.github/workflows/keygen.yml

@@ -0,0 +1,123 @@
+name: WinRAR Keygen
+on: 
+  workflow_dispatch:
+    inputs:
+      KEY_ENCODING:
+        type: string
+        description: License encoding ascii, ansi or utf8
+        default: 'utf8'
+        required: true
+
+      KEY_USERNAME:
+        type: string
+        description: Input your username
+        required: true
+        
+      KEY_LICENSE_NAME:
+        type: string
+        description: Input your license name
+        default: 'Single PC usage license'
+        required: true
+
+jobs:
+  keygen-ascii:
+    name: Generating ASCII License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ github.event.inputs.KEY_USERNAME }}
+      KEY_LICENSE_NAME: ${{ github.event.inputs.KEY_LICENSE_NAME }}
+    if: github.event.inputs.KEY_ENCODING == 'ascii'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+    
+    - name: Generating License (ASCII)
+      # Use PowerShell 5
+      shell: powershell
+      run: |
+        $OutputEncoding = [console]::InputEncoding = [console]::OutputEncoding = New-Object System.Text.UTF8Encoding
+        $PSVersionTable.PSVersion
+        bin/x64-Release/winrar-keygen.exe "${{ env.KEY_USERNAME }}" "${{ env.KEY_LICENSE_NAME }}" | Out-File -Encoding ${{ env.KEY_ENCODING }} rarreg.key
+
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.key
+        if-no-files-found: error
+        retention-days: 90
+
+
+  keygen-ansi:
+    name: Generating ANSI License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ github.event.inputs.KEY_USERNAME }}
+      KEY_LICENSE_NAME: ${{ github.event.inputs.KEY_LICENSE_NAME }}
+    if: github.event.inputs.KEY_ENCODING == 'ansi'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+    
+    - name: Generating License (ANSI)
+      # Use PowerShell 7
+      shell: pwsh
+      run: |
+        [System.Text.Encoding]::Default
+        $OutputEncoding
+        bin/x64-Release/winrar-keygen.exe "${{ env.KEY_USERNAME }}" "${{ env.KEY_LICENSE_NAME }}" | Out-File -Encoding ${{ env.KEY_ENCODING }} rarreg.key
+
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.key
+        if-no-files-found: error
+        retention-days: 90
+
+
+  keygen-uft8:
+    name: Generating UTF8 License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ github.event.inputs.KEY_USERNAME }}
+      KEY_LICENSE_NAME: ${{ github.event.inputs.KEY_LICENSE_NAME }}
+    if: github.event.inputs.KEY_ENCODING == 'utf8'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+
+    - name: Generating License (UTF-8)
+      # Use PowerShell 7
+      shell: pwsh
+      run: |
+        $OutputEncoding = [console]::InputEncoding = [console]::OutputEncoding = New-Object System.Text.UTF8Encoding
+        $PSVersionTable.PSVersion
+        $user = "utf8:${{ env.KEY_USERNAME }}"
+        $license = "${{ env.KEY_LICENSE_NAME }}"
+
+        $allAscii = $true
+        foreach ($c in $license.ToCharArray()) {
+          if ([int][char]$c -gt 127) {
+            $allAscii = $false
+            break
+          }
+        }
+
+        if (-not $allAscii) {
+          $license = "utf8:" + $license
+        }
+
+        Write-Host "License string: $license"
+        bin/x64-Release/winrar-keygen.exe "$user" "$license" | Out-File -Encoding utf8NoBOM rarreg.key
+  
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.key
+        if-no-files-found: error
+        retention-days: 90

.github/workflows/keygen_secrets.yml

@@ -0,0 +1,118 @@
+name: WinRAR Keygen with secrets
+on: 
+  workflow_dispatch:
+    inputs:
+      KEY_ENCODING:
+        type: string
+        description: License encoding ascii, ansi or utf8
+        default: 'utf8'
+        required: true
+
+jobs:
+  keygen-ascii:
+    name: Generating ASCII License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ secrets.TEXT1 }}
+      KEY_LICENSE_NAME: ${{ secrets.TEXT2 }}
+      ZIP_PWD: ${{ secrets.PWD }}
+    if: github.event.inputs.KEY_ENCODING == 'ascii'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+    
+    - name: Generating License (ASCII)
+      # Use PowerShell 5
+      shell: powershell
+      run: |
+        $OutputEncoding = [console]::InputEncoding = [console]::OutputEncoding = New-Object System.Text.UTF8Encoding
+        $PSVersionTable.PSVersion
+        bin/x64-Release/winrar-keygen.exe "${{ env.KEY_USERNAME }}" "${{ env.KEY_LICENSE_NAME }}" | Out-File -Encoding ${{ env.KEY_ENCODING }} rarreg.key
+        7z a rarreg.7z rarreg.key -p"${{ env.ZIP_PWD }}"
+
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.7z
+        if-no-files-found: error
+        retention-days: 1
+
+
+  keygen-ansi:
+    name: Generating ANSI License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ secrets.TEXT1 }}
+      KEY_LICENSE_NAME: ${{ secrets.TEXT2 }}
+      ZIP_PWD: ${{ secrets.PWD }}
+    if: github.event.inputs.KEY_ENCODING == 'ansi'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+    
+    - name: Generating License (ANSI)
+      # Use PowerShell 7
+      shell: pwsh
+      run: |
+        [System.Text.Encoding]::Default
+        $OutputEncoding
+        bin/x64-Release/winrar-keygen.exe "${{ env.KEY_USERNAME }}" "${{ env.KEY_LICENSE_NAME }}" | Out-File -Encoding ${{ env.KEY_ENCODING }} rarreg.key
+        7z a rarreg.7z rarreg.key -p"${{ env.ZIP_PWD }}"
+
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.7z
+        if-no-files-found: error
+        retention-days: 1
+
+
+  keygen-uft8:
+    name: Generating UTF8 License
+    runs-on: windows-2022
+    env:
+      KEY_ENCODING: ${{ github.event.inputs.KEY_ENCODING }}
+      KEY_USERNAME: ${{ secrets.TEXT1 }}
+      KEY_LICENSE_NAME: ${{ secrets.TEXT2 }}
+      ZIP_PWD: ${{ secrets.PWD }}
+    if: github.event.inputs.KEY_ENCODING == 'utf8'
+
+    steps:
+    - uses: actions/checkout@v6.0.2
+
+    - name: Generating License (UTF-8)
+      # Use PowerShell 7
+      shell: pwsh
+      run: |
+        $OutputEncoding = [console]::InputEncoding = [console]::OutputEncoding = New-Object System.Text.UTF8Encoding
+        $PSVersionTable.PSVersion
+        $user = "utf8:${{ env.KEY_USERNAME }}"
+        $license = "${{ env.KEY_LICENSE_NAME }}"
+        
+        $allAscii = $true
+        foreach ($c in $license.ToCharArray()) {
+          if ([int][char]$c -gt 127) {
+            $allAscii = $false
+            break
+          }
+        }
+
+        if (-not $allAscii) {
+          $license = "utf8:" + $license
+        }
+
+        Write-Host "Final license: $license"
+        bin/x64-Release/winrar-keygen.exe "$user" "$license" | Out-File -Encoding utf8NoBOM rarreg.key
+        7z a rarreg.7z rarreg.key -p"${{ env.ZIP_PWD }}"
+      
+    - name: Uploading License
+      uses: actions/upload-artifact@v6.0.0
+      with:
+        name: rarreg_file_${{ env.KEY_ENCODING }}
+        path: rarreg.7z
+        if-no-files-found: error
+        retention-days: 1

.gitignore

@@ -0,0 +1,47 @@
+# Development
+.pdb
+.vs/
+obj/
+
+# Windows image file caches
+Thumbs.db
+ehthumbs.db
+
+# Folder config file
+Desktop.ini
+
+# Recycle Bin used on file shares
+$RECYCLE.BIN/
+
+# Windows Installer files
+*.cab
+*.msi
+*.msm
+*.msp
+
+# Windows shortcuts
+*.lnk
+
+# macOS
+*/.DS_Store
+.DS_Store
+.LSOverride
+.AppleDouble
+
+# Thumbnails
+._*
+
+# Files that might appear in the root of a volume
+.DocumentRevisions-V100
+.fseventsd
+.Spotlight-V100
+.TemporaryItems
+.Trashes
+.VolumeIcon.icns
+
+# Directories potentially created on remote AFP share
+.AppleDB
+.AppleDesktop
+Network Trash Folder
+Temporary Items
+.apdisk

.vs/ProjectSettings.json

@@ -1,3 +0,0 @@
-{
-  "CurrentProjectSetting": "无配置"
-}

.vs/VSWorkspaceState.json

@@ -1,7 +0,0 @@
-{
-  "ExpandedNodes": [
-    ""
-  ],
-  "SelectedNode": "\\winrar-keygen.vcxproj",
-  "PreviewInSolutionExplorer": false
-}

.vs/winrar-keygen/project-colors.json

@@ -1,11 +0,0 @@
-{
-  "Version": 1,
-  "ProjectMap": {
-    "2443aa55-9534-4451-9bcc-48ac0982a0cc": {
-      "ProjectGuid": "2443aa55-9534-4451-9bcc-48ac0982a0cc",
-      "DisplayName": "winrar-keygen",
-      "ColorIndex": 0
-    }
-  },
-  "NextColorIndex": 1
-}

LICENSE

@@ -1,6 +1,6 @@
 MIT License
 
-Copyright (c) 2021 BitCookies
+Copyright (c) 2021 Bitcookies
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

README.HOW_DOES_IT_WORK.md

@@ -1,100 +1,85 @@
-[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].
+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](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only).
 
-## 1. Composite field ![GF2p15p17-inlined]
+## 1. Composite field ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only)
 
-Elements in ground field ![GF2p15-inlined] are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is
+Elements in ground field ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/1-light.svg#gh-light-mode-only">
+    <img src="assets/formula/1-dark.svg#gh-dark-mode-only">
 </p>
 
-where each coefficients is in ![GF2-inlined]. If we use 
+where each coefficients is in ![GF2-inlined](assets/formula/GF2-inlined-light.svg#gh-light-mode-only)![GF2-inlined](assets/formula/GF2-inlined-dark.svg#gh-dark-mode-only). 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")
+    <img src="assets/formula/2-light.svg#gh-light-mode-only">
+    <img src="assets/formula/2-dark.svg#gh-dark-mode-only">
 </p>
 
-as the standard basis of the ground field, an element ![A-inlined] in ![GF2p15-inlined] can be denoted as
+as the standard basis of the ground field, an element ![A](assets/formula/AA-inlined-light.svg#gh-light-mode-only)![A](assets/formula/AA-inlined-dark.svg#gh-dark-mode-only) in ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/3-light.svg#gh-light-mode-only">
+    <img src="assets/formula/3-dark.svg#gh-dark-mode-only">
 </p>
 
 ---
 
-The irreducible polynomial of composite field ![GF2p15p17-inlined] is
+The irreducible polynomial of composite field ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/4-light.svg#gh-light-mode-only">
+    <img src="assets/formula/4-dark.svg#gh-dark-mode-only">
 </p>
 
-where each coefficients is in ![GF2p15-inlined]. If we use 
+where each coefficients is in ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only). 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")
+    <img src="assets/formula/5-light.svg#gh-light-mode-only">
+    <img src="assets/formula/5-dark.svg#gh-dark-mode-only">
 </p>
 
-as the standard basis of the composite field, an element ![B-inlined] in ![GF2p15p17-inlined] can be denoted as
+as the standard basis of the composite field, an element ![B](assets/formula/BB-inlined-light.svg#gh-light-mode-only)![B](assets/formula/BB-inlined-dark.svg#gh-dark-mode-only) in ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/6-light.svg#gh-light-mode-only">
+    <img src="assets/formula/6-dark.svg#gh-dark-mode-only">
 </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
+For clarity, we use ![D](assets/formula/DD-inlined-light.svg#gh-light-mode-only)![D](assets/formula/DD-inlined-dark.svg#gh-dark-mode-only) , which is a 255-bits-long integer to denote an element ![B](assets/formula/BB-inlined-light.svg#gh-light-mode-only)![B](assets/formula/BB-inlined-dark.svg#gh-dark-mode-only) in ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only). 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")
+    <img src="assets/formula/7-light.svg#gh-light-mode-only">
+    <img src="assets/formula/7-dark.svg#gh-dark-mode-only">
 </p>
 
-## 2. Elliptic curve over ![GF2p15p17-inlined]
+## 2. Elliptic curve over ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only)
 
 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")
+    <img src="assets/formula/8-light.svg#gh-light-mode-only">
+    <img src="assets/formula/8-dark.svg#gh-dark-mode-only">
 </p>
 
-The base point ![G-inlined] is
+The base point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/9-light.svg#gh-light-mode-only">
+    <img src="assets/formula/9-dark.svg#gh-dark-mode-only">
 </p>
 
-whose order ![n-inlined] is
+A [verification example](README.VERIFY_Point_G.md) of the base point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) on the curve.
+
+whose order ![n](assets/formula/n-inlined-light.svg#gh-light-mode-only)![n](assets/formula/n-inlined-dark.svg#gh-dark-mode-only)  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")
+    <img src="assets/formula/10-light.svg#gh-light-mode-only">
+    <img src="assets/formula/10-dark.svg#gh-dark-mode-only">
 </p>
 
