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XPKeygen
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Update README.md

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@ -240,6 +240,7 @@ To compute the private key, we will need to supply the tool with the public ECC
The order of the base point can be computed using SageMath.
**Here's the basic algorithm I used to reverse the Windows 98 private key:**
1. Compute the order of the base point using **SageMath**. In SageMath, execute the following commands:
1) `E = EllipticCurve(GF(p), [0, 0, 0, a, b])`, where `p`, `a` and `b` are decimally represented elliptic curve parameters from the BINK resource.
2) `G = E(Gx, Gy)`, where `Gx` and `Gy` are decimally represented base point coordinates from the BINK resource.
@ -254,7 +255,7 @@ The order of the base point can be computed using SageMath.
3) Insert the factors of the base point order `n` and specify the factor count. It will very likely be `1`, as Microsoft mainly uses primes for their generator orders.
4) Run the tool `<arch> ECDLP Solver.exe <job_name>.txt` and wait until it calculates the private key `k = %d` for you.
Here's an example of the Windows XP job `job_xp.txt` that yields the correct private key for the ECDLP Solver.
**Here's an example of the Windows XP job `job_xp.txt` that yields the correct private key for the ECDLP Solver.**
```pascal
GF := GF(22604814143135632990679956684344311209819952803216271952472204855524756275151440456421260165232069708317717961315241);
@ -267,9 +268,15 @@ FactorCount:=1;
*/
```
And the ECDLP Solver output for it:
**And the ECDLP Solver output for it:**
![ECDLP Solver Output](https://github.com/Endermanch/XPKeygen/assets/44542704/ca018eae-ae33-41e5-a689-2c17da972184)
**Important note:**
Be wary that I could not generate a correct Windows XP x64 key using the private key I've reversed, even using the `Ky` coordinate instead of usual `-Ky`.
For some reason, I also failed to calculate the Windows Server 2003 base point order using SageMath. **I gave it 12 hours to compute on my i7-12700K, but it was still stuck calculating.**
### Validating / generating product keys
The rest of the job is done within the code of this keygen.