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[GF2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%29
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[GF2p15-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%5E%7B15%7D%29
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[GF2p15p17-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29
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[A-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20A
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[B-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20B
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[D-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20D
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[G-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20G
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[M-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20M
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[P-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20P
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[h-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20h
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[k-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20k
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[l-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20l
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[n-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20n
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[r-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20r
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[s-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20s
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[T-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20T
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[UU-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20U
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[LL-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20L
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[Rnd-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd
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[Temp-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Temp
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[UID-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20UID
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[Data-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data
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[Data0-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E0
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[Data1-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E1
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[Data2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E2
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[Data3-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E3
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# How is "rarreg.key" generated?
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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].
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@ -1,49 +1,24 @@
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[GF2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%29
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[GF2p15-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%5E%7B15%7D%29
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[GF2p15p17-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29
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[A-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20A
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[B-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20B
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[D-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20D
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[G-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20G
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[M-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20M
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[P-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20P
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[h-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20h
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[k-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20k
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[l-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20l
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[n-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20n
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[r-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20r
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[s-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20s
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[T-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20T
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[UU-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20U
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[LL-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20L
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[Rnd-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd
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[Temp-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Temp
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[UID-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20UID
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[Data-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data
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[Data0-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E0
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[Data1-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E1
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[Data2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E2
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[Data3-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E3
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# "rarreg.key"是如何生成的？
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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。
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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   上的曲线。
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## 1. 复合域 ![GF2p15p17-inlined]
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## 1. 复合域  
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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：
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基域  采用标准基（多项式基)来表达，采用的不可约多项式为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?P%28%5Calpha%29%3D%5Calpha%5E%7B15%7D+%5Calpha+1")
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<img src="assets/formula/1-light.svg#gh-light-mode-only">
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<img src="assets/formula/1-dark.svg#gh-dark-mode-only">
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</p>
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各项系数全部位于 ![GF2-inlined]。设基域的标准基为：
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各项系数全部位于 。设基域的标准基为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B_1%3D%5C%7B1%2C%5Calpha%2C%5Calpha%5E2%2C%5Cldots%2C%5Calpha%5E%7B14%7D%5C%7D")
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</p>
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则位于基域 ![GF2p15-inlined] 上的元素 ![A-inlined] 可以用如下方式表达：
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则位于基域  上的元素 ![A-inlined] 可以用如下方式表达：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?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")
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@ -51,19 +26,19 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
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---
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复合域 ![GF2p15p17-inlined] 的不可约多项式为：
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复合域   的不可约多项式为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?Q%28%5Cbeta%29%3D%5Cbeta%5E%7B17%7D+%5Cbeta%5E3+1")
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</p>
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各项系数全部位于 ![GF2p15-inlined]。设复合域的标准基为：
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各项系数全部位于 。设复合域的标准基为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B_2%3D%5C%7B1%2C%5Cbeta%2C%5Cbeta%5E2%2C%5Cldots%2C%5Cbeta%5E%7B16%7D%5C%7D")
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</p>
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则位于复合域 ![GF2p15p17-inlined] 上的元素 ![B-inlined] 可以用如下方式表达：
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则位于复合域   上的元素 ![B-inlined] 可以用如下方式表达：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%28%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%29%5Cbeta%5Ej%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cquad%20%5Cquad%20%5Cquad%20a_%7Bj%2Ci%7D%5Cin%5Ctextrm%7BGF%7D%282%29")
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@ -71,7 +46,7 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
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---
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为了方便表述我们用255比特的大数 ![D-inlined] 来表示位于复合域 ![GF2p15p17-inlined] 上的元素 ![B-inlined]。它们的对应关系为：
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为了方便表述我们用255比特的大数 ![D-inlined] 来表示位于复合域   上的元素 ![B-inlined]。它们的对应关系为：
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cleftrightarrow%20D%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Ccdot%202%5E%7B15j+i%7D")
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@ -317,4 +292,3 @@ WinRAR的私钥 ![k-inlined] 为：
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</p>
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* 将 ![Data-inlined] 按照每行54个字符输出。
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321
assets/README.HOW_DOES_IT_WORK.md.bak
Normal file
321
assets/README.HOW_DOES_IT_WORK.md.bak
Normal file
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[GF2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%29
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[GF2p15-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%5E%7B15%7D%29
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[GF2p15p17-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29
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[A-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20A
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[B-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20B
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[D-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20D
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[G-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20G
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[M-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20M
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[P-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20P
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[h-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20h
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[k-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20k
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[l-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20l
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[n-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20n
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[r-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20r
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[s-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20s
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[T-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20T
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[UU-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20U
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[LL-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20L
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[Rnd-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd
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[Temp-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Temp
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[UID-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20UID
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[Data-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data
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[Data0-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E0
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[Data1-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E1
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[Data2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E2
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[Data3-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E3
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# How is "rarreg.key" generated?