 ## 3. Message hash algorithm
@@ -102,119 +87,136 @@ whose order ![n-inlined] is
 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")
+    <img src="assets/formula/11-light.svg#gh-light-mode-only">
+    <img src="assets/formula/11-dark.svg#gh-dark-mode-only">
 </p>
 
-to denote a message whose length is ![l-inlined]. So the SHA1 value of ![M-inlined] should be 
+to denote a message whose length is ![l](assets/formula/l-inlined-light.svg#gh-light-mode-only)![l](assets/formula/l-inlined-dark.svg#gh-dark-mode-only). So the SHA1 value of ![M](assets/formula/MM-inlined-light.svg#gh-light-mode-only)![M](assets/formula/MM-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/12-light.svg#gh-light-mode-only">
+    <img src="assets/formula/12-dark.svg#gh-dark-mode-only">
 </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.
+where ![s0,4](assets/formula/13-light.svg#gh-light-mode-only)![s0,4](assets/formula/13-dark.svg#gh-dark-mode-only) 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.
+However, WinRAR doesn't serialize the 5 state values. Instead, it use a big integer ![h](assets/formula/h-inlined-light.svg#gh-light-mode-only)![h](assets/formula/h-inlined-dark.svg#gh-dark-mode-only) 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")
+    <img src="assets/formula/15-light.svg#gh-light-mode-only">
+    <img src="assets/formula/15-dark.svg#gh-dark-mode-only">
 </p>
 
 ## 4. ECC digital signature algorithm
 
-We use ![k-inlined] to denote private key, ![P-inlined] to denote public key. So there must be
+We use ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only) to denote private key, ![P](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only) to denote public key. So there must be
 
 <p align="center">
-    <img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
+    <img src="assets/formula/16-light.svg#gh-light-mode-only">
+    <img src="assets/formula/16-dark.svg#gh-dark-mode-only">
 </p>
 
-If we use ![h-inlined] to denote the hash of input data, WinRAR use the following algorithm to perform signing:
+If we use ![h](assets/formula/h-inlined-light.svg#gh-light-mode-only)![h](assets/formula/h-inlined-dark.svg#gh-dark-mode-only) 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).
+1. Generate a random big integer ![Rnd](assets/formula/Rnd-inlined-light.svg#gh-light-mode-only)![Rnd](assets/formula/Rnd-inlined-dark.svg#gh-dark-mode-only) which satisfies ![RND](assets/formula/18-light.svg#gh-light-mode-only)![RND](assets/formula/18-dark.svg#gh-dark-mode-only).
 
-2. Calculate ![r-inlined]
+2. Calculate ![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="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">
+       <img src="assets/formula/19-light.svg#gh-light-mode-only">
+       <img src="assets/formula/19-dark.svg#gh-dark-mode-only">
    </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.
+   where ![RNDGx](assets/formula/20-light.svg#gh-light-mode-only)![RNDGx](assets/formula/20-dark.svg#gh-dark-mode-only)  means we take X coordinate of ![RNDG](assets/formula/21-light.svg#gh-light-mode-only)![RNDG](assets/formula/21-dark.svg#gh-dark-mode-only) and convert it from ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) to a big integer.
 
-3. Calculate ![s-inlined]
+   If ![r=0](assets/formula/22-light.svg#gh-light-mode-only)![r=0](assets/formula/22-dark.svg#gh-dark-mode-only)  or ![rRnd](assets/formula/23-light.svg#gh-light-mode-only)![rRnd](assets/formula/23-dark.svg#gh-dark-mode-only), go back to step 1.
+
+3. Calculate ![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="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
+       <img src="assets/formula/24-light.svg#gh-light-mode-only">
+       <img src="assets/formula/24-dark.svg#gh-dark-mode-only">
    </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).
+   If ![s=0](assets/formula/25-light.svg#gh-light-mode-only)![s=0](assets/formula/25-dark.svg#gh-dark-mode-only), go back to step 1.
+
+4. Output ![(r,s)](assets/formula/17-light.svg#gh-light-mode-only)![(r,s)](assets/formula/17-dark.svg#gh-dark-mode-only).
 
 ## 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">
+    <img src="assets/formula/26-light.svg#gh-light-mode-only">
+    <img src="assets/formula/26-dark.svg#gh-dark-mode-only">
 </p>
 
-to denote input data whose length is ![l-inlined]. WinRAR use it to generate private key ![k-inlined].
+to denote input data whose length is ![l](assets/formula/l-inlined-light.svg#gh-light-mode-only)![l](assets/formula/l-inlined-dark.svg#gh-dark-mode-only). WinRAR use it to generate private key ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only).
 
-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
+1. We use ![g0-5](assets/formula/27-light.svg#gh-light-mode-only)![g0-5](assets/formula/27-dark.svg#gh-dark-mode-only) 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">
+       <img src="assets/formula/28-light.svg#gh-light-mode-only">
+       <img src="assets/formula/28-dark.svg#gh-dark-mode-only">
    </p>
 
-2. Let ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%3D0).
+2. Let ![g0=0](assets/formula/29-light.svg#gh-light-mode-only)![g0=0](assets/formula/29-dark.svg#gh-dark-mode-only).
 
-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):
+3. If ![l!=0](assets/formula/30-light.svg#gh-light-mode-only)![l!=0](assets/formula/30-dark.svg#gh-dark-mode-only), we calculate SHA1 value of ![T](assets/formula/TT-inlined-light.svg#gh-light-mode-only)![T](assets/formula/TT-inlined-dark.svg#gh-dark-mode-only). Then assign SHA1 state value ![Si](assets/formula/31-light.svg#gh-light-mode-only)![Si](assets/formula/31-dark.svg#gh-dark-mode-only) to ![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="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">
+       <img src="assets/formula/33-light.svg#gh-light-mode-only">
+       <img src="assets/formula/33-dark.svg#gh-dark-mode-only">
    </p>
 
-   Otherwise, when ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%3D0), we let 
+   Otherwise, when ![l=0](assets/formula/34-light.svg#gh-light-mode-only)![l=0](assets/formula/34-dark.svg#gh-dark-mode-only), 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">
+       <img src="assets/formula/35-light.svg#gh-light-mode-only">
+          <img src="assets/formula/35-dark.svg#gh-dark-mode-only">
    </p>
 
-4. Regard ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0) as counter, add itself by 1.
+4. Regard ![g0](assets/formula/36-light.svg#gh-light-mode-only)![g0](assets/formula/36-dark.svg#gh-dark-mode-only)  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">
+       <img src="assets/formula/37-light.svg#gh-light-mode-only">
+       <img src="assets/formula/37-dark.svg#gh-dark-mode-only">
    </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).
+   We takes the lowest 16 bits of ![S0](assets/formula/38-light.svg#gh-light-mode-only)![S0](assets/formula/38-dark.svg#gh-dark-mode-only) and donote it as ![Kg0](assets/formula/39-light.svg#gh-light-mode-only)![Kg0](assets/formula/39-dark.svg#gh-dark-mode-only).
 
 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
+6. After that, we will get ![k1-15](assets/formula/40-light.svg#gh-light-mode-only)![k1-15](assets/formula/40-dark.svg#gh-dark-mode-only). 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">
+       <img src="assets/formula/41-light.svg#gh-light-mode-only">
+       <img src="assets/formula/41-dark.svg#gh-dark-mode-only">
    </p>
 
 ## 6. The private key and public key of WinRAR
 
-Private key ![k-inlined] is
+Private key ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only) 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">
+    <img src="assets/formula/42-light.svg#gh-light-mode-only">
+    <img src="assets/formula/42-dark.svg#gh-dark-mode-only">
 </p>
 
-This private key is generated by the algorithm describled in section 5 where the length of data ![T-inlined] is zero.
+This private key is generated by the algorithm describled in section 5 where the length of data ![T](assets/formula/TT-inlined-light.svg#gh-light-mode-only)![T](assets/formula/TT-inlined-dark.svg#gh-dark-mode-only) is zero.
 
-Public key ![P-inlined] is
+Public key ![P](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only) 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">
+    <img src="assets/formula/43-light.svg#gh-light-mode-only">
+    <img src="assets/formula/43-dark.svg#gh-dark-mode-only">
 </p>
 
+
 ## 7. Generation of "rarreg.key"
 
 The generation of license file `rarreg.key` requires 2 arguments:
@@ -222,85 +224,94 @@ 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">
+       <img src="assets/formula/44-light.svg#gh-light-mode-only">
+       <img src="assets/formula/44-dark.svg#gh-dark-mode-only">
    </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">
+       <img src="assets/formula/45-light.svg#gh-light-mode-only">
+       <img src="assets/formula/45-dark.svg#gh-dark-mode-only">
    </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].
+1. Use the algorithm describled in section 5, with argument ![U](assets/formula/UU-inlined-light.svg#gh-light-mode-only)![U](assets/formula/UU-inlined-dark.svg#gh-dark-mode-only), to generate private key ![ku](assets/formula/46-light.svg#gh-light-mode-only)![ku](assets/formula/46-dark.svg#gh-dark-mode-only)  and public key ![pu](assets/formula/47-light.svg#gh-light-mode-only)![pu](assets/formula/47-dark.svg#gh-dark-mode-only). Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only).
 
-   The length of ![Temp-inlined] should be 64. If less, pad with `'0'` until the length is 64.
+   The length of ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) should be 64. If less, pad with `'0'` until the length is 64.
 
-2. Let ![Data3-inlined] be 
+2. Let ![Data3](assets/formula/Data3-inlined-light.svg#gh-light-mode-only)![Data3](assets/formula/Data3-inlined-dark.svg#gh-dark-mode-only) 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">
+       <img src="assets/formula/48-light.svg#gh-light-mode-only">
+       <img src="assets/formula/48-dark.svg#gh-dark-mode-only">
    </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].
+3. Use the algorithm describled in section 5, with argument ![Data3](assets/formula/Data3-inlined-light.svg#gh-light-mode-only)![Data3](assets/formula/Data3-inlined-dark.svg#gh-dark-mode-only), to generate private key ![kdata3](assets/formula/49-light.svg#gh-light-mode-only)![kdata3](assets/formula/49-dark.svg#gh-dark-mode-only) and public key ![pdata3](assets/formula/50-light.svg#gh-light-mode-only)![pdata3](assets/formula/50-dark.svg#gh-dark-mode-only). Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Data0](assets/formula/Data0-inlined-light.svg#gh-light-mode-only)![Data0](assets/formula/Data0-inlined-dark.svg#gh-dark-mode-only).
 
-   The length of ![Data0-inlined] should be 64. If less, pad with `'0'` until the length is 64.
+   The length of ![Data0](assets/formula/Data0-inlined-light.svg#gh-light-mode-only)![Data0](assets/formula/Data0-inlined-dark.svg#gh-dark-mode-only) should be 64. If less, pad with `'0'` until the length is 64.
 
-4. Let ![UID-inlined] be
+4. Let ![UID](assets/formula/UID-inlined-light.svg#gh-light-mode-only)![UID](assets/formula/UID-inlined-dark.svg#gh-dark-mode-only) 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">
+       <img src="assets/formula/51-light.svg#gh-light-mode-only">
+       <img src="assets/formula/51-dark.svg#gh-dark-mode-only">
    </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).
+5. Use the algorithm describled in section 4, with argument ![L](assets/formula/LL-inlined-light.svg#gh-light-mode-only)![L](assets/formula/LL-inlined-dark.svg#gh-dark-mode-only)  and private key ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only)  describled section 6, to get signature ![(rl,sl)](assets/formula/52-light.svg#gh-light-mode-only)![(rl,sl)](assets/formula/52-dark.svg#gh-dark-mode-only).
 
-   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.
+   The bit length of ![rl](assets/formula/53-light.svg#gh-light-mode-only)![rl](assets/formula/53-dark.svg#gh-dark-mode-only) and ![sl](assets/formula/54-light.svg#gh-light-mode-only)![sl](assets/formula/54-dark.svg#gh-dark-mode-only) 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. 
+6. Convert ![rl](assets/formula/53-light.svg#gh-light-mode-only)![rl](assets/formula/53-dark.svg#gh-dark-mode-only) and ![sl](assets/formula/54-light.svg#gh-light-mode-only)![sl](assets/formula/54-dark.svg#gh-dark-mode-only) to hex-integer string ![SZrl](assets/formula/55-light.svg#gh-light-mode-only)![SZrl](assets/formula/55-dark.svg#gh-dark-mode-only) and ![SZsl](assets/formula/56-light.svg#gh-light-mode-only)![SZsl](assets/formula/56-dark.svg#gh-dark-mode-only), 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.
+   If the length of ![SZrl](assets/formula/55-light.svg#gh-light-mode-only)![SZrl](assets/formula/55-dark.svg#gh-dark-mode-only) or ![SZsl](assets/formula/56-light.svg#gh-light-mode-only)![SZsl](assets/formula/56-dark.svg#gh-dark-mode-only) is less than 60, pad character `'0'` until the length is 60.
 
