Guys, let's have some fun one more time, a mini-puzzle for puzzle #135

16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v
Thank you Satoshi Nakamoto!
ICVZGMwpPuca4krotcpwEzTyJXBUQF+w25M2TLnFHzIiAKYS+4c6taNLaMM7ZChJ2oMPQXiuzsYDCeF9xZFBMZg=

There is about 280$ in BCH there, so hurry up!

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5577390

Guys, let's have some fun again, I have one more mini-puzzle for you 
There is 0.01 BTC on that address, so hurry up!

03BBF1AFF1B753DFA4C58835C2C135D7D2C7CEA8635D483D37A8997B666CC1FA61
Hint: private key is 1BA27FB025xxxxxxxxxx6F34348EE6B14E9D8A3581C0B01xxxxxxxxxxA90D587

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5538285

Guys, let's have some fun again, I have one more mini-puzzle for you 
There is 0.01 BTC on that address, so hurry up!

03150992937967192EBCD2539E5A949689AC69E6458F9178E7251356FFE079B7F0
Hint: private key is ABCD
where A (lowest bits of privkey) - some 64bit value
B = 2*A
C =  3*A
D = 4*A

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5526453

Guys, let's have some fun again, I have one more mini-puzzle for you
There is 0.01 BTC on that address, so hurry up!

03C8F139DAD58B4786D3649992849733C2A7626F011089E87508CCDF8B0758C493
Hint: It's a strong point so you cannot solve it by kangaroos. But it's a special point, you can solve it easily if you use some feature of secp256k1.

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5522785

Guys, I'm bored today again, so let's have some fun: a mini-puzzle for puzzle #130.
As you requested, this time it's a bit more challenging

Message: Anything one man can imagine, other men can make real
Signature: IIONt3uYHbMh+vUnqDBGHP2gGu1Q2Fw0WnsKj05eT9P8KI2kGgPniiPirCd5IeLRnRdxeiehDxxsyn/VujUaX8o=

There is about 700$ in BCH there, so hurry up!
And thanks to creator of original puzzles (Satoshi??) for a lot of fun!

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5518896

Guys, I'm bored today again, so let's have some fun: a mini-puzzle for puzzle #125.
The key fell and shattered into 12 pieces:

804
E09
77
1C5
225
AC
960
33B
7F0
E4
6BB
48

The order of the pieces is unknown, assemble the key back together!

There is about 500$ in BCH there, so hurry up!
And thanks to creator of original puzzles (Satoshi??) for a lot of fun!

PS. No BS here please, I will remove it.
PPS. For history, previous mini-puzzle is here: https://bitcointalk.org/index.php?topic=5513047

[Part 1]

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 several 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 2.10 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 1.60 for this method.

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 1.30 for this method.
The main issue with this method is that the kangaroos loop continuously.

4 - SOTA v1 (check old versions to see it). This method uses three groups of kangaroos and the symmetry of the elliptic curve.
In practice, K is approximately 1.15 for this method. The main issue is the same as in the Mirror 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.

5 - SOTA v2 (new). This method has same K=1.15 but uses only two groups of kangaroos and the symmetry of the elliptic curve.

6 - SOTA+. This method is the 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.

Guys, I'm bored today, so let's have some fun: a mini-puzzle for puzzle #120.
Here is a priv key for puzzle #120, but I changed three characters randomly.
It's easy to find correct key even if you have minimal skills.

0xB50F22572A497A836EA18AF2E1FC23

There is about 400$ in BCH there, so hurry up
And thanks to creator of original puzzles (Satoshi is it you??) for a lot of fun!

PS. No bs here please, I will remove it.