From 6a562661cd1ff993b913e2eed1506deb9713f37a Mon Sep 17 00:00:00 2001 From: bitcookies Date: Thu, 10 Feb 2022 14:00:19 +0800 Subject: [PATCH] =?UTF-8?q?=F0=9F=8C=99=20Adapt=20the=20Github=20Dark=20Th?= =?UTF-8?q?eme?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 🌙 Adapt the Github Dark Theme --- README.HOW_DOES_IT_WORK.md | 238 +++++++++++++++++++------------ README.HOW_DOES_IT_WORK.zh-CN.md | 36 +---- 2 files changed, 150 insertions(+), 124 deletions(-) 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 ![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

- +

-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

- +

-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

- +

+ --- -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

- +

-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

- +

-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

- +

+ --- -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

- +

-## 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

- +

-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

- +

-whose order ![n-inlined] is + +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

- +

+ ## 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 ![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

- +

-where ![](http://latex.codecogs.com/svg.latex?%5Cinline%20S_0%2CS_1%2CS_2%2CS_3%2CS_4) are 5 state values when SHA1 outputs. Generally speaking, the final SHA1 value should be the join of these 5 state values while each of state values is serialized in big-endian. -However, WinRAR doesn't serialize the 5 state values. Instead, it use a big integer ![h-inlined] as the hash of the input message. +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](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.

- +

+ ## 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

- +

-If we use ![h-inlined] to denote the hash of input data, WinRAR use the following algorithm to perform signing: -1. Generate a random big integer ![Rnd-inlined] which satisfies ![](http://latex.codecogs.com/svg.latex?%5Cinline%200%3CRnd%3Cn). +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: -2. Calculate ![r-inlined] +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](assets/formula/r-inlined-light.svg#gh-light-mode-only)![r](assets/formula/r-inlined-dark.svg#gh-dark-mode-only)

- + +

- 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+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)

- + +

- 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

- + +

-to denote input data whose length is ![l-inlined]. WinRAR use it to generate private key ![k-inlined]. -1. We use ![](http://latex.codecogs.com/svg.latex?%5Cinline%20g_0%2Cg_1%2Cg_2%2Cg_3%2Cg_4%2Cg_5) to denote 6 32-bits-long integer. So there is +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 ![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

- + +

-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+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):

- + +

- 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

- + +

-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:

- + +

- 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

- + +

## 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

- + +

-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 ![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](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only) 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 ![](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

- + +

-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

- + +

-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

- + +

-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

- + +

- Use the algorithm describled in section 4, with argument ![Temp-inlined] and private key ![k-inlined] describled section 6, to get signature ![](http://latex.codecogs.com/svg.latex?%5Cinline%20%28r_%7BTemp%7D%2Cs_%7BTemp%7D%29). - The bit length of ![](http://latex.codecogs.com/svg.latex?%5Cinline%20r_%7BTemp%7D) and ![](http://latex.codecogs.com/svg.latex?%5Cinline%20s_%7BTemp%7D) shall not be more than 240. Otherwise, repeat this step. + 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). -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. + 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. - 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. +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. -10. Let ![Data2-inlined] be + 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](assets/formula/Data2-inlined-light.svg#gh-light-mode-only)![Data2](assets/formula/Data2-inlined-dark.svg#gh-dark-mode-only) be

- + +

11. Calculate CRC32 value of

- + +

+ The final checksum the complement of CRC32 value. - Then convert the checksum to decimal string ![](http://latex.codecogs.com/svg.latex?%5Cinline%20SZ%5E%7Bchecksum%7D). If the length is less than 10, pad character `'0'` until the length is 10. + 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. -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

- + +

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 ![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. 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 ![GF2p15-inlined](assets/formula/GF2-inlined-light.svg#gh-light-mode-only)![GF2p15-inlined](assets/formula/GF2-inlined-dark.svg#gh-dark-mode-only)。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：

- - 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：

- - --- 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： @@ -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 ![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：

- - 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：

- - --- 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： @@ -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 ![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： @@ -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 ![G](assets/formula/GG-inlined-light.svg#gh-light-mode-only)![G](assets/formula/GG-inlined-dark.svg#gh-dark-mode-only) 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) 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：

- - ## 3. 消息哈希算法 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： @@ -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 ![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：

- - 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](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： @@ -124,8 +102,6 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h](assets/formula/h-inlined-lig

- - 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](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)。 @@ -162,8 +138,6 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h](assets/formula/h-inlined-lig

- - 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 ![g0-5](assets/formula/27-light.svg#gh-light-mode-only)![g0-5](assets/formula/27-dark.svg#gh-dark-mode-only)，则有 @@ -175,7 +149,7 @@ WinRAR 在做完 SHA1 计算后，采用大数 ![h](assets/formula/h-inlined-lig 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 ![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 ![TT](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)： +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)：

@@ -219,8 +193,6 @@ WinRAR 的私钥 ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k]

- - 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](assets/formula/PP-inlined-light.svg#gh-light-mode-only)![P](assets/formula/PP-inlined-dark.svg#gh-dark-mode-only) 为： @@ -229,8 +201,6 @@ WinRAR 的私钥 ![k](assets/formula/k-inlined-light.svg#gh-light-mode-only)![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](assets/formula/k-inlined-light.svg#gh-light-mode-only)![k] * UID，占一行：

- +