-7. Let ![Data1-inlined] be
+7. Let ![Data1](assets/formula/Data1-inlined-light.svg#gh-light-mode-only)![Data1](assets/formula/Data1-inlined-dark.svg#gh-dark-mode-only) 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">
+       <img src="assets/formula/57-light.svg#gh-light-mode-only">
+       <img src="assets/formula/57-dark.svg#gh-dark-mode-only">
    </p>
 
-8. Let ![Temp-inlined] be 
+8. Let ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) be 
 
    <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>
 
-   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).
+   Use the algorithm describled in section 4, with argument ![Temp](assets/formula/Temp-inlined-light.svg#gh-light-mode-only)![Temp](assets/formula/Temp-inlined-dark.svg#gh-dark-mode-only) and private key ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k](assets/formula/k-inlined-dark.svg#gh-dark-mode-only) describled section 6, to get signature ![(rTemp,sTemp)](assets/formula/59-light.svg#gh-light-mode-only)![(rTemp,sTemp)](assets/formula/59-dark.svg#gh-dark-mode-only).
 
-   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.
+   The bit length of ![rTemp](assets/formula/60-light.svg#gh-light-mode-only)![rTemp](assets/formula/60-dark.svg#gh-dark-mode-only) and ![sTemp](assets/formula/61-light.svg#gh-light-mode-only)![sTemp](assets/formula/61-dark.svg#gh-dark-mode-only) 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. 
+9. Convert ![rTemp](assets/formula/60-light.svg#gh-light-mode-only)![rTemp](assets/formula/60-dark.svg#gh-dark-mode-only) and ![sTemp](assets/formula/61-light.svg#gh-light-mode-only)![sTemp](assets/formula/61-dark.svg#gh-dark-mode-only) to hex-integer string ![SZrTemp](assets/formula/62-light.svg#gh-light-mode-only)![SZrTemp](assets/formula/62-dark.svg#gh-dark-mode-only)  and ![SZsTemp](assets/formula/63-light.svg#gh-light-mode-only)![SZsTemp](assets/formula/63-dark.svg#gh-dark-mode-only), 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.
+   If the length of ![SZrTemp](assets/formula/62-light.svg#gh-light-mode-only)![SZrTemp](assets/formula/62-dark.svg#gh-dark-mode-only)  or ![SZsTemp](assets/formula/63-light.svg#gh-light-mode-only)![SZsTemp](assets/formula/63-dark.svg#gh-dark-mode-only) is less than 60, pad character `'0'` until the length is 60.
 
-10. Let ![Data2-inlined] be
+10. Let ![Data2](assets/formula/Data2-inlined-light.svg#gh-light-mode-only)![Data2](assets/formula/Data2-inlined-dark.svg#gh-dark-mode-only) 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">
+        <img src="assets/formula/64-light.svg#gh-light-mode-only">
+        <img src="assets/formula/64-dark.svg#gh-dark-mode-only">
     </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">
+        <img src="assets/formula/65-light.svg#gh-light-mode-only">
+        <img src="assets/formula/65-dark.svg#gh-dark-mode-only">
     </p>
 
     The final checksum the complement of CRC32 value. 
+    
+    Then convert the checksum to decimal string ![SZchecksum](assets/formula/66-light.svg#gh-light-mode-only)![SZchecksum](assets/formula/66-dark.svg#gh-dark-mode-only). If the length is less than 10, pad character `'0'` until the length is 10.
 
-    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 
+12. Let ![Data](assets/formula/Data-inlined-light.svg#gh-light-mode-only)![Data](assets/formula/Data-inlined-dark.svg#gh-dark-mode-only) 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">
+        <img src="assets/formula/67-light.svg#gh-light-mode-only">
+        <img src="assets/formula/67-dark.svg#gh-dark-mode-only">
     </p>
 
 13. Output with format
@@ -314,8 +325,8 @@ The following is the algorithm to generate `rarreg.key`.
     * 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">
+        <img src="assets/formula/68-light.svg#gh-light-mode-only">
+          <img src="assets/formula/68-dark.svg#gh-dark-mode-only">
       </p>
-
-    * Output ![Data-inlined], with 54 characters a line.
-
+    
+    * Output ![Data](assets/formula/Data-inlined-light.svg#gh-light-mode-only)![Data](assets/formula/Data-inlined-dark.svg#gh-dark-mode-only), with 54 characters a line.

README.HOW_DOES_IT_WORK.zh-CN.md

@@ -1,310 +1,322 @@
-[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。
+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](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 上的曲线。
 
-## 1. 复合域 ![GF2p15p17-inlined]
+## 1. 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)
 
-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：
+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) 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")
+    <img src="assets/formula/1-light.svg#gh-light-mode-only">
+    <img src="assets/formula/1-dark.svg#gh-dark-mode-only">
 </p>
 
-各项系数全部位于 ![GF2-inlined]。设基域的标准基为：
+各项系数全部位于 ![GF2-inlined](assets/formula/GF2-inlined-light.svg#gh-light-mode-only)![GF2-inlined](assets/formula/GF2-inlined-dark.svg#gh-dark-mode-only)。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")
+    <img src="assets/formula/2-light.svg#gh-light-mode-only">
+    <img src="assets/formula/2-dark.svg#gh-dark-mode-only">
 </p>
 
-则位于基域 ![GF2p15-inlined] 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="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")
+    <img src="assets/formula/3-light.svg#gh-light-mode-only">
+    <img src="assets/formula/3-dark.svg#gh-dark-mode-only">
 </p>
 
 ---
 
-复合域 ![GF2p15p17-inlined] 的不可约多项式为：
+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) 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")
+    <img src="assets/formula/4-light.svg#gh-light-mode-only">
+    <img src="assets/formula/4-dark.svg#gh-dark-mode-only">
 </p>
 
-各项系数全部位于 ![GF2p15-inlined]。设复合域的标准基为：
+各项系数全部位于 ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only)。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")
+    <img src="assets/formula/5-light.svg#gh-light-mode-only">
+    <img src="assets/formula/5-dark.svg#gh-dark-mode-only">
 </p>
 
-则位于复合域 ![GF2p15p17-inlined] 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="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")
+    <img src="assets/formula/6-light.svg#gh-light-mode-only">
+    <img src="assets/formula/6-dark.svg#gh-dark-mode-only">
 </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：
+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="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")
+    <img src="assets/formula/7-light.svg#gh-light-mode-only">
+    <img src="assets/formula/7-dark.svg#gh-dark-mode-only">
 </p>
 
-## 2. 复合域 ![GF2p15p17-inlined] 上的椭圆曲线
+## 2. 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")
+    <img src="assets/formula/8-light.svg#gh-light-mode-only">
+    <img src="assets/formula/8-dark.svg#gh-dark-mode-only">
 </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="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")
+    <img src="assets/formula/9-light.svg#gh-light-mode-only">
+    <img src="assets/formula/9-dark.svg#gh-dark-mode-only">
 </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) 在曲线上的[验证示例](README.VERIFY_Point_G.zh-CN.md)。
+
+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="http://latex.codecogs.com/svg.latex?n%3D%5Ctextrm%7B0x1026dd85081b82314691ced9bbec30547840e4bf72d8b5e0d258442bbcd31%7D%20%5Cquad%20n%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D")
+    <img src="assets/formula/10-light.svg#gh-light-mode-only">
+    <img src="assets/formula/10-dark.svg#gh-dark-mode-only">
 </p>
 
 ## 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="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")
+    <img src="assets/formula/11-light.svg#gh-light-mode-only">
+    <img src="assets/formula/11-dark.svg#gh-dark-mode-only">
 </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="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")
+    <img src="assets/formula/12-light.svg#gh-light-mode-only">
+    <img src="assets/formula/12-dark.svg#gh-dark-mode-only">
 </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)。
+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="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")
+    <img src="assets/formula/15-light.svg#gh-light-mode-only">
+    <img src="assets/formula/15-dark.svg#gh-dark-mode-only">
 </p>
 
-
 ## 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="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
+    <img src="assets/formula/16-light.svg#gh-light-mode-only">
+    <img src="assets/formula/16-dark.svg#gh-dark-mode-only">
 </p>
 
-消息哈希为 ![h-inlined]，则签名 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r%2Cs%29) 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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%200%3CRnd%3Cn)。
+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="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">
+       <img src="assets/formula/19-light.svg#gh-light-mode-only">
+       <img src="assets/formula/19-dark.svg#gh-dark-mode-only">
    </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。
+   其中 ![RNDGx](assets/formula/20-light.svg#gh-light-mode-only)![RNDGx](assets/formula/20-dark.svg#gh-dark-mode-only) 表示取 ![RNDG](assets/formula/21-light.svg#gh-light-mode-only)![RNDG](assets/formula/21-dark.svg#gh-dark-mode-only) 的 X 坐标，同时将 X 坐标从 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only) 转换为大数。
 
-3. 计算 ![s-inlined]
+   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](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="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
+       <img src="assets/formula/24-light.svg#gh-light-mode-only">
+       <img src="assets/formula/24-dark.svg#gh-dark-mode-only">
    </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)。
+   若 ![s=0](assets/formula/25-light.svg#gh-light-mode-only)![s=0](assets/formula/25-dark.svg#gh-dark-mode-only) 则回到步骤1。
+
+4. 输出 ![(r,s)](assets/formula/17-light.svg#gh-light-mode-only)![(r,s)](assets/formula/17-dark.svg#gh-dark-mode-only)。
 
 ## 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="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">
+    <img src="assets/formula/26-light.svg#gh-light-mode-only">
+    <img src="assets/formula/26-dark.svg#gh-dark-mode-only">
 </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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%2Cg_1%2Cg_2%2Cg_3%2Cg_4%2Cg_5)，则有
+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
 
    <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">
+       <img src="assets/formula/28-light.svg#gh-light-mode-only">
+       <img src="assets/formula/28-dark.svg#gh-dark-mode-only">
    </p>
 
-2. 令 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%3D0)。
+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 ![](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)：
+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](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="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">
+       <img src="assets/formula/33-light.svg#gh-light-mode-only">
+       <img src="assets/formula/33-dark.svg#gh-dark-mode-only">
    </p>
 
-   否则，即 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20l%3D0) 时，令：
+
+   否则，即 ![l=0](assets/formula/34-light.svg#gh-light-mode-only)![l=0](assets/formula/34-dark.svg#gh-dark-mode-only) 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">
+       <img src="assets/formula/35-light.svg#gh-light-mode-only">
+       <img src="assets/formula/35-dark.svg#gh-dark-mode-only">
    </p>
 
-4. 把 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0) 作为计数器，自增1。
+4. 把 ![g0](assets/formula/36-light.svg#gh-light-mode-only)![g0](assets/formula/36-dark.svg#gh-dark-mode-only)  作为计数器，自增1。
 
-   计算SHA1值：
+   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">
+       <img src="assets/formula/37-light.svg#gh-light-mode-only">
+       <img src="assets/formula/37-dark.svg#gh-dark-mode-only">
    </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)。
+
+   取 ![S0](assets/formula/38-light.svg#gh-light-mode-only)![S0](assets/formula/38-dark.svg#gh-dark-mode-only) 的低16位并记为 ![Kg0](assets/formula/39-light.svg#gh-light-mode-only)![Kg0](assets/formula/39-dark.svg#gh-dark-mode-only)。
 
 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
+6. 重复执行完后会得到 ![k1-15](assets/formula/40-light.svg#gh-light-mode-only)![k1-15](assets/formula/40-dark.svg#gh-dark-mode-only)，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">
+       <img src="assets/formula/41-light.svg#gh-light-mode-only">
+       <img src="assets/formula/41-dark.svg#gh-dark-mode-only">
    </p>
 
 ## 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="http://latex.codecogs.com/svg.latex?k%3D%5Ctextrm%7B0x59fe6abcca90bdb95f0105271fa85fb9f11f467450c1ae9044b7fd61d65e%7D%20%5Cquad%20%5Cquad%20k%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D">
+    <img src="assets/formula/42-light.svg#gh-light-mode-only">
+    <img src="assets/formula/42-dark.svg#gh-dark-mode-only">
 </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="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">
+    <img src="assets/formula/43-light.svg#gh-light-mode-only">
+    <img src="assets/formula/43-dark.svg#gh-dark-mode-only">
 </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 
+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">
+       <img src="assets/formula/44-light.svg#gh-light-mode-only">
+       <img src="assets/formula/44-dark.svg#gh-dark-mode-only">
    </p>
 
-2. 授权类型的ANSI字符串，不包括null-terminator；记为
+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">
+       <img src="assets/formula/45-light.svg#gh-light-mode-only">
+       <img src="assets/formula/45-dark.svg#gh-dark-mode-only">
    </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]。
+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="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 ![](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]。
+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="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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_L%2Cs_L%29)，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/formula/LL-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 ![](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。
+   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。
 
-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)。
+6. 将 ![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) 以16进制形式输出（无 `"0x"` 前缀），分别记为 ![SZrl](assets/formula/55-light.svg#gh-light-mode-only)![SZrl](assets/formula/55-dark.svg#gh-dark-mode-only) 和 ![SZsl](assets/formula/56-light.svg#gh-light-mode-only)![SZsl](assets/formula/56-dark.svg#gh-dark-mode-only)。
 
-   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
+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="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
+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="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 ![](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)。
+   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。
 
-   若长度不满60，则在前面补字符`'0'`，直到长度为60。
+   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。
 
