diff --git a/README.HOW_DOES_IT_WORK.md b/README.HOW_DOES_IT_WORK.md
index 585d17b..02cfe7f 100644
--- a/README.HOW_DOES_IT_WORK.md
+++ b/README.HOW_DOES_IT_WORK.md
@@ -1,193 +1,238 @@
# 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  .
-## 1. Composite field ![GF2p15p17-inlined]
+## 1. Composite field  
-Elements in ground field ![GF2p15-inlined] are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is
+Elements in ground field  are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is
- 
+ 
-where each coefficients is in ![GF2-inlined]. If we use
+
+where each coefficients is in . If we use
- 
+ 
-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  in  can be denoted as
- 
+ 
+
---
-The irreducible polynomial of composite field ![GF2p15p17-inlined] is
+The irreducible polynomial of composite field   is
- 
+ 
-where each coefficients is in ![GF2p15-inlined]. If we use
+
+where each coefficients is in . If we use
- 
+ 
-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  in   can be denoted as
- 
+ 
+
---
-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  , which is a 255-bits-long integer to denote an element  in  . The map between them is
- 
+ 
-## 2. Elliptic curve over ![GF2p15p17-inlined]
+
+## 2. Elliptic curve over  
The equation of the elliptic curve that WinRAR uses is
- 
+ 
-The base point ![G-inlined] is
+
+The base point  is
- 
+ 
-whose order ![n-inlined] is
+
+whose order  is
- 
+ 
+
## 3. Message hash algorithm
We use
- 
+ 
-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 . So the SHA1 value of  should be
- 
+ 
-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.
+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  as the hash of the input message.
- 
+ 
+
## 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  to denote private key,  to denote public key. So there must be
- 
+ 
-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 .
+If we use  to denote the hash of input data, WinRAR use the following algorithm to perform signing:
-2. Calculate ![r-inlined]
+1. Generate a random big integer  which satisfies .
+
+2. Calculate 
- 
+ 
+ 
- where  means we take X coordinate of  and convert it from ![GF2p15p17-inlined] to a big integer.
- If  or , go back to step 1.
+ where  means we take X coordinate of  and convert it from   to a big integer.
-3. Calculate ![s-inlined]
+ If  or , go back to step 1.
+
+3. Calculate 
- 
+ 
+ 
- If , go back to step 1.
-4. Output .
+ If , go back to step 1.
+
+4. Output .
## 5. WinRAR private key generation algorithm
We use
- 
+ 
+ 
-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
+to denote input data whose length is . WinRAR use it to generate private key .
+
+1. We use  to denote 6 32-bits-long integer. So there is
- 
+ 
+ 
-2. Let .
+2. Let .
-3. If , we calculate SHA1 value of ![T-inlined]. Then assign SHA1 state value  to :
+3. If , we calculate SHA1 value of . Then assign SHA1 state value  to :
- 
+ 
+ 
- Otherwise, when , we let
+
+ Otherwise, when , we let
- 
+ 
+ 
-4. Regard  as counter, add itself by 1.
+4. Regard  as counter, add itself by 1.
Calculate SHA1:
- 
+ 
+ 
- We takes the lowest 16 bits of  and donote it as .
+
+ 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
+6. After that, we will get . Then output private key
- 
+ 
+ 
## 6. The private key and public key of WinRAR
-Private key ![k-inlined] is
+Private key  is
- 
+ 
+ 
-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
+This private key is generated by the algorithm describled in section 5 where the length of data  is zero.
+
+Public key  is
- 
+ 
+ 
+
## 7. Generation of "rarreg.key"
The generation of license file `rarreg.key` requires 2 arguments:
@@ -195,85 +240,96 @@ The generation of license file `rarreg.key` requires 2 arguments:
1. Username, an ANSI-encoded string, without null-terminator. Denoted as
- 
+ 
+ 
2. License type, an ANSI-encoded string, without null-terminator. Denoted as
- 
+ 
+ 
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].
+1. Use the algorithm describled in section 5, with argument , 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 .
- The length of ![Temp-inlined] should be 64. If less, pad with `'0'` until the length is 64.
+ The length of  should be 64. If less, pad with `'0'` until the length is 64.
-2. Let ![Data3-inlined] be
+2. Let  be
- 
+ 
+ 
-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].
+3. Use the algorithm describled in section 5, with argument , 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 .