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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].
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## 1. Composite field ![GF2p15p17-inlined]
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Elements in ground field ![GF2p15-inlined] are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?P%28%5Calpha%29%3D%5Calpha%5E%7B15%7D+%5Calpha+1")
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</p>
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where each coefficients is in ![GF2-inlined]. If we use
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<p align="center">
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<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")
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</p>
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as the standard basis of the ground field, an element ![A-inlined] in ![GF2p15-inlined] can be denoted as
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<p align="center">
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<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")
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</p>
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---
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The irreducible polynomial of composite field ![GF2p15p17-inlined] is
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?Q%28%5Cbeta%29%3D%5Cbeta%5E%7B17%7D+%5Cbeta%5E3+1")
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</p>
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where each coefficients is in ![GF2p15-inlined]. If we use
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B_2%3D%5C%7B1%2C%5Cbeta%2C%5Cbeta%5E2%2C%5Cldots%2C%5Cbeta%5E%7B16%7D%5C%7D")
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</p>
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as the standard basis of the composite field, an element ![B-inlined] in ![GF2p15p17-inlined] can be denoted as
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%28%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%29%5Cbeta%5Ej%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cquad%20%5Cquad%20%5Cquad%20a_%7Bj%2Ci%7D%5Cin%5Ctextrm%7BGF%7D%282%29")
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</p>
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---
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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
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cleftrightarrow%20D%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Ccdot%202%5E%7B15j+i%7D")
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</p>
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## 2. Elliptic curve over ![GF2p15p17-inlined]
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The equation of the elliptic curve that WinRAR uses is
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?y%5E2+xy%3Dx%5E3+161%20%5Cquad%20%5Cquad%20%5Cquad%20161%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29")
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</p>
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The base point ![G-inlined] is
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<p align="center">
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<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20G%26%3D%28G_x%2CG_y%29%20%5C%5C%20G_x%26%3D%5Ctextrm%7B0x56fdcbc6a27acee0cc2996e0096ae74feb1acf220a2341b898b549440297b8cc%7D%20%5Cquad%20G_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%5C%5C%20G_y%26%3D%5Ctextrm%7B0x20da32e8afc90b7cf0e76bde44496b4d0794054e6ea60f388682463132f931a7%7D%20%5Cquad%20G_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D")
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</p>
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whose order ![n-inlined] is
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<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?n%3D%5Ctextrm%7B0x1026dd85081b82314691ced9bbec30547840e4bf72d8b5e0d258442bbcd31%7D%20%5Cquad%20n%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D")
|
||||
</p>
|
||||
|
||||
## 3. Message hash algorithm
|
||||
|
||||
We use
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?M%3Dm_0m_1%20%5Cldots%20m_%7Bl-1%7D%20%5Cquad%20%5Cquad%20m_i%5Cin%5B0%2C%20256%29")
|
||||
</p>
|
||||
|
||||
to denote a message whose length is ![l-inlined]. So the SHA1 value of ![M-inlined] should be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28M%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5Cquad%20%5Cquad%20S_i%5Cin%5B0%2C%202%5E%7B32%7D%29")
|
||||
</p>
|
||||
|
||||
where  are 5 state values when SHA1 outputs. Generally speaking, the final SHA1 value should be the join of these 5 state values while each of state values is serialized in big-endian.
|
||||
|
||||
However, WinRAR doesn't serialize the 5 state values. Instead, it use a big integer ![h-inlined] as the hash of the input message.