-10. 令字符串 ![Data2-inlined]为
+9. 将 ![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) 以16进制形式输出（无 `"0x"` 前缀），分别记为 ![SZrTemp](assets/formula/62-light.svg#gh-light-mode-only)![SZrTemp](assets/formula/62-dark.svg#gh-dark-mode-only) 和 ![SZsTemp](assets/formula/63-light.svg#gh-light-mode-only)![SZsTemp](assets/formula/63-dark.svg#gh-dark-mode-only)。
+
+   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](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="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 ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bchecksum%7D)。
+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="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。
 
@@ -313,8 +325,8 @@ 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。
-
+    
+    * 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。

README.VERIFY_Point_G.md

@@ -0,0 +1,155 @@
+# Verifying point G lies on the curve
+
+## 1. Composite field, curves and point G
+
+Composite field is ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only).
+
+And the base field is ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only) ![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only), i.e. each element in the domain is a `15-bit` number. The number of extensions is 17, so the entire composite domain element can be viewed as a 17-term polynomial, each term being ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only).
+
+The equation of the elliptic curve that WinRAR uses is
+
+<p align="center">
+    <img src="assets/formula/8-light.svg#gh-light-mode-only">
+    <img src="assets/formula/8-dark.svg#gh-dark-mode-only">
+</p>
+
+The base point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) is
+
+<p align="center">
+    <img src="assets/formula/9-light.svg#gh-light-mode-only">
+    <img src="assets/formula/9-dark.svg#gh-dark-mode-only">
+</p>
+
+## 2. Conversion point G
+
+Convert the point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) (in large integer format) into the required little-endian representation of `15-bit` segments for the field  ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only). A Python for converting the point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) is as follows.
+
+```python
+def to_field_repr(val, bits=15, count=17):
+    mask = (1 << bits) - 1
+    result = []
+    for _ in range(count):
+        result.append(val & mask)
+        val >>= bits
+    return result
+
+def print_field(label, field_data):
+    print(f"{label} = to_field([")
+    for i in range(len(field_data)):
+        print(f"    0x{field_data[i]:04X},", end="\n" if (i + 1) % 4 == 0 else " ")
+    print("])")
+
+Gx_int = 0x56fdcbc6a27acee0cc2996e0096ae74feb1acf220a2341b898b549440297b8cc
+Gy_int = 0x20da32e8afc90b7cf0e76bde44496b4d0794054e6ea60f388682463132f931a7
+
+Gx_field = to_field_repr(Gx_int)
+Gy_field = to_field_repr(Gy_int)
+
+print_field("Gx", Gx_field)
+print()
+print_field("Gy", Gy_field)
+```
+
+The output can be seen in lines 435 to 456 of the WinRarConfig.hpp file.
+
+```
+Gx = to_field([
+    0x38CC,     0x052F,     0x2510,     0x45AA,
+    0x1B89,     0x4468,     0x4882,     0x0D67,
+    0x4FEB,     0x55CE,     0x0025,     0x4CB7,
+    0x0CC2,     0x59DC,     0x289E,     0x65E3,
+    0x56FD
+])
+
+Gy = to_field([
+    0x31A7,     0x65F2,     0x18C4,     0x3412,
+    0x7388,     0x54C1,     0x539B,     0x4A02,
+    0x4D07,     0x12D6,     0x7911,     0x3B5E,
+    0x4F0E,     0x216F,     0x2BF2,     0x1974,
+    0x20DA
+])
+```
+
+## 3. Verify whether the Point G and PK are on the curve
+
+A Python code to verify whether the base point ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) and PK are on the curve is as follows.
+
+```python
+#  GF(((2^15)^17))
+def gf2_15_add(a, b):
+    return a ^ b
+
+def gf2_15_mul(a, b):
+    # Modulus: x^15 + x + 1
+    res = 0
+    for i in range(15):
+        if (b >> i) & 1:
+            res ^= a << i
+    # Irreducible polynomial: x^15 + x + 1
+    for i in range(29, 14, -1):
+        if (res >> i) & 1:
+            res ^= 0b1000000000000011 << (i - 15)
+    return res & 0x7FFF  # 15-bit mask
+
+def gf2_15_poly_add(a, b):
+    return [gf2_15_add(x, y) for x, y in zip(a, b)]
+
+def gf2_15_poly_mul(a, b):
+    res = [0] * 33
+    for i in range(17):
+        for j in range(17):
+            res[i + j] ^= gf2_15_mul(a[i], b[j])
+    return res
+
+def gf2_15_17_mod(poly):
+    # Modulus: y^17 + y^3 + 1
+    for i in range(len(poly) - 1, 16, -1):
+        if poly[i]:
+            poly[i - 17] ^= poly[i]
+            poly[i - 14] ^= poly[i]
+            poly[i] = 0
+    return poly[:17]
+
+def gf2_15_17_mul(a, b):
+    return gf2_15_17_mod(gf2_15_poly_mul(a, b))
+
+def gf2_15_17_square(a):
+    return gf2_15_17_mul(a, a)
+
+def gf2_15_17_add(a, b):
+    return gf2_15_poly_add(a, b)
+
+def gf2_15_17_eq(a, b):
+    return all(x == y for x, y in zip(a, b))
+
+def is_on_curve(x, y, b):
+    y2 = gf2_15_17_square(y)
+    xy = gf2_15_17_mul(x, y)
+    lhs = gf2_15_17_add(y2, xy)
+    x2 = gf2_15_17_square(x)
+    x3 = gf2_15_17_mul(x2, x)
+    rhs = gf2_15_17_add(x3, b)
+    return gf2_15_17_eq(lhs, rhs)
+
+def to_field(arr):
+    assert len(arr) == 17
+    return arr[:]
+
+# Parameter definition
+b = [0x00] * 17
+b = [161] + [0]*16  # Constant element in GF((2^15)^17), equivalent to b[0] = 0xA1
+
+Gx = to_field([0x38CC, 0x052F, 0x2510, 0x45AA, 0x1B89, 0x4468, 0x4882, 0x0D67,
+               0x4FEB, 0x55CE, 0x0025, 0x4CB7, 0x0CC2, 0x59DC, 0x289E, 0x65E3, 0x56FD])
+Gy = to_field([0x31A7, 0x65F2, 0x18C4, 0x3412, 0x7388, 0x54C1, 0x539B, 0x4A02,
+               0x4D07, 0x12D6, 0x7911, 0x3B5E, 0x4F0E, 0x216F, 0x2BF2, 0x1974, 0x20DA])
+
+PKx = to_field([0x3A1A, 0x1109, 0x268A, 0x12F7, 0x3734, 0x75F0, 0x576C, 0x2EA4,
+                0x4813, 0x3F62, 0x0567, 0x784D, 0x753D, 0x6D92, 0x366C, 0x1107, 0x3861])
+PKy = to_field([0x6C20, 0x6027, 0x1B22, 0x7A87, 0x43C4, 0x1908, 0x2449, 0x4675,
+                0x7933, 0x2E66, 0x32F5, 0x2A58, 0x1145, 0x74AC, 0x36D0, 0x2731, 0x12B6])
+
+# Verification
+print("Verify whether the point G is on the curve:", is_on_curve(Gx, Gy, b))
+print("Verify whether the PK is on the curve:", is_on_curve(PKx, PKy, b))
+```

README.VERIFY_Point_G.zh-CN.md

@@ -0,0 +1,155 @@
+# 验证基点G在曲线上
+
+## 1. 复合域、曲线和基点G
+
+复合域为 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only)。
+
+基域为 ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) ，即域中每个元素是一个 `15-bit` 的数字。扩展次数是17，所以整个复合域元素可以看作是一个17项的多项式，每项都是 ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2p15-inlined-dark.svg#gh-dark-mode-only) 中的数。
+
+曲线方程为：
+
+<p align="center">
+    <img src="assets/formula/8-light.svg#gh-light-mode-only">
+    <img src="assets/formula/8-dark.svg#gh-dark-mode-only">
+</p>
+
+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">
+    <img src="assets/formula/9-dark.svg#gh-dark-mode-only">
+</p>
+
+## 2. 转换基点G
+
+将基点 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only)（以大整数形式）转换为 ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-light.svg#gh-light-mode-only) ![GF2p15p17-inlined](assets/formula/GF2p15p17-inlined-dark.svg#gh-dark-mode-only)所需的 `15-bit` 小端表示形式。一个转换基点 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 的 Python 脚本如下：
+
+```python
+def to_field_repr(val, bits=15, count=17):
+    mask = (1 << bits) - 1
+    result = []
+    for _ in range(count):
+        result.append(val & mask)
+        val >>= bits
+    return result
+
+def print_field(label, field_data):
+    print(f"{label} = to_field([")
+    for i in range(len(field_data)):
+        print(f"    0x{field_data[i]:04X},", end="\n" if (i + 1) % 4 == 0 else " ")
+    print("])")
+
+Gx_int = 0x56fdcbc6a27acee0cc2996e0096ae74feb1acf220a2341b898b549440297b8cc
+Gy_int = 0x20da32e8afc90b7cf0e76bde44496b4d0794054e6ea60f388682463132f931a7
+
+Gx_field = to_field_repr(Gx_int)
+Gy_field = to_field_repr(Gy_int)
+
+print_field("Gx", Gx_field)
+print()
+print_field("Gy", Gy_field)
+```
+
+输出结果可以看到正是 WinRarConfig.hpp 文件中 435~456 行的内容：
+
+```
+Gx = to_field([
+    0x38CC,     0x052F,     0x2510,     0x45AA,
+    0x1B89,     0x4468,     0x4882,     0x0D67,
+    0x4FEB,     0x55CE,     0x0025,     0x4CB7,
+    0x0CC2,     0x59DC,     0x289E,     0x65E3,
+    0x56FD
+])
+
+Gy = to_field([
+    0x31A7,     0x65F2,     0x18C4,     0x3412,
+    0x7388,     0x54C1,     0x539B,     0x4A02,
+    0x4D07,     0x12D6,     0x7911,     0x3B5E,
+    0x4F0E,     0x216F,     0x2BF2,     0x1974,
+    0x20DA
+])
+```
+
+## 3. 验证基点G和PK是否在曲线上
+
+一个验证基点 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 和PK是否在曲线上的 Python 脚本如下：
+
+```python
+#  GF(((2^15)^17))
+def gf2_15_add(a, b):
+    return a ^ b
+
+def gf2_15_mul(a, b):
+    # 模 x^15 + x + 1
+    res = 0
+    for i in range(15):
+        if (b >> i) & 1:
+            res ^= a << i
+    # 模多项式 x^15 + x + 1
+    for i in range(29, 14, -1):
+        if (res >> i) & 1:
+            res ^= 0b1000000000000011 << (i - 15)
+    return res & 0x7FFF  # 15-bit mask
+
+def gf2_15_poly_add(a, b):
+    return [gf2_15_add(x, y) for x, y in zip(a, b)]
+
+def gf2_15_poly_mul(a, b):
+    res = [0] * 33
+    for i in range(17):
+        for j in range(17):
+            res[i + j] ^= gf2_15_mul(a[i], b[j])
+    return res
+
+def gf2_15_17_mod(poly):
+    # 模 y^17 + y^3 + 1
+    for i in range(len(poly) - 1, 16, -1):
+        if poly[i]:
+            poly[i - 17] ^= poly[i]
+            poly[i - 14] ^= poly[i]
+            poly[i] = 0
+    return poly[:17]
+
+def gf2_15_17_mul(a, b):
+    return gf2_15_17_mod(gf2_15_poly_mul(a, b))
+
+def gf2_15_17_square(a):
+    return gf2_15_17_mul(a, a)
+
+def gf2_15_17_add(a, b):
+    return gf2_15_poly_add(a, b)
+
+def gf2_15_17_eq(a, b):
+    return all(x == y for x, y in zip(a, b))
+
+def is_on_curve(x, y, b):
+    y2 = gf2_15_17_square(y)
+    xy = gf2_15_17_mul(x, y)
+    lhs = gf2_15_17_add(y2, xy)
+    x2 = gf2_15_17_square(x)
+    x3 = gf2_15_17_mul(x2, x)
+    rhs = gf2_15_17_add(x3, b)
+    return gf2_15_17_eq(lhs, rhs)
+
+def to_field(arr):
+    assert len(arr) == 17
+    return arr[:]
+
+# 参数定义
+b = [0x00] * 17
+b = [161] + [0]*16  # GF((2^15)^17) 中的常数元素，等价于 b[0] = 0xA1
+
+Gx = to_field([0x38CC, 0x052F, 0x2510, 0x45AA, 0x1B89, 0x4468, 0x4882, 0x0D67,
+               0x4FEB, 0x55CE, 0x0025, 0x4CB7, 0x0CC2, 0x59DC, 0x289E, 0x65E3, 0x56FD])
+Gy = to_field([0x31A7, 0x65F2, 0x18C4, 0x3412, 0x7388, 0x54C1, 0x539B, 0x4A02,
+               0x4D07, 0x12D6, 0x7911, 0x3B5E, 0x4F0E, 0x216F, 0x2BF2, 0x1974, 0x20DA])
+
+PKx = to_field([0x3A1A, 0x1109, 0x268A, 0x12F7, 0x3734, 0x75F0, 0x576C, 0x2EA4,
+                0x4813, 0x3F62, 0x0567, 0x784D, 0x753D, 0x6D92, 0x366C, 0x1107, 0x3861])
+PKy = to_field([0x6C20, 0x6027, 0x1B22, 0x7A87, 0x43C4, 0x1908, 0x2449, 0x4675,
+                0x7933, 0x2E66, 0x32F5, 0x2A58, 0x1145, 0x74AC, 0x36D0, 0x2731, 0x12B6])
+
+# 验证
+print("验证基点 G 是否在曲线上：", is_on_curve(Gx, Gy, b))
+print("验证 PK 是否在曲线上：", is_on_curve(PKx, PKy, b))
+```

