/README.HOW_DOES_IT_WORK.md.bak
@ -1,321 +0,0 @@
 [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
 # How is "rarreg.key" generated?
 WinRAR uses an ECC-based signature algorithm to generate `rarreg.key`. The algorithm it used is a variant of Chinese SM2 digital signature algorithm. Different to many standard ECDSAs, the curve that WinRAR selected is a curve over composite field ![GF2p15p17-inlined].
 ## 1. Composite field ![GF2p15p17-inlined]
 Elements in ground field ![GF2p15-inlined] are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is
 <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>
 where each coefficients is in ![GF2-inlined]. If we use 
 <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>
 as the standard basis of the ground field, an element ![A-inlined] in ![GF2p15-inlined] can be denoted as
 <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>
 ---
 The irreducible polynomial of composite field ![GF2p15p17-inlined] is
 <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>
 where each coefficients is in ![GF2p15-inlined]. If we use 
 <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>
 as the standard basis of the composite field, an element ![B-inlined] in ![GF2p15p17-inlined] can be denoted as
 <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>
 ---
 For clarity, we use ![D-inlined], which is a 255-bits-long integer to denote an element ![B-inlined] in ![GF2p15p17-inlined]. The map between them is
 <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. Elliptic curve over ![GF2p15p17-inlined]
 The equation of the elliptic curve that WinRAR uses is
 <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>
 The base point ![G-inlined] is
 <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>
 whose order ![n-inlined] is
 <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. Message hash algorithm
 We use 
 <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>
 to denote a message whose length is ![l-inlined]. So the SHA1 value of ![M-inlined] should be 
 <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>
 where ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_0%2CS_1%2CS_2%2CS_3%2CS_4) are 5 state values when SHA1 outputs. Generally speaking, the final SHA1 value should be the join of these 5 state values while each of state values is serialized in big-endian.
 However, WinRAR doesn't serialize the 5 state values. Instead, it use a big integer ![h-inlined] as the hash of the input message.
 <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 digital signature algorithm
 We use ![k-inlined] to denote private key, ![P-inlined] to denote public key. So there must be
 <p align="center">
    <img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
 </p>
 If we use ![h-inlined] to denote the hash of input data, WinRAR use the following algorithm to perform signing:
 1. Generate a random big integer ![Rnd-inlined] which satisfies ![](http://latex.codecogs.com/svg.latex?%5Cinline%200%3CRnd%3Cn).
 2. Calculate ![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>
   where ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28Rnd%20%5Ccdot%20G%29_x) means we take X coordinate of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd%20%5Ccdot%20G) and convert it from ![GF2p15p17-inlined] to a big integer.
   If ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r%3D0) or ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r&plus;Rnd%3Dn), go back to step 1.
 3. Calculate ![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>
   If ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s%3D0), go back to step 1.
 4. Output ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r%2Cs%29).
 ## 5. WinRAR private key generation algorithm
 We use 
 <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>
 to denote input data whose length is ![l-inlined]. WinRAR use it to generate private key ![k-inlined].
 1. We use ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%2Cg_1%2Cg_2%2Cg_3%2Cg_4%2Cg_5) to denote 6 32-bits-long integer. So there is
   <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. Let ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%3D0).
 3. If ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%5Cneq%200), we calculate SHA1 value of ![T-inlined]. Then assign SHA1 state value ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_i) to ![](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>
   Otherwise, when ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%3D0), we let 
   <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. Regard ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0) as counter, add itself by 1.
   Calculate SHA1:
   <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>
   We takes the lowest 16 bits of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_0) and donote it as ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_%7Bg_0%7D).
 5. Repeat step 4 again with 14 times.
 6. After that, we will get ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_1%2Ck_2%2Ck_3%2C%5Cldots%2Ck_%7B15%7D). Then output private key
   <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. The private key and public key of WinRAR
 Private key ![k-inlined] is
 <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>
 This private key is generated by the algorithm describled in section 5 where the length of data ![T-inlined] is zero.
 Public key ![P-inlined] is
 <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. Generation of "rarreg.key"
 The generation of license file `rarreg.key` requires 2 arguments:
 1. Username, an ANSI-encoded string, without null-terminator. Denoted as
   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?U%3Du_0u_1%20%5Cldots%20u_%7Bl-1%7D">
   </p>
 2. License type, an ANSI-encoded string, without null-terminator. Denoted as 
   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?L%3Dl_0l_1%20%5Cldots%20l_%7Bl-1%7D">
   </p>
 The following is the algorithm to generate `rarreg.key`.