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?h%3D%28%5Csum_%7Bi%3D0%7D%5E%7B4%7DS_i%20%5Ccdot%202%5E%7B32i%7D%29+%5Ctextrm%7B0x1bd10xb4e33c7c0ffd8d43%7D%20%5Ccdot%202%5E%7B32*5%7D")
|
||||
</p>
|
||||
|
||||
## 4. ECC digital signature algorithm
|
||||
|
||||
We use ![k-inlined] to denote private key, ![P-inlined] to denote public key. So there must be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
|
||||
</p>
|
||||
|
||||
If we use ![h-inlined] to denote the hash of input data, WinRAR use the following algorithm to perform signing:
|
||||
|
||||
1. Generate a random big integer ![Rnd-inlined] which satisfies .
|
||||
|
||||
2. Calculate ![r-inlined]
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?r%3D%28%28Rnd%20%5Ccdot%20G%29_x+h%29%5C%20%5C%20Mod%5C%20%5C%20n">
|
||||
</p>
|
||||
|
||||
where  means we take X coordinate of  and convert it from ![GF2p15p17-inlined] to a big integer.
|
||||
|
||||
If  or , go back to step 1.
|
||||
|
||||
3. Calculate ![s-inlined]
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
|
||||
</p>
|
||||
|
||||
If , go back to step 1.
|
||||
|
||||
4. Output .
|
||||
|
||||
## 5. WinRAR private key generation algorithm
|
||||
|
||||
We use
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?T%3Dt_0t_1%20%5Cldots%20t_%7Bl-1%7D%20%5Cquad%20%5Cquad%20t_i%5Cin%5B0%2C256%29">
|
||||
</p>
|
||||
|
||||
to denote input data whose length is ![l-inlined]. WinRAR use it to generate private key ![k-inlined].
|
||||
|
||||
1. We use  to denote 6 32-bits-long integer. So there is
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?g_j%3D%5Csum_%7Bi%3D0%7D%5E%7B3%7Dg_%7Bj%2Ci%7D%20%5Ccdot%202%5E%7B8i%7D%20%5Cquad%20%5Cquad%20g_%7Bj%2Ci%7D%5Cin%5B0%2C256%29">
|
||||
</p>
|
||||
|
||||
2. Let .
|
||||
|
||||
3. If , we calculate SHA1 value of ![T-inlined]. Then assign SHA1 state value  to :
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20%5Ctextrm%7BSHA%7D_1%28T%29%26%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5C%5C%20g_1%26%3DS_0%20%5C%5C%20g_2%26%3DS_1%20%5C%5C%20g_3%26%3DS_2%20%5C%5C%20g_4%26%3DS_3%20%5C%5C%20g_5%26%3DS_4%20%5C%5C%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
Otherwise, when , we let
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20g_1%26%3D%5Ctextrm%7B0xeb3eb781%7D%20%5C%5C%20g_2%26%3D%5Ctextrm%7B0x50265329%7D%20%5C%5C%20g_3%26%3D%5Ctextrm%7B0xdc5ef4a3%7D%20%5C%5C%20g_4%26%3D%5Ctextrm%7B0x6847b9d5%7D%20%5C%5C%20g_5%26%3D%5Ctextrm%7B0xcde43b4c%7D%20%5C%5C%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
4. Regard  as counter, add itself by 1.
|
||||
|
||||
Calculate SHA1:
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28g_%7B0%2C0%7D%7C%7Cg_%7B0%2C1%7D%7C%7Cg_%7B0%2C2%7D%7C%7Cg_%7B0%2C3%7D%7C%7Cg_%7B1%2C0%7D%7C%7Cg_%7B1%2C1%7D%7C%7C%5Cldots%7C%7Cg_%7B5%2C0%7D%7C%7Cg_%7B5%2C1%7D%7C%7Cg_%7B5%2C2%7D%7C%7Cg_%7B5%2C3%7D%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4">
|
||||
</p>
|
||||
|
||||
We takes the lowest 16 bits of  and donote it as .
|
||||
|
||||
5. Repeat step 4 again with 14 times.
|
||||
|
||||
6. After that, we will get . Then output private key
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?k%3D%5Csum_%7Bi%3D1%7D%5E%7B15%7Dk_i%20%5Ccdot%202%5E%7B16i%7D">
|
||||
</p>
|
||||
|
||||
## 6. The private key and public key of WinRAR
|
||||
|
||||
Private key ![k-inlined] is
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?k%3D%5Ctextrm%7B0x59fe6abcca90bdb95f0105271fa85fb9f11f467450c1ae9044b7fd61d65e%7D%20%5Cquad%20%5Cquad%20k%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D">
|
||||
</p>
|
||||
|
||||
This private key is generated by the algorithm describled in section 5 where the length of data ![T-inlined] is zero.