README.md

@@ -1,24 +1,20 @@
 <p align="center">
- <img width="100px" src="icon.svg" align="center" alt="WinRAR Keygen" />
+ <img width="100px" src="icon.png" align="center" alt="WinRAR Keygen" />
  <h2 align="center">WinRAR Keygen</h2>
  <p align="center">Principle of WinRAR key generation</p>
 </p>
 <p align="center">
-  <img src="https://img.shields.io/github/v/release/bitcookies/winrar-keygen?label=version" />
-  <a href="https://github.com/bitcookies/winrar-keygen/issues">
-  	<img alt="Issues" src="https://img.shields.io/github/issues/bitcookies/winrar-keygen?color=F48D73" />
-  </a>
-  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298" />
-  <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" />
-  </a>
+  <a href="https://github.com/bitcookies/winrar-keygen/releases"><img src="https://img.shields.io/github/v/release/bitcookies/winrar-keygen?label=version" /></a>
+  <a href="https://github.com/bitcookies/winrar-keygen/issues"><img alt="Issues" src="https://img.shields.io/github/issues/bitcookies/winrar-keygen?color=F48D73" /></a>
+  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298?logo=data:image/svg+xml;base64,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" />
+  <a href="https://github.com/bitcookies/winrar-keygen/actions"><img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/keygen.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" /></a>
 </p>
-
-
 <p align="center">
   <a href="README.zh-CN.md">简体中文</a> | <a href="README.md">English</a>
 </p>
 
+
 ## 1. What is WinRAR?
 
 WinRAR is a trialware file archiver utility for Windows, developed by Eugene Roshal of win.rar GmbH. 
@@ -33,37 +29,205 @@ This repository will tell you how WinRAR license file `"rarreg.key"` is generate
 
 See [here](README.HOW_DOES_IT_WORK.md).
 
-## 3. How to build?
+## 3. How to use?
 
-If you don't want to compile it yourself, you can also go to the [release page](https://github.com/bitcookies/winrar-keygen/releases/) to get `winrar-keygen.exe`.
+There are several ways to use it.
 
-### 3.1 Prerequisites
+- [Use Github Actions](#4-Use-Github-Actions) 
+- [Use Github Actions with secrets](#5-Use-Github-Actions-with-secrets)
+- [Build in Visual Studio](#6-Build-in-Visual-Studio)
 
-1. Please make sure that you have **Visual Studio 2022**. Because this is a VS2022 project. If you are still using Visual Studio 2019, you can find projects for VS2019 in the [vs2019](https://github.com/bitcookies/winrar-keygen/tree/vs2019) branch.
+### 3.1 Encoding
 
-2. Please make sure you have installed `vcpkg` and the following libraries: 
+WinRAR Keygen supports `ASCII`, `ANSI` and `UTF8NoBOM` encoding types, the corresponding supported characters are listed in the table below.
 
-   * `mpir:x86-windows-static`
-   * `mpir:x64-windows-static`
+> [!NOTE]
+> The default is `utf8`, but you can specify the encoding as `ascii` or `ansi`.
+
+| Encoding                                     | Supported Characters                                         | Character Examples                                           |
+| -------------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------ |
+| [ascii](https://en.wikipedia.org/wiki/ASCII) | Only full ASCII characters are supported.                    | <img width="300px" src="assets/ascii-characters-light.svg#gh-light-mode-only"><img width="300px" src="assets/ascii-characters-dark.svg#gh-dark-mode-only"> |
+| ansi                                         | There is no one fixed ANSI code, usually [Windows-1252](https://en.wikipedia.org/wiki/Windows-1252), but other local codes are also possible. | <img width="300px" src="assets/windows-1252-characters-light.svg#gh-light-mode-only"><img width="300px" src="assets/windows-1252-characters-dark.svg#gh-dark-mode-only"> |
+| [utf8](https://en.wikipedia.org/wiki/UTF-8)  | Supports UTF-8 without BOM.                                  | ASCII characters, English, 简体中文, 繁體中文, Deutsch, Français, Русский, Italiano, 日本語, 한국어, Lengua española, Ελληνική γλώσσα, et al. |
+
+### 3.2 License type
+
+There are two types of WinRAR licenses, `rarreg.key` and `rarkey.rar`, which differ only in their import.
+
+|                   rarreg.key                   |                    rarkey.rar                    |
+| :--------------------------------------------: | :----------------------------------------------: |
+| <img width="100px" src="assets/file-icon.svg"> | <img width="100px" src="assets/winrar-icon.svg"> |
+|     Drag to import or place in a location      |       Double-click to run automatic import       |
+
+If you are unable to drag, you can try to put the `rarreg.key` in the following directory.
+
+```shell
+C:\Users\<yourname>\AppData\Roaming\WinRAR\rarreg.key
+```
+
+You can also compress `rarreg.key` into `rarkey.rar` and double-click it to run it, and the license import will take place automatically.
+
+## 4. Use Github Actions
+
+<details>
+<summary>Click to expand</summary>
+
+The new workflow can easily help you generate a license, you just need to follow these steps.
+
+> Your `Username` and `License Name` will appear in the actions log, if you don't want to give out this information, see [5. Using Github Actions with secrets](#5-Use-Github-Actions-with-secrets).
+
+### 4.1 Fork
+
+**Fork** this repo.
+
+![Fork](assets/fork-light.png#gh-light-mode-only)
+
+![Fork](assets/fork-dark.png#gh-dark-mode-only)
+
+### 4.2 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)
+
+### 4.3 Run workflow
+
+After allowing the workflow, go to **Actions > WinRAR Keygen > Run workflow** and fill in the information to start generating.
+
+> For the difference of license encoding, please refer to [3.1 Encoding](#31-Encoding).
+
+![Secrets](assets/run-ketgen-light.png#gh-light-mode-only)
+
+![Secrets](assets/run-ketgen-dark.png#gh-dark-mode-only)
+
+After running successfully, open the corresponding task and select **rarreg_file** to download.
+
+> File retention 90 days.
+
+![Download](assets/file-download-light.png#gh-light-mode-only)
+
+![Download](assets/file-download-dark.png#gh-dark-mode-only)
+
+Extract rarreg_file.zip to get `rarreg.key` and drag to import into WinRAR. You can also compress `rarreg.key` into `rarkey.rar`, then double-click it to run it, and the license import will be done automatically.
+
+If you get an invalid key, please check [the specific solution](#7-invalid-key).
+
+</details>
+
+## 5. Use Github Actions with secrets
+
+<details>
+<summary>Click to expand</summary>
+
+Using [secrets](https://docs.github.com/en/actions/security-guides/encrypted-secrets) can help you hide license information.
+
+### 5.1 Fork
+
+**Fork** this repo.
+
+![Fork](assets/fork-light.png#gh-light-mode-only)
+
+![Fork](assets/fork-dark.png#gh-dark-mode-only)
+
+### 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 Create secrets
+
+After allowing the workflow, go to **Settings > Secrets and variables > Actions > New repository secret** to create a secret.
+
+![Secrets](assets/secrets-light.png#gh-light-mode-only)
+
+![Secrets](assets/secrets-dark.png#gh-dark-mode-only)
+
+Create three secrets with the names `TEXT1`, `TEXT2` and `PWD` and fill in the relevant values.
+
+> The value filled in should be consistent with the type of code you have chosen.
+
+| Secrets Name<img width="120px"> | Explanation<img width="120px"> |
+| ------------------------------- | ------------------------------ |
+| TEXT1                           | Your Name                      |
+| TEXT2                           | Your License Name              |
+| PWD                             | 7-Zip Password                 |
+
+![Add Secrets](assets/secrets-add-light.png#gh-light-mode-only)
+
+![Add Secrets](assets/secrets-add-dark.png#gh-dark-mode-only)
+
+Once created, you will see it.
+
+![Secrets Repo](assets/secrets-repo-light.png#gh-light-mode-only)
+
+![Secrets Repo](assets/secrets-repo-dark.png#gh-dark-mode-only)
+
+### 5.4 Run workflow
+
+Go to **Actions** and select **WinRAR Keygen with secrets** to run workflow manually.
+
+For the difference of license encoding, please refer to [3.1 Encoding](#31-Encoding).
+
+![Run](assets/run-workflow-light.png#gh-light-mode-only)
+
+![Run](assets/run-workflow-dark.png#gh-dark-mode-only)
+
+After running successfully, open the corresponding task and select **rarreg_file** to download.
+
+> File retained for **1 day** only.
+
+![Download](assets/file-download-light.png#gh-light-mode-only)
+
+![Download](assets/file-download-dark.png#gh-dark-mode-only)
+
+Extract `rarreg_file.zip` to get `rarreg.7z`, unzip it with the password to get `rarreg.key`, then drag and drop to import into WinRAR. You can also compress `rarreg.key` into `rarkey.rar`, then double-click it to run it, and the license import will be done automatically.
+
+If you get an invalid key, please check [the specific solution](#7-invalid-key).
+
+</details>
+
+## 6. Build in Visual Studio
+
+<details>
+<summary>Click to expand</summary>
+
+I recommend using the Github Actions, but you can still do your own compilation.
+
+If you don't want to compile it yourself, you can also go to the [release](https://github.com/bitcookies/winrar-keygen/releases/) page to get `winrar-keygen.exe`.
+
+### 6.1 Prerequisites
+
+1. Please make sure that you have **Visual Studio 2022**. Because this is a VS2022 project. If you are still using Visual Studio 2019, you can find projects for VS2019 in the [vs2019](https://github.com/bitcookies/winrar-keygen/tree/vs2019) branch, but this branch will no longer be maintained.
+
+2. Please make sure you have installed `vcpkg` and the following libraries:
+
+   + `mpir:x86-windows-static`
+   + `mpir:x64-windows-static`
+   + `mpir:gmp:x64-windows`
 
    is installed.
 
    You can install them by:
 
-   ```console
+   ```shell
    $ vcpkg install mpir:x86-windows-static
    $ vcpkg install mpir:x64-windows-static
+   $ vcpkg install gmp:x64-windows
    ```
 
-3. Your `vcpkg` has been integrated into your __Visual Studio__, which means you have run 
+3. Your `vcpkg` has been integrated into your __Visual Studio__, which means you have run successfully.
 
-   ```console
+   ```shell
    $ vcpkg integrate install
    ```
    
-   successfully.
 
-### 3.2 Build
+### 6.2 Build
 
 1. Open this project in __Visual Studio__.
 
@@ -73,81 +237,117 @@ If you don't want to compile it yourself, you can also go to the [release page](
 
 You will see executable files in `bin/` directory. 
 
-## 4. How to Use?
+### 6.3 How to use?
 
 Execute the following code in the terminal and configure two parameters to generate `rarreg.key`.
 
-Here is an example use `Github` and `Github.com`:
+Here is an example of ASCII encoding for `Github` and `Single PC usage license`:
 
-```
+```shell
 Usage:
-        winrar-keygen.exe <your name> <license type>
+        winrar-keygen.exe <Username> <License Name>
 
 Example:
 
-        winrar-keygen.exe "Github" "Github.com"
-  or:
-        winrar-keygen.exe "Github" "Github.com" > rarreg.key
+        winrar-keygen.exe "Github" "Single PC usage license"
 ```
 
-![Terminal](terminal.png)
+![Terminal](assets/terminal.png)
 
-Now you can see the newly generated file. 
+Now you can see the newly generated file.
 
