Solving ECDLP with Kangaroos: Part 1 + 2 + RCKangaroo

[Cricktor]

~~~

How about you learn to use a search engine (e.g. ninjastic.space) or even read a bit in this thread?

It took me barely a minute or two to find this post on the second page here:

Less than 37BTC, check you calculations.
Most of GPU code from RCKangaroo was used for #130.
I spent two months, about 400 RTX4090, I was lucky and solved it twice faster than expected.

[Nuclearkeys]

Thank you for pointing it out.

[bisovskiy]

Hello,

I am facing an issue when trying to calculate the private key at the collision of two checkpoint types. Specifically, I am working with the following pair:

Code:

82B0FB9D086D11223F7FD179 69267708D563F46CEEFFFFFFFFFFFFFFFFFFFFFFFFFF TYPE:0
82B0FB9D086D11223F7FD179 EE651EB9551FDBC41800000000000000000000000000 TYPE:2

For other combinations of types, I am able to successfully recover the private key. However, with this particular pair (TYPE:0 and TYPE:2), I am unable to find or compute the private key correctly.

Could anyone point out where I might be making a mistake? Are there any specific details or differences in the calculation logic when a collision involves TYPE:0 and TYPE:2 checkpoints? Any advice or suggestions on how to troubleshoot this would be greatly appreciated.

Thank you.

[kTimesG]

Hello,

I am facing an issue when trying to calculate the private key at the collision of two checkpoint types. Specifically, I am working with the following pair:

Code:

82B0FB9D086D11223F7FD179 69267708D563F46CEEFFFFFFFFFFFFFFFFFFFFFFFFFF TYPE:0
82B0FB9D086D11223F7FD179 EE651EB9551FDBC41800000000000000000000000000 TYPE:2

For other combinations of types, I am able to successfully recover the private key. However, with this particular pair (TYPE:0 and TYPE:2), I am unable to find or compute the private key correctly.

Could anyone point out where I might be making a mistake? Are there any specific details or differences in the calculation logic when a collision involves TYPE:0 and TYPE:2 checkpoints? Any advice or suggestions on how to troubleshoot this would be greatly appreciated.

Thank you.

Unless it's a bug, in some cases a collision can't solve the private key.

Example: Q is the target point.

Wild1 DP at Q + delta*G = {x, y}
Wild2 DP at -Q - delta*G = {x, -y}

The delta is identical in absolute size, so Q's scalar can't be solved, as all possible points satisfy such an equation.

[bisovskiy]

@RetiredCoder
Hello!
I really appreciate your work and would be grateful if you could clarify a few technical points. I’m sure your insights will be helpful for everyone interested in optimizing this method.

Could you please describe the behavior of the points in the algorithm? Do they always move in one direction, or are there situations where they move towards each other? If they do move towards each other, doesn’t this create a large number of small cycles? Why is the option where points move strictly in one direction until reaching the distance, and then start the path again, not used?

Why, with a smaller DP parameter on the same range, does a collision occur faster, while with a larger DP value, checkpoints are fixed approximately once per second but the collision may take minutes to occur?

How does the DP value affect the probability of a collision? If DP is simply the interval at which collision checks are performed.

Thank you in advance for your explanation, and I look forward to any details you can share!