|
||||
|
||||
Public key ![P-inlined] is
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20P%26%3D%28P_x%2CP_y%29%20%5C%5C%20P_x%26%3D%5Ctextrm%7B0x3861220ed9b36c9753df09a159dfb148135d495db3af8373425ee9a28884ba1a%7D%20%5Cquad%20P_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5C%5C%20P_y%26%3D%5Ctextrm%7B0x12b64e62db43a56114554b0cbd573379338cea9124c8443c4f50e6c8b013ec20%7D%20%5Cquad%20P_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
## 7. Generation of "rarreg.key"
|
||||
|
||||
The generation of license file `rarreg.key` requires 2 arguments:
|
||||
|
||||
1. Username, an ANSI-encoded string, without null-terminator. Denoted as
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?U%3Du_0u_1%20%5Cldots%20u_%7Bl-1%7D">
|
||||
</p>
|
||||
|
||||
2. License type, an ANSI-encoded string, without null-terminator. Denoted as
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?L%3Dl_0l_1%20%5Cldots%20l_%7Bl-1%7D">
|
||||
</p>
|
||||
|
||||
The following is the algorithm to generate `rarreg.key`.
|
||||
|
||||
1. Use the algorithm describled in section 5, with argument ![UU-inlined], to generate private key  and public key . Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Temp-inlined].
|
||||
|
||||
The length of ![Temp-inlined] should be 64. If less, pad with `'0'` until the length is 64.
|
||||
|
||||
2. Let ![Data3-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E3%3D%5Ctexttt%7B%2260%22%7D%7C%7CTemp_0%7C%7CTemp_1%7C%7C%5Cldots%7C%7CTemp_%7B47%7D">
|
||||
</p>
|
||||
|
||||
3. Use the algorithm describled in section 5, with argument ![Data3-inlined], to generate private key  and public key . Then output hexlified public key string with SM2 compressed public key format. The hexlified public key is denoted as ![Data0-inlined].
|
||||
|
||||
The length of ![Data0-inlined] should be 64. If less, pad with `'0'` until the length is 64.
|
||||
|
||||
4. Let ![UID-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?UID%3DTemp_%7B48%7D%7C%7CTemp_%7B49%7D%7C%7C%5Cldots%7C%7CTemp_%7B63%7D%7C%7CData%5E0_0%7C%7CData%5E0_1%7C%7CData%5E0_2%7C%7CData%5E0_3">
|
||||
</p>
|
||||
|
||||
5. Use the algorithm describled in section 4, with argument ![LL-inlined] and private key ![k-inlined] describled section 6, to get signature .
|
||||
|
||||
The bit length of  and  shall not be more than 240. Otherwise, repeat this step.
|
||||
|
||||
6. Convert  and  to hex-integer string  and , without `"0x"` prefix.
|
||||
|
||||
If the length of  or  is less than 60, pad character `'0'` until the length is 60.
|
||||
|
||||
7. Let ![Data1-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E1%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_L%7D%7C%7CSZ%5E%7Br_L%7D">
|
||||
</p>
|
||||
|
||||
8. Let ![Temp-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Temp%3DU%7C%7CData%5E0">
|
||||
</p>
|
||||
|
||||
Use the algorithm describled in section 4, with argument ![Temp-inlined] and private key ![k-inlined] describled section 6, to get signature .
|
||||
|
||||
The bit length of  and  shall not be more than 240. Otherwise, repeat this step.
|
||||
|
||||
9. Convert  and  to hex-integer string  and , without `"0x"` prefix.
|
||||
|
||||
If the length of  or  is less than 60, pad character `'0'` until the length is 60.
|
||||
|
||||
10. Let ![Data2-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E2%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_%7BTemp%7D%7D%7C%7CSZ%5E%7Br_%7BTemp%7D%7D">
|
||||
</p>
|
||||
|
||||
11. Calculate CRC32 value of
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?L%7C%7CU%7C%7CData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3">
|
||||
</p>
|
||||
|
||||
The final checksum the complement of CRC32 value.
|
||||
|
||||
Then convert the checksum to decimal string . If the length is less than 10, pad character `'0'` until the length is 10.
|
||||
|
||||
12. Let ![Data-inlined] be
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cinline%20Data%3DData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3%7C%7CSZ%5E%7Bchecksum%7D">
|
||||
</p>
|
||||
|
||||
13. Output with format
|
||||
|
||||
* A fixed header `"RAR registration data"`, taking one line.
|
||||
|
||||
* Username, taking one line.
|
||||
|
||||
* License type, taking one line
|
||||
|
||||
* UID, taking one line, with format:
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctexttt%7B%22UID%3D%22%7D%7C%7CUID">
|
||||
</p>
|
||||
|
||||
* Output ![Data-inlined], with 54 characters a line.