 ```console
 RAR registration data
 Github
-Github.com
+Single PC usage license
 UID=3a3d02329a32b63da7d8
 6412212250a7d8753c5e7037d83011171578c57042fa30c506caae
-9954e4853d415ec594e46076cc9a65338309b66c50453ba72158c0
-656de97acb2f2a48cf3b75329283544c3e1b366a5062b85d0022f6
-de3cdc56b311475b484e80b48157a0c3af60ca4f7f9c75d49bc50d
-6bad616c1c58caa922d3ed0cd19771e8191522a586544c3e1b366a
-5062b85d29db066f02e777ad78100865f2c31f2dd3a86998609b18
-5eede7ed46566b10bf033daa6384062b259194b1acbd1443042646
+9954e4853d415ec594e46017cb3db740bc4b32e47aea25db62f350
+9f22065a27da4f8216d2938e1050b6e3347501a3767d1fdd7ee130
+dd4ab952600ba16a99236d910bfa995d5f60651ec451f462511507
+95b3722d059f2d5303a231e396cf21f17098edeec0b6e3347501a3
+767d1fdd7ee45388769767642338ee8a63178f3458b71de5609b18
+5eede7ed46566b10bf033daa6384062b259194b1acbd0378116064
 ```
 
-Save the generated information as `rarreg.key`.
+Save the generated information in **ASCII encoding** as `rarreg.key`.
 
-## 5. Invalid Key
+### 6.4 More character support
+
+In addition to using ASCII encoding, you can use ANSI and UTF8NoBOM to support more characters, but you will need to install [PowerShell 7.4 or later](https://learn.microsoft.com/en-us/powershell/scripting/install/installing-powershell-on-windows?view=powershell-7.4).
+
+| `-Encoding` | PowerShell 5.x | PowerShell 7.4+ |
+| :------------: | :------------: | :-------------: |
+|     ASCII      |       ✅        |        ✅        |
+|      ANSI      |                |        ✅        |
+|   UTF8NoBOM    |                |        ✅        |
+
+In PowerShell 5.x, you cannot output licenses in ANSI or UTF8NoBOM format. You must generate the content via commands, manually copy it, and save it as ANSI or UTF8NoBOM.
+
+In PowerShell 7.4+, you can generate licenses encoded in ANSI or UTF8NoBOM:
+
+> `utf8:` is to ensure constant character representation in WinRAR across languages.
+
+```shell
+./winrar-keygen.exe "utf8:简体中文" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:Français" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:日本語" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:한국어" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+```
+
+</details>
+
+## 7. Invalid key
 
 Why is my `rarreg.key` invalid?
 
-### 5.1 Contains non-English characters
+### 7.1 Character encoding
 
-If `text1` and `text2` contain **non-English characters**, although a key can be generated, the key is invalid.
+`TEXT1` and `TEXT2` are required to fulfill [corresponding coding requirements](#31-Encoding).
 
 ```console
-winrar-keygen.exe <text1> <text2>
+./winrar-keygen.exe <TEXT1> <TEXT2>
 ```
 
-### 5.2 Terminal Encode
+You can refer to: [Generation of "rarreg.key"](https://github.com/bitcookies/winrar-keygen/blob/master/README.HOW_DOES_IT_WORK.md#7-generation-of-rarregkey)
 
-There may be a terminal encoding problem, you can use `chcp` to switch temporarily.
+### 7.2 Text encoding
 
-You can refer to the Microsoft documentation: [chcp | Microsoft Docs](https://docs.microsoft.com/en-us/windows-server/administration/windows-commands/chcp)
+If you use the following command:
 
-## 6. Encounter problems?
+```shell
+./winrar-keygen.exe "Github" "Single PC usage license" > rarreg.key
+```
 
-### 6.1 Feedback
+In the newer Windows 10 / 11, PowerShell will export in **UTF16-LE** format by default, which will cause the error.
+
+Please use the following command:
+
+```shell
+./winrar-keygen.exe "Github" "license" | Out-File -Encoding ascii rarreg.key
+
+./winrar-keygen.exe "Github" "license" | Out-File -Encoding ansi rarreg.key
+
+./winrar-keygen.exe "utf8:Github" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+```
+
+## 8. Contributing
+
+### 8.1 Suggestion
 
 If you encounter some problems, you can report on the [Issues](https://github.com/bitcookies/winrar-keygen/issues) page. There will be many enthusiastic developers or Github users to help you.
 
-### 6.2 Security
+This project welcomes contributions and suggestions. You can make suggestions in [Issues](https://github.com/bitcookies/winrar-keygen/issues), or submit a pull request 😄
 
-[Issues #1](https://github.com/bitcookies/winrar-keygen/issues/1) Some Anti-Virus Software may falsely report. If you do not trust this binary executable file, your only option is to compile the code yourself.
-
-### 6.3 Download
-
-[Issues #4](https://github.com/bitcookies/winrar-keygen/issues/4) IDM and other download tools may have problems, please use a browser (e.g. chrome, edge) to download.
-
-### 6.4 Thanks
+### 8.2 Thanks
 
 Thank you very much to some enthusiastic developers for helping answer some questions in [Issues](https://github.com/bitcookies/winrar-keygen/issues).
 
-Thanks [@Sonic-The-Hedgehog-LNK1123](https://github.com/Sonic-The-Hedgehog-LNK1123) and [@nitu2003](https://github.com/nitu2003).
+🏆 Special Thanks [@Sonic-The-Hedgehog-LNK1123](https://github.com/Sonic-The-Hedgehog-LNK1123)
 
-## 7. License
+## 9. License
 
-The code is available under the [MIT license](https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE)
+The code is available under the [MIT license](https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE)

README.zh-CN.md

@@ -1,152 +1,395 @@
 <p align="center">
- <img width="100px" src="icon.svg" align="center" alt="WinRAR Keygen" />
+ <img width="100px" src="icon.png" align="center" alt="WinRAR Keygen" />
  <h2 align="center">WinRAR Keygen</h2>
  <p align="center">Principle of WinRAR key generation</p>
 </p>
 <p align="center">
-  <img src="https://img.shields.io/github/v/release/bitcookies/winrar-keygen?label=version" />
-  <a href="https://github.com/bitcookies/winrar-keygen/issues">
-  	<img alt="Issues" src="https://img.shields.io/github/issues/bitcookies/winrar-keygen?color=F48D73" />
-  </a>
-  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298" />
-  <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" />
-  </a>
+  <a href="https://github.com/bitcookies/winrar-keygen/releases"><img src="https://img.shields.io/github/v/release/bitcookies/winrar-keygen?label=version" /></a>
+  <a href="https://github.com/bitcookies/winrar-keygen/issues"><img alt="Issues" src="https://img.shields.io/github/issues/bitcookies/winrar-keygen?color=F48D73" /></a>
+  <img src="https://img.shields.io/badge/Visual%20Studio-2022-5D4298?logo=data:image/svg+xml;base64,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" />
+  <a href="https://github.com/bitcookies/winrar-keygen/actions"><img src="https://github.com/bitcookies/winrar-keygen/actions/workflows/keygen.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" /></a>
 </p>
-
-
 <p align="center">
   <a href="README.zh-CN.md">简体中文</a> | <a href="README.md">English</a>
 </p>
 
+
 ## 1. WinRAR是什么？
 
-WinRAR是一款用于管理压缩包文件的共享软件。其算法由作者尤金·罗谢尔研发，享有原创专利。
+WinRAR 是一款用于管理压缩包文件的共享软件。其算法由作者尤金·罗谢尔研发，享有原创专利。
 
-它可以用来创建或浏览RAR、ZIP等众多格式的压缩包。
+它可以用来创建或浏览 RAR、ZIP 等众多格式的压缩包。
 
-WinRAR不是免费软件。如果你想使用它，你应当向 [__RARLAB__](https://www.rarlab.com/) 付费，然后获得一个授权文件 `rarreg.key`。
+WinRAR 不是免费软件。如果你想使用它，你应当向 [__RARLAB__](https://www.rarlab.com/) 付费，然后获得一个授权文件 `rarreg.key`。
 
-这份repo将会告诉你 `rarreg.key` 是如何生成的。
+这份 repo 将会告诉你 `rarreg.key` 是如何生成的。
 
 ## 2. "rarreg.key"是如何生成的？
 
 见 [这里](README.HOW_DOES_IT_WORK.zh-CN.md)。
 
-## 3. 如何编译？
+## 3. 使用方法
 
-如果你不想自己编译，也可以到 [Release](https://github.com/bitcookies/winrar-keygen/releases/) 页面获取对应版本的 `winrar-keygen.exe`。
+有多种方法可供选择：
 
-### 3.1 前提条件
++ [使用 Github Actions](#4-使用-Github-Actions)
++ [使用 Github Actions with secrets](#5-使用-Github-Actions-with-secrets)
++ [通过 Visual Studio 编译使用](#6-通过-Visual-Studio-编译使用)
 
-1. 请确保你有 **Visual Studio 2022**，因为这是一个 VS2022 项目。如果你仍在使用 Visual Studio 2019，可以在 [vs2019](https://github.com/bitcookies/winrar-keygen/tree/vs2019) 分支中找到适合 VS2019 的项目。
+### 3.1 编码说明
+
+WinRAR Keygen 支持 `ASCII`、`ANSI` 和 `UTF8NoBOM` 三种编码类型，对应支持的字符如下表：
+
+> [!NOTE]
+> 默认使用 `utf8`，但是你也可以指定编码为 `ascii` 或 `ansi`。
+
+| 编码                                         | 支持的字符                                                   | 字符示例                                                     |
+| -------------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------ |
+| [ascii](https://en.wikipedia.org/wiki/ASCII) | 仅支持 ASCII 编码字符                                        | <img width="300px" src="assets/ascii-characters-light.svg#gh-light-mode-only"><img width="300px" src="assets/ascii-characters-dark.svg#gh-dark-mode-only"> |
+| ansi                                         | 没有一种固定的 ANSI 编码，通常是 [Windows-1252](http://en.wikipedia.org/wiki/Windows-1252)，但也可以是其他本地 | <img width="300px" src="assets/windows-1252-characters-light.svg#gh-light-mode-only"><img width="300px" src="assets/windows-1252-characters-dark.svg#gh-dark-mode-only"> |
+| [utf8](https://en.wikipedia.org/wiki/UTF-8)  | 支持无 BOM 的 UTF-8                                          | ASCII characters, English, 简体中文, 繁體中文, Deutsch, Français, Русский, Italiano, 日本語, 한국어, Lengua española, Ελληνική γλώσσα 等。 |
+
+### 3.2 License 类型
+
+WinRAR license 有 `rarreg.key` 和 `rarkey.rar` 两种类型，它们仅在导入上有区别：
+
+| <img width="60px">rarreg.key<img width="60px"> |  <img width="60px">rarkey.rar<img width="60px">  |
+| :--------------------------------------------: | :----------------------------------------------: |
+| <img width="100px" src="assets/file-icon.svg"> | <img width="100px" src="assets/winrar-icon.svg"> |
+|             拖动导入或放于指定位置             |                 双击运行自动导入                 |
+
+如果你无法执行拖动操作，你可以尝试把 `rarreg.key` 放置于以下目录中：
+
+```shell
+C:\Users\<yourname>\AppData\Roaming\WinRAR\rarreg.key
+```
+
+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。
+
+## 4. 使用 Github Actions
+
+<details>
+<summary>点击展开</summary>
+
+新的 workflow 能很方便的帮助你生成 license，你只需跟随以下步骤即可：
+
+> 你的 `Username` 和 `License Name` 会出现在 actions 的日志中，如果你不想泄露这些信息，请参考 [5. 使用 Github Actions with secrets](#5-使用-Github-Actions-with-secrets)。
+
+### 4.1 Fork
+
+点击该项目右上角的 **Fork** 按钮，fork 一份代码到你的 Github：
+
+![Fork](assets/fork-light.png#gh-light-mode-only)
+
+![Fork](assets/fork-dark.png#gh-dark-mode-only)
+
+### 4.2 允许 fork 仓库运行 workflows
+
+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 运行 workflow
+
+允许 workflow 后，选择 **WinRAR Keygen > Run workflow** 并填入信息就可以开始生成了：
+
+> License 编码的区别请参考 [3.1 编码说明](#31-编码说明)。
+
+![Secrets](assets/run-ketgen-light.png#gh-light-mode-only)
+
+![Secrets](assets/run-ketgen-dark.png#gh-dark-mode-only)
+
+运行成功之后，打开对应的任务，选择 **rarreg_file** 下载：
+
+> 文件保留 90 天，超出时间后会自动销毁。
+
+![Download](assets/file-download-light.png#gh-light-mode-only)
+
+![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. 使用 Github Actions with secrets
+
+<details>
+<summary>点击展开</summary>
+
+使用 [secrets](https://docs.github.com/en/actions/security-guides/encrypted-secrets) 可以帮助你隐藏 license 信息。
+
+### 5.1 Fork
+
+点击该项目右上角的 **Fork** 按钮，fork 一份代码到你的 Github：
+
+![Fork](assets/fork-light.png#gh-light-mode-only)
+
+![Fork](assets/fork-dark.png#gh-dark-mode-only)
+
+### 5.2 允许 fork 仓库运行 workflows
+
+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 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)
+
+![Secrets](assets/secrets-dark.png#gh-dark-mode-only)
+
+创建三个 secrets，名称为 `TEXT1` 、 `TEXT2` 和 `PWD`，并填入相关值：
+
+> 填入的值应与你选择的编码类型保持一致。
+
+| Secrets Name<img width="120px"> | Explanation<img width="120px"> |
+| ------------------------------- | ------------------------------ |
+| TEXT1                           | 用户名                         |
+| TEXT2                           | 许可名                         |
+| PWD                             | 压缩包密码                     |
+
+![Add Secrets](assets/secrets-add-light.png#gh-light-mode-only)
+
+![Add Secrets](assets/secrets-add-dark.png#gh-dark-mode-only)
+
+创建完成后，你将会看到：
+
+![Secrets Repo](assets/secrets-repo-light.png#gh-light-mode-only)
+
+![Secrets Repo](assets/secrets-repo-dark.png#gh-dark-mode-only)
+
+### 5.4 运行 workflow
+
+进入 **Actions** 选择 **WinRAR Keygen with secrets  >  Run workflow** 并填入信息：
+
+> License 编码的区别请参考 [3.1 编码说明](#31-编码说明)。
+
+![Run](assets/run-workflow-light.png#gh-light-mode-only)
+
+![Run](assets/run-workflow-dark.png#gh-dark-mode-only)
+
+运行成功之后，打开对应的任务，选择 **rarreg_file** 下载：
+
+> 文件仅保留 **1 天**，请及时下载。
+
+![Download](assets/file-download-light.png#gh-light-mode-only)
+
+![Download](assets/file-download-dark.png#gh-dark-mode-only)
+
+将 `rarreg_file.zip` 解压缩后会得到 `rarreg.7z`，使用你设置的密码进行解压缩获得 `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>
+
+## 6. 通过 Visual Studio 编译使用
+
+<details>
+<summary>点击展开</summary>
+
+我建议通过 Github Actions 的方法来使用，但是你仍然可以选择自行编译。
+
+如果你不想自行编译，也可以到 [Release](https://github.com/bitcookies/winrar-keygen/releases/) 页面获取对应版本的 `winrar-keygen.exe`。
+
+### 6.1 前提条件
+
+1. 请确保你有 **Visual Studio 2022**，因为这是一个 VS2022 项目。如果你仍在使用 Visual Studio 2019，可以在 [vs2019](https://github.com/bitcookies/winrar-keygen/tree/vs2019) 分支中找到适合 VS2019 的项目，但是此分支将不再维护。
 
 2. 请确保你安装了 `vcpkg` 以及下面几个库：
 
-   - `mpir:x86-windows-static`
-
-   * `mpir:x64-windows-static`
+   + `mpir:x86-windows-static`
+   + `mpir:x64-windows-static`
+   + `mpir:gmp:x64-windows`
 
    你可以通过下的命令来安装：
 
