[WhoCares]

can be done in 3 days if 10 cards of RTX 4090?

I ask Gemini (Antigravity) to read the project source code and doc, it gives the following estimation.

The total computational power required for this project can be estimated very precisely mathematically. By combining the theoretical baseline with the optimizations mentioned in the

README.md
, we can calculate the exact requirements.

1. Baseline Mathematical Scale
This system targets ECDSA-113, which is based on a binary Koblitz curve over the finite field $GF(2^{113})$.

Group Order (Total Points): For a 113-bit curve, the order of its large prime subgroup $n \approx 2^{112}$.
Original Pollard's Rho Difficulty: Theoretically, to find a collision in a group of size $n$, the expected average number of steps is $\sqrt{\frac{\pi \cdot n}{2}}$.
Here, $\sqrt{n} = \sqrt{2^{112}} = 2^{56} \approx 7.2 \times 10^{16}$ (about 72 quadrillion iterations).
2. Massive Dimensionality Reduction via Optimization
According to the

README.md
, this project utilizes extremely powerful mathematical optimizations: "Frobenius + negation canonicalization — 226x search space reduction".

Frobenius Endomorphism: On Koblitz curves over $GF(2^{113})$, this mapping can compress 113 different points into a single equivalence class.
Negation: Utilizing the fact that $P$ and $-P$ belong to the same group, the space is halved again (reduced by a factor of 2).
Total Search Space Reduction: $113 \times 2 = 226$ times smaller.
It's crucial to note that reducing the search space by a factor of 226 means the required number of iteration steps is reduced by a factor of $\sqrt{226} \approx 15.03$.

3. Absolute Computing Power Required (Total Steps)
Combining the above two conditions:

Expected Total Steps $\approx \frac{\sqrt{\frac{\pi \cdot 2^{112}}{2}}}{\sqrt{226}}$
Estimated Result: $\approx 6.0 \times 10^{15}$ steps (That is 6,000 Tera-steps or 6 quadrillion steps).
This is the expected value of the total steps required to break this curve.

4. Conversion to Physical Time
We can plug this astronomical number into the GPU performance benchmarks provided in the

README.md
:

1x RTX 5090 has an approximate speed of ~3.5 G/s (3.5 billion steps per second).
$6,000,000,000,000,000 \div 3,500,000,000 \approx 1,714,285$ seconds $\approx$ 19.8 days.
1x RTX 4090 has a speed of ~2.5 G/s (2.5 billion steps per second).
Estimated time $\approx$ 27.7 days.
1x RTX 3060 Ti has a speed of ~1.0 G/s (1.0 billion steps per second).
Estimated time $\approx$ 69.4 days.
Summary
In the face of modern computing power, a 113-bit elliptic curve has completely lost its security.

Since this is a distributed system, if dozens of hackers or security researchers participate and pool together the equivalent computing power of ten RTX 4090 GPUs, it would take less than 3 days (around 66 hours) to compute the required 6 quadrillion steps globally, triggering a hash collision and capturing the private key.

Originally Posted by cjack

Hey everyone,

I've been working on a GPU-accelerated ECDLP solver specifically targeting Armadillo's ECDSA-113 protection (binary Koblitz curve over GF(2^113)).
The goal: crack the ECDSA-113 certificates used by Encryptionizer (protected with Armadillo) via distributed Pollard's Rho with distinguished points.

Live dashboard: https://ecdlp.protect.cx/