Hi all,

Here is my research about using kangaroo methods to solve ECDLP, Part 1.
Open source:  https://github.com/RetiredC/Kang-1

This software demonstrates various ways to solve the ECDLP using Kangaroos.
The required number of operations is approximately K * sqrt(range), where K is a coefficient that depends on the method used.
This software demonstrates fourfive methods:

1 - Classic. The simplest method. There are two groups of kangaroos: tame and wild.
As soon as a collision between any tame and wild kangaroos happens, the ECDLP is solved.
In practice, K is approximately 2.110 for this method.

2 - 3-way. A more advanced method. There are three groups of kangaroos: tame, wild1, and wild2.
As soon as a collision happens between any two types of kangaroos, the ECDLP is solved.
In practice, K is approximately 1.760 for this method, but it can be improved to 1.6 if the range of tame kangaroos is reduced.

3 - Mirror. This method uses two groups of kangaroos and the symmetry of the elliptic curve to improve K.
Another trick is to reduce the range for wild kangaroos.
In practice, K is approximately 1.3530 for this method.
The main issue with this method is that the kangaroos loop continuously.

4 - SOTA. This method uses three groups of kangaroos and the symmetry of the elliptic curve.
In practice, K is approximately 1.2315 for this method. The main issue is the same as in the 3-wayMirror method.
I couldn’t find any papers about this method, so let's assume that I invented it
See "diagram.jpg" for details. Also there are several other good option sets, one of them is used in the application by default, check the sources.
Important note: this software handles kangaroo looping in a very simple way.
5 - SOTA+. This method is bad for large ranges higher than 100 bitsthe same as SOTA, but also uses cheap second point.
When we calculate "NextPoint = PreviousPoint + JumpPoint" we can also quickly calculate "PreviousPoint - JumpPoint" because inversion is the same.
If inversion calculation takes a lot of time, this second point is cheap for us and we can use it to improve K.
Using cheap point costs only (1MUL+1SQR)/2. K is approximately 1.02 for this method (assuming cheap point is free and not counted as 1op).
Or you can pay 1MUL+1SQR and get K about 0.99 (preferable for GPU implementation).
Or you can pay only (1MUL+1SQR)/4 and get K about 1.05.
Again, I couldn’t find any papers about this method applied to Kangaroo, so let's assume that I invented it.

Important note: this software handles kangaroo looping in a very simple way, this method is bad for high ranges.
Next part will demonstrate a good way to handle loops.

PS. Please don't post any stupid messages here, I will remove them; also don't post AI-generated messages and other spam.

Hi all,

Here is my research about using kangaroo methods to solve ECDLP, Part 1.
Open source:  https://github.com/RetiredC/Kang-1

This software demonstrates various ways to solve the ECDLP using Kangaroos.
The required number of operations is approximately K * sqrt(range), where K is a coefficient that depends on the method used.
This software demonstrates four methods:

1 - Classic. The simplest method. There are two groups of kangaroos: tame and wild.
As soon as a collision between any tame and wild kangaroos happens, the ECDLP is solved.
In practice, K is approximately 2.1 for this method.

2 - 3-way. A more advanced method. There are three groups of kangaroos: tame, wild1, and wild2.
As soon as a collision happens between any two types of kangaroos, the ECDLP is solved.
In practice, K is approximately 1.7 for this method, but it can be improved to 1.6 if the range of tame kangaroos is reduced.

3 - Mirror. This method uses two groups of kangaroos and the symmetry of the elliptic curve to improve K.
Another trick is to reduce the range for wild kangaroos.
In practice, K is approximately 1.35 for this method.
The main issue with this method is that the kangaroos loop continuously.

4 - SOTA. This method uses three groups of kangaroos and the symmetry of the elliptic curve.
In practice, K is approximately 1.23 for this method. The main issue is the same as in the 3-way method.
I couldn’t find any papers about this method, so let's assume that I invented it

Important note: this software handles kangaroo looping in a very simple way.
This method is bad for large ranges higher than 100 bits.
Next part will demonstrate a good way to handle loops.

PS. Please don't post any stupid messages here, I will remove them.