- The length of ![Data0-inlined] should be 64. If less, pad with `'0'` until the length is 64.
+ The length of  should be 64. If less, pad with `'0'` until the length is 64.
-4. Let ![UID-inlined] be
+4. Let  be
- 
+ 
+ 
-5. Use the algorithm describled in section 4, with argument ![LL-inlined] and private key ![k-inlined] describled section 6, to get signature .
+5. Use the algorithm describled in section 4, with argument  and private key  describled section 6, to get signature .
- The bit length of  and  shall not be more than 240. Otherwise, repeat this step.
+ 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.
+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.
+ If the length of  or  is less than 60, pad character `'0'` until the length is 60.
-7. Let ![Data1-inlined] be
+7. Let  be
- 
+ 
+ 
-8. Let ![Temp-inlined] be
+8. Let  be
- 
+ 
+ 
- 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.
+ Use the algorithm describled in section 4, with argument  and private key  describled section 6, to get signature .
-9. Convert  and  to hex-integer string  and , without `"0x"` prefix.
+ The bit length of  and  shall not be more than 240. Otherwise, repeat this step.
- If the length of  or  is less than 60, pad character `'0'` until the length is 60.
+9. Convert  and  to hex-integer string  and , without `"0x"` prefix.
-10. Let ![Data2-inlined] be
+ If the length of  or  is less than 60, pad character `'0'` until the length is 60.
+
+10. Let  be
- 
+ 
+ 
11. Calculate CRC32 value of
- 
+ 
+ 
+
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.
+ 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
+12. Let  be
- 
+ 
+ 
13. Output with format
@@ -287,8 +343,8 @@ The following is the algorithm to generate `rarreg.key`.
* UID, taking one line, with format:
- 
+ 
+ 
-
- * Output ![Data-inlined], with 54 characters a line.
-
+
+ * Output , with 54 characters a line.
diff --git a/README.HOW_DOES_IT_WORK.zh-CN.md b/README.HOW_DOES_IT_WORK.zh-CN.md
index ecbf04b..1587e06 100644
--- a/README.HOW_DOES_IT_WORK.zh-CN.md
+++ b/README.HOW_DOES_IT_WORK.zh-CN.md
@@ -11,22 +11,18 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
-各项系数全部位于 。设基域的标准基为：
+各项系数全部位于 。设基域的标准基为：
-
-
则位于基域  上的元素  可以用如下方式表达：
-
-
---
复合域   的不可约多项式为：
@@ -35,24 +31,18 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
-
-
各项系数全部位于 。设复合域的标准基为：
-
-
则位于复合域   上的元素  可以用如下方式表达：
-
-
---
为了方便表述我们用255比特的大数  来表示位于复合域   上的元素 。它们的对应关系为：
@@ -61,8 +51,6 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
-
-
## 2. 复合域   上的椭圆曲线
曲线方程为：
@@ -71,24 +59,18 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
-
-
基点  为：
-
-
基点  的阶  为：
-
-
## 3. 消息哈希算法
设长度为  的消息为：
@@ -97,16 +79,12 @@ WinRAR 使用了基于 ECC 的签名算法来生成 `rarreg.key` 文件，其使
-
-
则消息  的 SHA1 值为：
-
-
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  作为 ECC 签名时消息的哈希：
@@ -124,8 +102,6 @@ WinRAR 在做完 SHA1 计算后，采用大数 
-
-
消息哈希为 ，则签名  为：
1. 生成随机数 ，满足 。
@@ -162,8 +138,6 @@ WinRAR 在做完 SHA1 计算后，采用大数 。
1. 设6个32位整数为 ，则有
@@ -175,7 +149,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 。
-3. 如果  则计算  的 SHA1 值，并将状态值  赋值给 ：
+3. 如果  则计算  的 SHA1 值，并将状态值  赋值给 ：
@@ -219,8 +193,6 @@ WinRAR 的私钥 ![k]
-
-
该私钥是通过算法5生成的，其中数据  的长度为0。
公钥  为：
@@ -229,8 +201,6 @@ WinRAR 的私钥 ![k]
-
-
## 7. 授权文件"rarreg.key"的生成
授权文件的生成需要两个参数：
@@ -338,7 +308,7 @@ WinRAR 的私钥 ![k]
* UID，占一行：
-
+