|
||||
|
||||
319
assets/README.HOW_DOES_IT_WORK.zh-CN.md.bak
Normal file
319
assets/README.HOW_DOES_IT_WORK.zh-CN.md.bak
Normal file
|
|
@ -0,0 +1,319 @@
|
|||
[GF2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%29
|
||||
[GF2p15-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%282%5E%7B15%7D%29
|
||||
[GF2p15p17-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29
|
||||
[A-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20A
|
||||
[B-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20B
|
||||
[D-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20D
|
||||
[G-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20G
|
||||
[M-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20M
|
||||
[P-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20P
|
||||
[h-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20h
|
||||
[k-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20k
|
||||
[l-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20l
|
||||
[n-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20n
|
||||
[r-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20r
|
||||
[s-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20s
|
||||
[T-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20T
|
||||
[UU-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20U
|
||||
[LL-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20L
|
||||
[Rnd-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Rnd
|
||||
[Temp-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Temp
|
||||
[UID-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20UID
|
||||
[Data-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data
|
||||
[Data0-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E0
|
||||
[Data1-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E1
|
||||
[Data2-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E2
|
||||
[Data3-inlined]: http://latex.codecogs.com/svg.latex?%5Cinline%20Data%5E3
|
||||
|
||||
# "rarreg.key"是如何生成的？
|
||||
|
||||
WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使用的签名算法是中国 SM2 数字签名算法的变体。与各种标准 ECDSA 不同的是，WinRAR 使用的椭圆曲线是一个基于复合域 ![GF2p15p17-inlined] 上的曲线。
|
||||
|
||||
## 1. 复合域 ![GF2p15p17-inlined]
|
||||
|
||||
基域 ![GF2p15-inlined] 采用标准基（多项式基）来表达，采用的不可约多项式为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?P%28%5Calpha%29%3D%5Calpha%5E%7B15%7D+%5Calpha+1">
|
||||
</p>
|
||||
|
||||
各项系数全部位于 ![GF2-inlined]。设基域的标准基为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?B_1%3D%5C%7B1%2C%5Calpha%2C%5Calpha%5E2%2C%5Cldots%2C%5Calpha%5E%7B14%7D%5C%7D")
|
||||
</p>
|
||||
|
||||
则位于基域 ![GF2p15-inlined] 上的元素 ![A-inlined] 可以用如下方式表达：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?A%3D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_i%5Calpha%5Ei%20%5Cquad%20%5Cquad%20%5Cquad%20a_i%5Cin%5Ctextrm%7BGF%7D%282%29")
|
||||
</p>
|
||||
|
||||
---
|
||||
|
||||
复合域 ![GF2p15p17-inlined] 的不可约多项式为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Q%28%5Cbeta%29%3D%5Cbeta%5E%7B17%7D+%5Cbeta%5E3+1")
|
||||
</p>
|
||||
|
||||
各项系数全部位于 ![GF2p15-inlined]。设复合域的标准基为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?B_2%3D%5C%7B1%2C%5Cbeta%2C%5Cbeta%5E2%2C%5Cldots%2C%5Cbeta%5E%7B16%7D%5C%7D")
|
||||
</p>
|
||||
|
||||
