README.HOW_DOES_IT_WORK.md

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 .

1. Composite field

Elements in ground field are represented with standard basis, i.e. polynomial basis. The irreducible polynomial is

where each coefficients is in . If we use

as the standard basis of the ground field, an element in can be denoted as

---

The irreducible polynomial of composite field is

where each coefficients is in . If we use

as the standard basis of the composite field, an element in can be denoted as

---

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

The equation of the elliptic curve that WinRAR uses is

The base point is

whose order is

3. Message hash algorithm

We use

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 as the hash of the input message.

4. ECC digital signature algorithm

We use to denote private key, to denote public key. So there must be

If we use to denote the hash of input data, WinRAR use the following algorithm to perform signing:

1. Generate a random big integer which satisfies .

2. Calculate

   

   where means we take X coordinate of and convert it from to a big integer.

   If or , go back to step 1.

3. Calculate

   

   If , go back to step 1.

4. Output .

5. WinRAR private key generation algorithm

We use

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 .

3. If , we calculate SHA1 value of . Then assign SHA1 state value to :

   

   Otherwise, when , we let

   

4. Regard as counter, add itself by 1.

   Calculate SHA1:

   

   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. The private key and public key of WinRAR

Private key 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:

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 , 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 should be 64. If less, pad with '0' until the length is 64.

2. Let be

   

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 should be 64. If less, pad with '0' until the length is 64.

4. Let be

   

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.

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 be

   

8. Let be

   

   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.

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 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.

12. Let be

    

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:

      

    • Output , with 54 characters a line.