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.
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.