-   ```console
+   ```shell
    $ vcpkg install mpir:x86-windows-static
    $ vcpkg install mpir:x64-windows-static
+   $ vcpkg install gmp:x64-windows
    ```
 
 3. 你的 `vcpkg` 与 __Visual Studio__ 整合了，即你曾成功运行了下面这条命令：
 
-   ```console
+   ```shell
    $ vcpkg integrate install
    ```
 
-### 3.2 编译
+### 6.2 编译
 
-1. 在 __Visual Studio__ 中打开这个项目。
-2. 选择 `Release` 配置。
+1. 在 __Visual Studio__ 中打开这个项目；
+2. 选择 `Release` 配置；
 3. 选择 __生成 > 生成解决方案__。
 
 你将在 `bin/` 目录下看到生成的文件。
 
-## 4. 如何使用？
+### 6.3 如何使用？
 
 直接在终端执行以下代码，配置两个参数即可生成 `rarreg.key`。
 
-这里以 `Github` 和 `Github.com` 为例：
+这里以 `Github` 和 `Single PC usage license` 参数和 ASCII 编码为例：
 
-```console
+```shell
 Usage:
-        winrar-keygen.exe <your name> <license type>
+        winrar-keygen.exe <Username> <License Name>
 
 Example:
 
-        winrar-keygen.exe "Github" "Github.com"
-  or:
-        winrar-keygen.exe "Github" "Github.com" > rarreg.key
+        winrar-keygen.exe "Github" "Single PC usage license"
 ```
 
-![Terminal](terminal.png)
+![Terminal](assets/terminal.png)
 
 现在你可以看到新生成的文件：
 
 ```console
 RAR registration data
 Github
-Github.com
+Single PC usage license
 UID=3a3d02329a32b63da7d8
 6412212250a7d8753c5e7037d83011171578c57042fa30c506caae
-9954e4853d415ec594e46076cc9a65338309b66c50453ba72158c0
-656de97acb2f2a48cf3b75329283544c3e1b366a5062b85d0022f6
-de3cdc56b311475b484e80b48157a0c3af60ca4f7f9c75d49bc50d
-6bad616c1c58caa922d3ed0cd19771e8191522a586544c3e1b366a
-5062b85d29db066f02e777ad78100865f2c31f2dd3a86998609b18
-5eede7ed46566b10bf033daa6384062b259194b1acbd1443042646
+9954e4853d415ec594e46017cb3db740bc4b32e47aea25db62f350
+9f22065a27da4f8216d2938e1050b6e3347501a3767d1fdd7ee130
+dd4ab952600ba16a99236d910bfa995d5f60651ec451f462511507
+95b3722d059f2d5303a231e396cf21f17098edeec0b6e3347501a3
+767d1fdd7ee45388769767642338ee8a63178f3458b71de5609b18
+5eede7ed46566b10bf033daa6384062b259194b1acbd0378116064
 ```
 
-将生成的信息以文本格式保存为 `rarreg.key ` ，拖动导入 WinRAR 即可。
+将生成的信息以 **ASCII 编码** 的文本格式保存为 `rarreg.key`。
 
-## 5. 无效的Key
+### 6.4 支持更多字符
+
+除了使用 ASCII 编码，你还可以使用 ANSI 和 UTF8NoBOM 以支持更多字符，但你需要[安装 PowerShell 7.4 及其后续版本](https://learn.microsoft.com/en-us/powershell/scripting/install/installing-powershell-on-windows?view=powershell-7.4)。
+
+| `-Encoding` 值 | PowerShell 5.x | PowerShell 7.4+ |
+| :------------: | :------------: | :-------------: |
+|     ASCII      |       ✅        |        ✅        |
+|      ANSI      |                |        ✅        |
+|   UTF8NoBOM    |                |        ✅        |
+
+在 PowerShell 5.x 中，你不能输出 ANSI 或 UTF8NoBOM 格式的 license，你只能通过命令生成并手动复制内容并保存为 ANSI 或 UTF8NoBOM 格式。
+
+在 PowerShell 7.4+ 中，你可以用 ANSI 或 UTF8NoBOM 编码生成 license：
+
+> `utf8:` 是为了保证在不同语言的 WinRAR 中做到不变的字符表示。
+
+```shell
+./winrar-keygen.exe "utf8:简体中文" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:Français" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:日本語" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+
+./winrar-keygen.exe "utf8:한국어" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+```
+
+</details>
+
+## 7. 无效的 Key
 
 为什么我生成的 `rarreg.key` 是无效的？
 
-### 5.1 包含非英文字符
+### 7.1 字符编码不正确
 
-如果 `text1` 和 `text2` 参数包含**非英文字符**，即使 WinRAR Keygen 能够生成 `rarreg.key`，但是是无效的。
+参数 `TEXT1` 和 `TEXT2` 需要满足[对应的编码要求](#31-编码说明)：
 
 ```console
-winrar-keygen.exe <text1> <text2>
+./winrar-keygen.exe <TEXT1> <TEXT2>
 ```
 
-### 5.2 终端编码的问题
+具体可参考原理文档：[授权文件"rarreg.key"的生成](https://github.com/bitcookies/winrar-keygen/blob/master/README.HOW_DOES_IT_WORK.zh-CN.md#7-%E6%8E%88%E6%9D%83%E6%96%87%E4%BB%B6rarregkey%E7%9A%84%E7%94%9F%E6%88%90)
 
-[Issues #5](https://github.com/bitcookies/winrar-keygen/issues/5) 有可能是终端编码的问题，你可以使用 `chcp` 命令暂时切换。
+### 7.2 文本储存编码不正确
 
-具体可参考 Microsoft 文档：[chcp | Microsoft Docs](https://docs.microsoft.com/en-us/windows-server/administration/windows-commands/chcp)
+如果你使用了如下命令：
 
-## 6. 遇到问题
+```shell
+./winrar-keygen.exe "Github" "Single PC usage license" > rarreg.key
+```
 
-### 6.1 反馈
+在较新的 Windows 10 / 11 系统中，PowerShell 将默认以 **UTF16-LE** 格式导出，这将会导致错误。
+
+请指定输出编码格式，例如：
+
+```shell
+./winrar-keygen.exe "Github" "license" | Out-File -Encoding ascii rarreg.key
+
+./winrar-keygen.exe "Github" "license" | Out-File -Encoding ansi rarreg.key
+
+./winrar-keygen.exe "utf8:Github" "license" | Out-File -Encoding UTF8NoBOM rarreg.key
+```
+
+### 7.3 关于简体中文版
+
+在 [__RARLAB__](https://www.rarlab.com/) 下载的简体中文版 WinRAR 将会自带广告组件，即使使用了 `rarreg.key` 授权，广告组件依旧会出现。这是由于简体中文代理商的一些意见，RARLAB 已将简体中文安装包的公开链接更换成了带有广告的简体中文安装包。
+
+感谢 [@hoochanlon](https://github.com/hoochanlon) 提供的一些方法。可以使用 [win-rar-extractor](https://github.com/lvtx/WinRAR-Extractor) 获取简体中文商业版的下载连接；也可以根据商业版的地址规律，获取相应版本的简体中文安装包：
+
+简体中文 **「商业版」** 下载地址：
+
+```
+# 7.13
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20250804/rrlb/winrar-x64-713sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20250804/wrr/winrar-x64-713sc.exe
+
+# 7.12
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20250627/rrlb/winrar-x64-712sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20250627/wrr/winrar-x64-712sc.exe
+
+# 7.11 （注意该版本的日期格式变更为了 YYYYDDMM）
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20253103/rrlb/winrar-x64-711sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20253103/wrr/winrar-x64-711sc.exe
+
+# 7.10 （注意该版本的日期格式变更为了 YYYYDDMM）
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20251003/rrlb/winrar-x64-710sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20251003/wrr/winrar-x64-710sc.exe
+
+# 6.24
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20231013/wrr/winrar-x32-624sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/sc/sc20231013/wrr/winrar-x64-624sc.exe
+
+```
+
+简体中文 **「广告版」** （以 `6.24` 版本为例），不要下载此类版本：
+
+```
+# 其链接特点是「不包含」日期信息
+
+win-rar 渠道：
+https://www.win-rar.com/fileadmin/winrar-versions/winrar/winrar-x32-624sc.exe
+https://www.win-rar.com/fileadmin/winrar-versions/winrar/winrar-x64-624sc.exe
+
+rarlab 渠道：
+https://www.rarlab.com/rar/winrar-x32-624sc.exe
+https://www.rarlab.com/rar/winrar-x64-624sc.exe
+```
+
+请注意区分上述连接地址，更多方法可以查看 [Issues #14](https://github.com/bitcookies/winrar-keygen/issues/14) 和 [Issues #19](https://github.com/bitcookies/winrar-keygen/issues/19)。
+
+## 8. 贡献
+
+### 8.1 反馈和建议
 
 如果您遇到了一些问题，可在 [Issues](https://github.com/bitcookies/winrar-keygen/issues) 页面反馈，会有很多热心的开发者及 Github 用户帮助你。
 
-### 6.2 安全
+该项目欢迎贡献和建议，您可以在 [Issues](https://github.com/bitcookies/winrar-keygen/issues) 提出建议，或者进行提交拉取请求 😄
 
-[Issues #1](https://github.com/bitcookies/winrar-keygen/issues/1) 一些杀毒软件可能会误报，如果您不信任此二进制可执行文件，您唯一的选择就是自己编译代码。
-
-### 6.3 下载
-
-[Issues #4](https://github.com/bitcookies/winrar-keygen/issues/4) IDM等下载工具可能会有问题，请使用浏览器（例如 chrome、edge）下载。
-
-### 6.4 感谢
+### 8.2 感谢
 
 非常感谢一些热心的开发者，在 [Issues](https://github.com/bitcookies/winrar-keygen/issues) 帮助解答一些问题。
 
-感谢 [@Sonic-The-Hedgehog-LNK1123](https://github.com/Sonic-The-Hedgehog-LNK1123) 和 [@nitu2003](https://github.com/nitu2003).
+🏆 特别感谢 [@Sonic-The-Hedgehog-LNK1123](https://github.com/Sonic-The-Hedgehog-LNK1123)
 
-## 7. 关于WinRAR广告
+## 9. 许可
 
-在 [__RARLAB__](https://www.rarlab.com/) 下载的简体中文版 WinRAR 将会自带广告组件，即使使用了 `rarreg.key` 授权，广告组件依旧会出现。如果您介意广告，可以尝试下载其他语言版。
-
-## 8. 许可
-
-使用 [MIT License](https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE)
+使用 [MIT License](https://github.com/bitcookies/winrar-keygen/blob/master/LICENSE)

