Armadillo ECDSA-113

[cjack]

After 74.5 hours of computation, we successfully extracted the private key for Encryptionizer Certificate #6!!!!!!!!

The collision was found by "Raziel" (RTX 5090) on March 17, 2026 at 22:06 UTC.

The solution is:

k = 0x0000002082DF1821D6E82CEE6880211228

Certificate: #6 of 12 (Encryptionizer / reg3.exe)
BasepointInit: 3254253397 (0xC1F7F755)
Checksum: 0xF4775F5E
Public key (ONB2):
Q.x = 3600264749883462755399490686438491
Q.y = 419754383946908414551514272523181
Curve: GF(2^113) Koblitz (y^2 + xy = x^3 + x^2 + 1)
Subgroup order: 5192296858534827627896703833467507


Statistics:

59 GPU workers (57x RTX 5090 + RTX 4070 + RTX 4070 Ti SUPER)
Peak speed: 32.78 billion iterations/second
210 million distinguished points collected
~7.84 × 10^15 effective iterations
Pollard's Rho with Frobenius canonicalization on GF(2^113) Koblitz curve
Architecture: Custom CUDA solver running on a distributed fleet coordinated by a central Python/FastAPI server. The solver uses table-free GF(2^113) arithmetic, Lopez-Dahab projective coordinates, and per-step Itoh-Tsujii affine normalization — achieving 96 registers, 0 spill on sm_120 (RTX 5090).

Special thanks to WhoCares whose independent audit identified a critical missing optimization (the negation map), which led to the development of v2.2.0 — our "GOLDEN" build that will deliver an additional 41% algorithmic speedup on future certificates. His RTX 4070 also contributed to the search alongside the main fleet.
We will be publishing the complete source code (GPU solver, CPU solver, and distributed server) on GitHub shortly. This includes the full v2.2.0-GOLDEN solver with negation map and fruitless cycle escape, ready for future ECDSA-113 targets.

The journey from a broken 3.5 G/s solver to a production-grade 32.78 G/s distributed system was quite a ride. Every bug caught made the code stronger. Every optimization attempt taught us something about the hardware.