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✔ Add an example of verifying the point G
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bitcookies
@@ -11,7 +11,6 @@ Elements in ground field ![GF2p15-inlined](assets/formula/GF2p15-inlined-light.s
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<img src="assets/formula/1-dark.svg#gh-dark-mode-only">
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</p>
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where each coefficients is in . If we use
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<p align="center">
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@@ -19,7 +18,6 @@ where each coefficients is in ![GF2-inlined](assets/formula/GF2-inlined-light.sv
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<img src="assets/formula/2-dark.svg#gh-dark-mode-only">
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</p>
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as the standard basis of the ground field, an element  in  can be denoted as
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<p align="center">
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@@ -27,7 +25,6 @@ as the standard basis of the ground field, an element ![A](assets/formula/AA-inl
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<img src="assets/formula/3-dark.svg#gh-dark-mode-only">
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</p>
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---
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The irreducible polynomial of composite field   is
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@@ -37,7 +34,6 @@ The irreducible polynomial of composite field ![GF2p15p17-inlined](assets/formul
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<img src="assets/formula/4-dark.svg#gh-dark-mode-only">
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</p>
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where each coefficients is in . If we use
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<p align="center">
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@@ -45,7 +41,6 @@ where each coefficients is in ![GF2p15-inlined](assets/formula/GF2p15-inlined-li
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<img src="assets/formula/5-dark.svg#gh-dark-mode-only">
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</p>
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as the standard basis of the composite field, an element  in   can be denoted as
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<p align="center">
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@@ -53,7 +48,6 @@ as the standard basis of the composite field, an element ![B](assets/formula/BB-
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<img src="assets/formula/6-dark.svg#gh-dark-mode-only">
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</p>
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---
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For clarity, we use  , which is a 255-bits-long integer to denote an element  in  . The map between them is
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@@ -63,7 +57,6 @@ For clarity, we use 
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<img src="assets/formula/7-dark.svg#gh-dark-mode-only">
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</p>
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## 2. Elliptic curve over  
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The equation of the elliptic curve that WinRAR uses is
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@@ -73,7 +66,6 @@ The equation of the elliptic curve that WinRAR uses is
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<img src="assets/formula/8-dark.svg#gh-dark-mode-only">
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</p>
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The base point  is
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<p align="center">
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@@ -81,6 +73,7 @@ The base point ![G](
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<img src="assets/formula/9-dark.svg#gh-dark-mode-only">
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</p>
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A [verification example](README.VERIFY_Point_G.md) of the base point  on the curve.
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whose order  is
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@@ -89,7 +82,6 @@ whose order ![n](asse
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<img src="assets/formula/10-dark.svg#gh-dark-mode-only">
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</p>
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## 3. Message hash algorithm
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We use
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@@ -99,7 +91,6 @@ We use
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<img src="assets/formula/11-dark.svg#gh-dark-mode-only">
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</p>
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to denote a message whose length is . So the SHA1 value of  should be
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<p align="center">
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@@ -107,7 +98,6 @@ to denote a message whose length is ![l](assets/formula/l-inlined-light.svg#gh-l
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<img src="assets/formula/12-dark.svg#gh-dark-mode-only">
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</p>
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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.
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However, WinRAR doesn't serialize the 5 state values. Instead, it use a big integer  as the hash of the input message.
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@@ -117,7 +107,6 @@ However, WinRAR doesn't serialize the 5 state values. Instead, it use a big inte
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<img src="assets/formula/15-dark.svg#gh-dark-mode-only">
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</p>
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## 4. ECC digital signature algorithm
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We use  to denote private key,  to denote public key. So there must be
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@@ -127,7 +116,6 @@ We use ![k](assets/fo
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<img src="assets/formula/16-dark.svg#gh-dark-mode-only">
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</p>
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If we use  to denote the hash of input data, WinRAR use the following algorithm to perform signing:
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1. Generate a random big integer  which satisfies .
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@@ -165,7 +153,6 @@ We use
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<img src="assets/formula/26-dark.svg#gh-dark-mode-only">
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</p>
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to denote input data whose length is . WinRAR use it to generate private key .
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1. We use  to denote 6 32-bits-long integer. So there is
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@@ -184,7 +171,6 @@ to denote input data whose length is ![l](assets/formula/l-inlined-light.svg#gh-
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<img src="assets/formula/33-dark.svg#gh-dark-mode-only">
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</p>
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Otherwise, when , we let
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<p align="center">
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@@ -201,7 +187,6 @@ to denote input data whose length is ![l](assets/formula/l-inlined-light.svg#gh-
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<img src="assets/formula/37-dark.svg#gh-dark-mode-only">
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</p>
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We takes the lowest 16 bits of  and donote it as .
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5. Repeat step 4 again with 14 times.
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@@ -222,7 +207,6 @@ Private key ![k](asse
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<img src="assets/formula/42-dark.svg#gh-dark-mode-only">
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</p>
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This private key is generated by the algorithm describled in section 5 where the length of data  is zero.
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Public key  is
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@@ -297,7 +281,6 @@ The following is the algorithm to generate `rarreg.key`.
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<img src="assets/formula/58-dark.svg#gh-dark-mode-only">
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</p>
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Use the algorithm describled in section 4, with argument  and private key  describled section 6, to get signature .
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The bit length of  and  shall not be more than 240. Otherwise, repeat this step.
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@@ -320,9 +303,8 @@ The following is the algorithm to generate `rarreg.key`.
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<img src="assets/formula/65-dark.svg#gh-dark-mode-only">
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</p>
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The final checksum the complement of CRC32 value.
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Then convert the checksum to decimal string . If the length is less than 10, pad character `'0'` until the length is 10.
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12. Let  be
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