则位于复合域 ![GF2p15p17-inlined] 上的元素 ![B-inlined] 可以用如下方式表达：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%28%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%29%5Cbeta%5Ej%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cquad%20%5Cquad%20%5Cquad%20a_%7Bj%2Ci%7D%5Cin%5Ctextrm%7BGF%7D%282%29")
|
||||
</p>
|
||||
|
||||
---
|
||||
|
||||
为了方便表述我们用255比特的大数 ![D-inlined] 来表示位于复合域 ![GF2p15p17-inlined] 上的元素 ![B-inlined]。它们的对应关系为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?B%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Calpha%5Ei%5Cbeta%5Ej%20%5Cleftrightarrow%20D%3D%5Csum_%7Bj%3D0%7D%5E%7B16%7D%5Csum_%7Bi%3D0%7D%5E%7B14%7Da_%7Bj%2Ci%7D%5Ccdot%202%5E%7B15j+i%7D")
|
||||
</p>
|
||||
|
||||
## 2. 复合域 ![GF2p15p17-inlined] 上的椭圆曲线
|
||||
|
||||
曲线方程为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?y%5E2+xy%3Dx%5E3+161%20%5Cquad%20%5Cquad%20%5Cquad%20161%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29")
|
||||
</p>
|
||||
|
||||
基点 ![G-inlined] 为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20G%26%3D%28G_x%2CG_y%29%20%5C%5C%20G_x%26%3D%5Ctextrm%7B0x56fdcbc6a27acee0cc2996e0096ae74feb1acf220a2341b898b549440297b8cc%7D%20%5Cquad%20G_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%5C%5C%20G_y%26%3D%5Ctextrm%7B0x20da32e8afc90b7cf0e76bde44496b4d0794054e6ea60f388682463132f931a7%7D%20%5Cquad%20G_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D")
|
||||
</p>
|
||||
|
||||
基点 ![G-inlined] 的阶 ![n-inlined] 为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?n%3D%5Ctextrm%7B0x1026dd85081b82314691ced9bbec30547840e4bf72d8b5e0d258442bbcd31%7D%20%5Cquad%20n%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D")
|
||||
</p>
|
||||
|
||||
## 3. 消息哈希算法
|
||||
|
||||
设长度为 ![l-inlined] 的消息为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?M%3Dm_0m_1%20%5Cldots%20m_%7Bl-1%7D%20%5Cquad%20%5Cquad%20m_i%5Cin%5B0%2C%20256%29")
|
||||
</p>
|
||||
|
||||
则消息 ![M-inlined] 的SHA1值为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28M%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5Cquad%20%5Cquad%20S_i%5Cin%5B0%2C%202%5E%7B32%7D%29")
|
||||
</p>
|
||||
|
||||
其中  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 。
|
||||
|
||||
WinRAR在做完SHA1计算后，采用大数 ![h-inlined] 作为ECC签名时消息的哈希：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?h%3D%28%5Csum_%7Bi%3D0%7D%5E%7B4%7DS_i%20%5Ccdot%202%5E%7B32i%7D%29+%5Ctextrm%7B0x1bd10xb4e33c7c0ffd8d43%7D%20%5Ccdot%202%5E%7B32*5%7D")
|
||||
</p>
|
||||
|
||||
|
||||
## 4. ECC签名算法
|
||||
|
||||
设私钥为 ![k-inlined]，公钥为 ![P-inlined]，即：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?P%3Dk%20%5Ccdot%20G")
|
||||
</p>
|
||||
|
||||
消息哈希为 ![h-inlined]，则签名  为：
|
||||
|
||||
1. 生成随机数 ![Rnd-inlined]，满足 。
|
||||
|
||||
2. 计算 ![r-inlined]
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?r%3D%28%28Rnd%20%5Ccdot%20G%29_x+h%29%5C%20%5C%20Mod%5C%20%5C%20n">
|
||||
</p>
|
||||
|
||||
其中  表示取  的X坐标，同时将X坐标从 ![GF2p15p17-inlined] 转换为大数。
|
||||
|
||||
若  或者  则回到步骤1。
|
||||
|
||||
3. 计算 ![s-inlined]
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?s%3D%28Rnd-kr%29%5C%20%5C%20Mod%5C%20%5C%20n">
|
||||
</p>
|
||||
|
||||
若  则回到步骤1。
|
||||
|
||||
4. 输出 。
|
||||
|
||||
## 5. WinRAR的私钥生成算法
|
||||
|
||||
该算法会利用长度为 ![l-inlined] 的数据
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?T%3Dt_0t_1%20%5Cldots%20t_%7Bl-1%7D%20%5Cquad%20%5Cquad%20t_i%5Cin%5B0%2C256%29">