 1. Use the algorithm describled in section 5, with argument ![UU-inlined], to generate private key ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_U) and public key ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_U). Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Temp-inlined].
   The length of ![Temp-inlined] should be 64. If less, pad with `'0'` until the length is 64.
 2. Let ![Data3-inlined] be 
   <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. Use the algorithm describled in section 5, with argument ![Data3-inlined], to generate private key ![](http://latex.codecogs.com/svg.latex?%5Cinline%20k_%7BData%5E3%7D) and public key ![](http://latex.codecogs.com/svg.latex?%5Cinline%20P_%7BData%5E3%7D). Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Data0-inlined].
   The length of ![Data0-inlined] should be 64. If less, pad with `'0'` until the length is 64.
 4. Let ![UID-inlined] be
   <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. Use the algorithm describled in section 4, with argument ![LL-inlined] and private key ![k-inlined] describled section 6, to get signature ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_L%2Cs_L%29).
   The bit length of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_L) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_L) shall not be more than 240. Otherwise, repeat this step.
 6. Convert ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_L) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_L) to hex-integer string ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_L%7D) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_L%7D), without `"0x"` prefix. 
   If the length of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_L%7D) or ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_L%7D) is less than 60, pad character `'0'` until the length is 60.
 7. Let ![Data1-inlined] be
   <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. Let ![Temp-inlined] be 
   <p align="center">
       <img src="http://latex.codecogs.com/svg.latex?Temp%3DU%7C%7CData%5E0">
   </p>
   Use the algorithm describled in section 4, with argument ![Temp-inlined] and private key ![k-inlined] describled section 6, to get signature ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_%7BTemp%7D%2Cs_%7BTemp%7D%29).
   The bit length of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_%7BTemp%7D) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_%7BTemp%7D) shall not be more than 240. Otherwise, repeat this step.
 9. Convert ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_%7BTemp%7D) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_%7BTemp%7D) to hex-integer string ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_%7BTemp%7D%7D) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_%7BTemp%7D%7D), without `"0x"` prefix. 
   If the length of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Br_%7BTemp%7D%7D) or ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bs_%7BTemp%7D%7D) is less than 60, pad character `'0'` until the length is 60.
 10. Let ![Data2-inlined] be
    <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. Calculate CRC32 value of 
    <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>
    The final checksum the complement of CRC32 value. 
    Then convert the checksum to decimal string ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bchecksum%7D). If the length is less than 10, pad character `'0'` until the length is 10.
 12. Let ![Data-inlined] be 
    <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. Output with format
    * A fixed header `"RAR registration data"`, taking one line.
    * Username, taking one line.
    * License type, taking one line
    * UID, taking one line, with format:
      <p align="center">
        <img src="http://latex.codecogs.com/svg.latex?%5Ctexttt%7B%22UID%3D%22%7D%7C%7CUID">
      </p>
    * Output ![Data-inlined], with 54 characters a line.
--- a/assets/README.HOW_DOES_IT_WORK.zh-CN.md.bak
+++ b/assets/README.HOW_DOES_IT_WORK.zh-CN.md.bak
@ -1,319 +0,0 @@
 [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。
--- a/assets/fork-dark.png
+++ b/assets/fork-dark.png
--- a/assets/fork-light.png
+++ b/assets/fork-light.png
--- a/assets/push-workflows-dark.png
+++ b/assets/push-workflows-dark.png
--- a/assets/push-workflows-light.png
+++ b/assets/push-workflows-light.png
--- a/assets/run-workflow-dark.png
+++ b/assets/run-workflow-dark.png
--- a/assets/run-workflow-light.png
+++ b/assets/run-workflow-light.png
--- a/assets/secrets-dark.png
+++ b/assets/secrets-dark.png
--- a/assets/secrets-light.png
+++ b/assets/secrets-light.png
--- a/assets/secrets-repo-dark.png
+++ b/assets/secrets-repo-dark.png
--- a/assets/secrets-repo-light.png
+++ b/assets/secrets-repo-light.png
--- a/bin/Win32-Release/winrar-keygen.exe
+++ b/bin/Win32-Release/winrar-keygen.exe
--- a/bin/x64-Release/winrar-keygen.exe
+++ b/bin/x64-Release/winrar-keygen.exe