WinRarConfig.hpp

@@ -483,4 +483,3 @@ public:
         }
     );
 };
-

WinRarKeygen.hpp

@@ -193,19 +193,32 @@ public:
             auto LicenseTypeSignature = Sign(RegInfo.LicenseType.c_str(), RegInfo.LicenseType.length());
             auto LicenseTypeSignatureR = LicenseTypeSignature.r.ToString(16, true);
             auto LicenseTypeSignatureS = LicenseTypeSignature.s.ToString(16, true);
-            if (LicenseTypeSignatureR.length() <= 60 && LicenseTypeSignatureS.length() <= 60) {
-                RegInfo.Items[1] = HelperStringFormat("60%060s%060s", LicenseTypeSignatureS.c_str(), LicenseTypeSignatureR.c_str());
+            if (LicenseTypeSignatureR.length() < 60) {
+                LicenseTypeSignatureR.insert(LicenseTypeSignatureR.begin(), 60 - LicenseTypeSignatureR.size(), '0');
+            }
+            if (LicenseTypeSignatureS.length() < 60) {
+                LicenseTypeSignatureS.insert(LicenseTypeSignatureS.begin(), 60 - LicenseTypeSignatureS.size(), '0');
+            }
+            if (LicenseTypeSignatureR.length() == 60 && LicenseTypeSignatureS.length() == 60) {
+                RegInfo.Items[1] = HelperStringFormat("60%s%s", LicenseTypeSignatureS.c_str(), LicenseTypeSignatureR.c_str());
                 break;
             }
         }
 
         temp = RegInfo.UserName + RegInfo.Items[0];
+
         while (true) {
             auto UserNameSignature = Sign(temp.c_str(), temp.length());
             auto UserNameSignatureR = UserNameSignature.r.ToString(16, true);
             auto UserNameSignatureS = UserNameSignature.s.ToString(16, true);
-            if (UserNameSignatureR.length() <= 60 || UserNameSignatureS.length() <= 60) {
-                RegInfo.Items[2] = HelperStringFormat("60%060s%060s", UserNameSignatureS.c_str(), UserNameSignatureR.c_str());
+            if (UserNameSignatureR.length() < 60) {
+                UserNameSignatureR.insert(UserNameSignatureR.begin(), 60 - UserNameSignatureR.size(), '0');
+            }
+            if (UserNameSignatureS.length() < 60) {
+                UserNameSignatureS.insert(UserNameSignatureS.begin(), 60 - UserNameSignatureS.size(), '0');
+            }
+            if (UserNameSignatureR.length() == 60 && UserNameSignatureS.length() == 60) {
+                RegInfo.Items[2] = HelperStringFormat("60%s%s", UserNameSignatureS.c_str(), UserNameSignatureR.c_str());
                 break;
             }
         }
@@ -224,6 +237,9 @@ public:
             RegInfo.Items[3].c_str(),
             RegInfo.Checksum
         );
+
+        // The length has been limited to 60 (issues #6)
+        // This problem has been fixed, this prompt should no longer appear
         if (RegInfo.HexData.length() % 54 != 0) {
             throw std::runtime_error("InternalError: The length of register data is not correct.");
         }

_tmain.cpp

@@ -1,74 +1,149 @@
-#include <tchar.h>
-#include <stdio.h>
 #include <windows.h>
+#include <fcntl.h>
+#include <io.h>
 #include <locale.h>
+#include <iostream>
+#include <string>
+#include <vector>
+#include <codecvt>
 #include "WinRarConfig.hpp"
 #include "WinRarKeygen.hpp"
 #include <system_error>
 
+#pragma comment(lib, "Version.lib")
+
+std::string WideToUtf8(const std::wstring& wstr) {
+    if (wstr.empty()) return {};
+    int size = WideCharToMultiByte(CP_UTF8, 0, wstr.data(), (int)wstr.size(), nullptr, 0, nullptr, nullptr);
+    std::string result(size, 0);
+    WideCharToMultiByte(CP_UTF8, 0, wstr.data(), (int)wstr.size(), &result[0], size, nullptr, nullptr);
+    return result;
+}
+
+std::wstring Utf8ToWide(const std::string& str) {
+    if (str.empty()) return {};
+    int size = MultiByteToWideChar(CP_UTF8, 0, str.data(), (int)str.size(), nullptr, 0);
+    std::wstring result(size, 0);
+    MultiByteToWideChar(CP_UTF8, 0, str.data(), (int)str.size(), &result[0], size);
+    return result;
+}
+
 void Help() {
-    _putts(TEXT("Usage:"));
-    _putts(TEXT("        winrar-keygen.exe <your name> <license type>"));
-    _putts(TEXT(""));
-    _putts(TEXT("Example:"));
-    _putts(TEXT(""));
-    _putts(TEXT("        winrar-keygen.exe \"Github\" \"Github.com\""));
-    _putts(TEXT("  or:"));
-    _putts(TEXT("        winrar-keygen.exe \"Github\" \"Github.com\" > rarreg.key\n"));
+    std::wcout << L"Please use the following command:\n";
+    std::wcout << L"Usage:\n";
+    std::wcout << L"        winrar-keygen.exe <Username> <License Name>\n\n";
+    std::wcout << L"Example:\n";
+    std::wcout << L"        winrar-keygen.exe \"GitHub\" \"Single PC usage license\"\n";
+}
+
+std::wstring GetExecutableVersion() {
+    wchar_t exePath[MAX_PATH] = {};
+    DWORD pathLen = GetModuleFileNameW(nullptr, exePath, MAX_PATH);
+    if (pathLen == 0) {
+        return L"unknown";
+    }
+
+    DWORD handle = 0;
+    DWORD versionSize = GetFileVersionInfoSizeW(exePath, &handle);
+    if (versionSize == 0) {
+        return L"unknown";
+    }
+
+    std::vector<BYTE> versionData(versionSize);
+    if (!GetFileVersionInfoW(exePath, 0, versionSize, versionData.data())) {
+        return L"unknown";
+    }
+
+    VS_FIXEDFILEINFO* fixedInfo = nullptr;
+    UINT len = 0;
+    if (!VerQueryValueW(versionData.data(), L"\\",
+                        reinterpret_cast<LPVOID*>(&fixedInfo),
+                        &len) ||
+        fixedInfo == nullptr) {
+        return L"unknown";
+    }
+
+    return std::to_wstring(HIWORD(fixedInfo->dwFileVersionMS)) + L"." +
+           std::to_wstring(LOWORD(fixedInfo->dwFileVersionMS)) + L"." +
+           std::to_wstring(HIWORD(fixedInfo->dwFileVersionLS)) + L"." +
+           std::to_wstring(LOWORD(fixedInfo->dwFileVersionLS));
 }
 
 void PrintRegisterInfo(const WinRarKeygen<WinRarConfig>::RegisterInfo& Info) {
-    _tprintf_s(TEXT("%hs\n"), "RAR registration data");
-    _tprintf_s(TEXT("%hs\n"), Info.UserName.c_str());
-    _tprintf_s(TEXT("%hs\n"), Info.LicenseType.c_str());
-    _tprintf_s(TEXT("UID=%hs\n"), Info.UID.c_str());
-    for (size_t i = 0; i < Info.HexData.length(); i += 54) {
-        _tprintf_s(TEXT("%.54hs\n"), Info.HexData.c_str() + i);
+    std::wstring user = Utf8ToWide(Info.UserName);
+    std::wstring license = Utf8ToWide(Info.LicenseType);
+    std::wstring uid = Utf8ToWide(Info.UID);
+    std::wstring data = Utf8ToWide(Info.HexData);
+
+    std::wcout << L"RAR registration data\n";
+    std::wcout << user << L"\n";
+    std::wcout << license << L"\n";
+    std::wcout << L"UID=" << uid << L"\n";
+
+    for (size_t i = 0; i < data.length(); i += 54) {
+        std::wcout << data.substr(i, 54) << L"\n";
     }
 }
 
-std::string ToACP(PCWSTR lpszUnicodeString) {
-    int len;
-
-    len = WideCharToMultiByte(CP_ACP, 0, lpszUnicodeString, -1, NULL, 0, NULL, NULL);
-    if (len == 0) {
-        auto err = GetLastError();
-        throw std::system_error(err, std::system_category());
+bool IsConsoleHandle(HANDLE handle) {
+    if (handle == nullptr || handle == INVALID_HANDLE_VALUE) {
+        return false;
     }
-
-    std::string Result(len, '\x00');
-
-    len = WideCharToMultiByte(CP_ACP, 0, lpszUnicodeString, -1, Result.data(), static_cast<int>(Result.length()), NULL, NULL);
-    if (len == 0) {
-        auto err = GetLastError();
-        throw std::system_error(err, std::system_category());
-    }
-
-    while (Result.back() == '\x00') {
-        Result.pop_back();
-    }
-
-    return Result;
+    DWORD mode = 0;
+    return GetConsoleMode(handle, &mode) != 0;
 }
 
-int _tmain(int argc, PTSTR argv[]) {
-    setlocale(LC_ALL, "");
-    if (argc == 3) {
+void ConfigureConsoleOutput() {
+    HANDLE stdoutHandle = GetStdHandle(STD_OUTPUT_HANDLE);
+    HANDLE stderrHandle = GetStdHandle(STD_ERROR_HANDLE);
+
+    int mode;
+
+    // console use UTF-16, file use UTF-8
+    if (IsConsoleHandle(stdoutHandle)) {
+        if ((mode = _setmode(_fileno(stdout), _O_WTEXT)) == -1)
+            std::wcerr << L"Failed to set stdout _O_WTEXT\n";
+    }
+    else {
+        // stdout is redirected to a file, use UTF-8
+        if ((mode = _setmode(_fileno(stdout), _O_U8TEXT)) == -1)
+            std::wcerr << L"Failed to set stdout _O_U8TEXT\n";
+    }
+
+    if (IsConsoleHandle(stderrHandle)) {
+        if ((mode = _setmode(_fileno(stderr), _O_WTEXT)) == -1)
+            std::wcerr << L"Failed to set stderr _O_WTEXT\n";
+    }
+    else {
+        if ((mode = _setmode(_fileno(stderr), _O_U8TEXT)) == -1)
+            std::wcerr << L"Failed to set stderr _O_U8TEXT\n";
+    }
+}
+
+int wmain(int argc, wchar_t* argv[]) {
+    ConfigureConsoleOutput();
+
+    if (argc == 2 &&
+        (_wcsicmp(argv[1], L"ver") == 0 || _wcsicmp(argv[1], L"--version") == 0 || _wcsicmp(argv[1], L"-v") == 0)) {
+        std::wcout << GetExecutableVersion() << L"\n";
+    }
+    else if (argc == 3) {
         try {
+            std::string user = WideToUtf8(argv[1]);
+            std::string license = WideToUtf8(argv[2]);
+
             PrintRegisterInfo(
-#if defined(_UNICODE) || defined(UNICODE)
-                WinRarKeygen<WinRarConfig>::GenerateRegisterInfo(ToACP(argv[1]).c_str(), ToACP(argv[2]).c_str())
-#else
-                WinRarKeygen<WinRarConfig>::GenerateRegisterInfo(argv[1], argv[2])
-#endif
+                WinRarKeygen<WinRarConfig>::GenerateRegisterInfo(user.c_str(), license.c_str())
             );
-        } catch (std::exception& e) {
-            _tprintf_s(TEXT("%hs\n"), e.what());
+        }
+        catch (std::exception& e) {
+            std::wcerr << L"Error: " << Utf8ToWide(e.what()) << L"\n";
             return -1;
         }
-    } else {
+    }
+    else {
         Help();
     }
+
     return 0;
 }
-

assets/ascii-characters-dark.svg

@@ -0,0 +1,8 @@
+<svg width="1720" height="760" viewBox="0 0 172 76" xmlns="http://www.w3.org/2000/svg">
+  <style type="text/css">.text{fill:#fff;}</style>
+  <text class="text" y="12" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14"> !&quot;#$%&amp;'()*+,-./012</text>
+  <text class="text" y="27" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">3456789:;&lt;=&gt;?@ABCDE</text>
+  <text class="text" y="42" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">FGHIJKLMNOPQRSTUVWX</text>
+  <text class="text" y="57" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">YZ[\]^_`abcdefghijk</text>
+  <text class="text" y="72" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">lmnopqrstuvwxyz{|}~</text>
+</svg>

assets/ascii-characters-light.svg

@@ -0,0 +1,7 @@
+<svg width="1720" height="760" viewBox="0 0 172 76" xmlns="http://www.w3.org/2000/svg">
+  <text y="12" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14"> !&quot;#$%&amp;'()*+,-./012</text>
+  <text y="27" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">3456789:;&lt;=&gt;?@ABCDE</text>
+  <text y="42" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">FGHIJKLMNOPQRSTUVWX</text>
+  <text y="57" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">YZ[\]^_`abcdefghijk</text>
+  <text y="72" x="2" textLength="170" style="white-space: pre" letter-spacing=".55" font-family="DejaVu Sans Mono" font-size="14">lmnopqrstuvwxyz{|}~</text>
+</svg>

assets/file-icon.svg

@@ -0,0 +1 @@
+<svg xmlns="http://www.w3.org/2000/svg"  viewBox="0 0 80 80" width="40px" height="40px"><path fill="#fff" d="M12.5 75.5L12.5 4.5 49.793 4.5 67.5 22.207 67.5 75.5z"/><path fill="#788b9c" d="M49.586,5L67,22.414V75H13V5H49.586 M50,4H12v72h56V22L50,4L50,4z"/><path fill="#fff" d="M49.5 22.5L49.5 4.5 49.793 4.5 67.5 22.207 67.5 22.5z"/><path fill="#788b9c" d="M50 5.414L66.586 22H50V5.414M50 4h-1v19h19v-1L50 4 50 4zM24 32H56V33H24zM24 38H48V39H24zM24 44H56V45H24zM24 50H48V51H24zM24 56H56V57H24z"/></svg>

assets/formula/1-dark.svg

@@ -0,0 +1,29 @@
+<?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='112.199176pt' height='14.957875pt' viewBox='-.239051 -.235254 112.199176 14.957875'>
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