|
||||
</p>
|
||||
|
||||
来生成私钥 ![k-inlined]。
|
||||
|
||||
1. 设6个32位整数为 ，则有
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?g_j%3D%5Csum_%7Bi%3D0%7D%5E%7B3%7Dg_%7Bj%2Ci%7D%20%5Ccdot%202%5E%7B8i%7D%20%5Cquad%20%5Cquad%20g_%7Bj%2Ci%7D%5Cin%5B0%2C256%29">
|
||||
</p>
|
||||
|
||||
2. 令 。
|
||||
|
||||
3. 如果  则计算 ![T-inlined] 的SHA1值，并将状态值  赋值给 ：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20%5Ctextrm%7BSHA%7D_1%28T%29%26%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4%20%5C%5C%20g_1%26%3DS_0%20%5C%5C%20g_2%26%3DS_1%20%5C%5C%20g_3%26%3DS_2%20%5C%5C%20g_4%26%3DS_3%20%5C%5C%20g_5%26%3DS_4%20%5C%5C%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
否则，即  时，令：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20g_1%26%3D%5Ctextrm%7B0xeb3eb781%7D%20%5C%5C%20g_2%26%3D%5Ctextrm%7B0x50265329%7D%20%5C%5C%20g_3%26%3D%5Ctextrm%7B0xdc5ef4a3%7D%20%5C%5C%20g_4%26%3D%5Ctextrm%7B0x6847b9d5%7D%20%5C%5C%20g_5%26%3D%5Ctextrm%7B0xcde43b4c%7D%20%5C%5C%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
4. 把  作为计数器，自增1。
|
||||
|
||||
计算SHA1值：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctextrm%7BSHA%7D_1%28g_%7B0%2C0%7D%7C%7Cg_%7B0%2C1%7D%7C%7Cg_%7B0%2C2%7D%7C%7Cg_%7B0%2C3%7D%7C%7Cg_%7B1%2C0%7D%7C%7Cg_%7B1%2C1%7D%7C%7C%5Cldots%7C%7Cg_%7B5%2C0%7D%7C%7Cg_%7B5%2C1%7D%7C%7Cg_%7B5%2C2%7D%7C%7Cg_%7B5%2C3%7D%29%3DS_0%7C%7CS_1%7C%7CS_2%7C%7CS_3%7C%7CS_4">
|
||||
</p>
|
||||
|
||||
取  的低16位并记为 。
|
||||
|
||||
5. 步骤4再重复14次。
|
||||
|
||||
6. 重复执行完后会得到 ，则输出私钥
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?k%3D%5Csum_%7Bi%3D1%7D%5E%7B15%7Dk_i%20%5Ccdot%202%5E%7B16i%7D">
|
||||
</p>
|
||||
|
||||
## 6. WinRAR的公钥和私钥
|
||||
|
||||
WinRAR的私钥 ![k-inlined] 为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?k%3D%5Ctextrm%7B0x59fe6abcca90bdb95f0105271fa85fb9f11f467450c1ae9044b7fd61d65e%7D%20%5Cquad%20%5Cquad%20k%5Cin%5Cnolinebreak%5Cmathbb%7BZ%7D">
|
||||
</p>
|
||||
|
||||
该私钥是通过算法5生成的，其中数据 ![T-inlined] 的长度为0。
|
||||
|
||||
公钥 ![P-inlined] 为：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cbegin%7Baligned%7D%20P%26%3D%28P_x%2CP_y%29%20%5C%5C%20P_x%26%3D%5Ctextrm%7B0x3861220ed9b36c9753df09a159dfb148135d495db3af8373425ee9a28884ba1a%7D%20%5Cquad%20P_x%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5C%5C%20P_y%26%3D%5Ctextrm%7B0x12b64e62db43a56114554b0cbd573379338cea9124c8443c4f50e6c8b013ec20%7D%20%5Cquad%20P_y%5Cin%5Ctextrm%7BGF%7D%28%282%5E%7B15%7D%29%5E%7B17%7D%29%20%5Cend%7Baligned%7D">
|
||||
</p>
|
||||
|
||||
## 7. 授权文件"rarreg.key"的生成
|
||||
|
||||
授权文件的生成需要两个参数：
|
||||
|
||||
1. 用户名的ANSI字符串，不包括null-terminator；记为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?U%3Du_0u_1%20%5Cldots%20u_%7Bl-1%7D">
|
||||
</p>
|
||||
|
||||
2. 授权类型的ANSI字符串，不包括null-terminator；记为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?L%3Dl_0l_1%20%5Cldots%20l_%7Bl-1%7D">
|
||||
</p>
|
||||
|
||||
`rarreg.key` 的生成算法如下：
|
||||
|
||||
1. 使用用户名 ![UU-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照SM2压缩公钥格式以Hex字符串（ASCII编码）的形式输出。得到的Hex字符串记为临时值 ![Temp-inlined]。
|
||||
|
||||
![Temp-inlined] 的长度应该为64；若长度不足，则在前面补字符`'0'`，直到长度为64。
|
||||
|
||||
2. 令字符串 ![Data3-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E3%3D%5Ctexttt%7B%2260%22%7D%7C%7CTemp_0%7C%7CTemp_1%7C%7C%5Cldots%7C%7CTemp_%7B47%7D">
|
||||
</p>
|
||||
|
||||
3. 使用 ![Data3-inlined] 通过算法5计算出私钥  以及公钥 ，并将公钥  按照SM2压缩公钥格式以Hex字符串（ASCII编码）的形式输出。得到的Hex字符串记为 ![Data0-inlined]。
|
||||
|
||||
![Data0-inlined] 的长度应该为64；若长度不足，则在前面补字符`'0'`，直到长度为64。
|
||||
|
||||
4. 令字符串 ![UID-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?UID%3DTemp_%7B48%7D%7C%7CTemp_%7B49%7D%7C%7C%5Cldots%7C%7CTemp_%7B63%7D%7C%7CData%5E0_0%7C%7CData%5E0_1%7C%7CData%5E0_2%7C%7CData%5E0_3">
|
||||
</p>
|
||||
|
||||
5. 对授权类型 ![LL-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
|
||||
6. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
|
||||
若长度不满60，则在前面补字符`'0'`，直到长度为60。
|
||||
|
||||
7. 令字符串 ![Data1-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E1%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_L%7D%7C%7CSZ%5E%7Br_L%7D">
|
||||
</p>
|
||||
|
||||
8. 令字符串 ![Temp-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Temp%3DU%7C%7CData%5E0">
|
||||
</p>
|
||||
|
||||
对 ![Temp-inlined] 使用算法4得到签名 ，其中私钥见第6节。
|
||||
|
||||
要求  和  的长度都不得超过240比特，否则重复该步骤。
|
||||
|
||||
9. 将  和  以16进制形式输出（无`"0x"`前缀），分别记为  和 。
|
||||
|
||||
若长度不满60，则在前面补字符`'0'`，直到长度为60。
|
||||
|
||||
10. 令字符串 ![Data2-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?Data%5E2%3D%5Ctexttt%7B%2260%22%7D%7C%7CSZ%5E%7Bs_%7BTemp%7D%7D%7C%7CSZ%5E%7Br_%7BTemp%7D%7D">
|
||||
</p>
|
||||
|
||||
11. 对
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?L%7C%7CU%7C%7CData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3">
|
||||
</p>
|
||||
|
||||
计算CRC32值，最终校验和为CRC32值的反。将校验和以10进制形式输出，若长度不满10，则在前面补字符`'0'`，直到长度为10，记为 。
|
||||
|
||||
12. 令字符串 ![Data-inlined]为
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Cinline%20Data%3DData%5E0%7C%7CData%5E1%7C%7CData%5E2%7C%7CData%5E3%7C%7CSZ%5E%7Bchecksum%7D">
|
||||
</p>
|
||||
|
||||
13. 格式化输出。
|
||||
|
||||
* 固定文件头`"RAR registration data"`，占一行。
|
||||
|
||||
* 用户名，占一行。
|
||||
|
||||
* 授权类型，占一行。
|
||||
|
||||
* UID，占一行：
|
||||
|
||||
<p align="center">
|
||||
<img src="http://latex.codecogs.com/svg.latex?%5Ctexttt%7B%22UID%3D%22%7D%7C%7CUID">
|
||||
</p>
|
||||
|
||||
* 将 ![Data-inlined] 按照每行54个字符输出。
|
||||
29
assets/formula/1-dark.svg
Normal file
29
assets/formula/1-dark.svg
Normal file
|
|
@ -0,0 +1,29 @@
|
|||
<?xml version='1.0' encoding='UTF-8'?>
|
||||
<!-- Generated by CodeCogs with dvisvgm 2.9.1 -->
|
||||
<svg 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'>
|
||||
<defs>
|
||||
<path id='g1-49' d='M2.502615-5.076961C2.502615-5.292154 2.486675-5.300125 2.271482-5.300125C1.944707-4.98132 1.522291-4.790037 .765131-4.790037V-4.527024C.980324-4.527024 1.41071-4.527024 1.872976-4.742217V-.653549C1.872976-.358655 1.849066-.263014 1.091905-.263014H.812951V0C1.139726-.02391 1.825156-.02391 2.183811-.02391S3.235866-.02391 3.56264 0V-.263014H3.283686C2.526526-.263014 2.502615-.358655 2.502615-.653549V-5.076961Z'/>
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1
assets/formula/Image display.txt
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1
assets/formula/Image display.txt
Normal file
|
|
@ -0,0 +1 @@
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|||
https://stackoverflow.com/questions/65413712/changing-readme-md-image-display-conditional-to-github-light-mode-dark-mode
|
||||
Loading…
Reference in a new issue