Just random idea

Can anyone help to develop tools like BitCrack with GPU fast calculation?
BitCrack version mutate (reform)

for scan puzzle #64

When the process multiplies with a private key each time calculate double and add will get a result to some point
So, I would like to use that point to convert to check the address
and write the result to the file by writing that private key that generates

So we will get a private key that has puzzle 64 address inside
What useful?  it is a point that found use with Pollard's kangaroo to find key
(puzzle64 64 bit may be scan on 72bit or 96 bit or 120bit any your want)

For example puzzle#16 address = 1BDyrQ6WoF8VN3g9SAS1iKZcPzFfnDVieY  (pvk=51510)
In this example puzzle#16 has no pubkey, we never know pubkey

We use this tools to scan  24-bit range will found address 1BDyrQ6WoF8VN3g9SAS1iKZcPzFfnDVieY  inside bit multiply of private key  206047, 824170, 13186582, and more

found address 1BDyrQ6WoF8VN3g9SAS1iKZcPzFfnDVieY   at private key = 13186582  and 206047 at multiply bit 15
15
ECdouble (71261119111627271268814301300816751730184609798722377831958734823956300761978, 59596021694081902311438976720015207351957060174440251698640379092733344351048)

maybe this method can possible use solve puzzle 64

I don't know how BitCrack it works in c++ (I read code but don't understand)
I try on python already but it is very slow

Thank you for advance if can have these tools

I think the operation is


z = Q * modInv(R, N) % N

1.  Modular Inverse R
2.  Q multiply Modular Inverse R
3.  Total Modular N
4.  the result is z

My understanding divided in the Elliptic Curve is not mean  10/2=5 is not divided by normal math
divided in Elliptic Curve = multiply the value with Inverse value  and the result is Modular with N

It is correct or not?
Did I understand wrong?

I just follow this topic about subtracting

how can I use subtracting to find some point that adds a point then the result is pubkey 120?
subtracting is not real subtracting like   9-1=8  and I can add 8+1=9  like this right
this subtracting will be subtracted to another point right
So, pubkey can not do reverse roll back one step before right?

maybe many of you are experts or known an advanced level higher level in knowledge than me
I learn when having some time (I just basic level)

I try to understand
divid pubkey for attack
it is not mean splitting part of pubkey number right ( like   12/4 =3 right )

divide pubkey is multiplication by number is divided number right
divided by using function multiplication same use calculate in privatekey to pubkey right
so the result is a number of multiplication is x,y right
all is always to calculate by elliptic curve medthod like fucntion modinv, add, double, multiplication
first tine I confused subtraction use add (right) , divided use multiplication

sorry just make sure I understand in basic math correct
I am not strong in basic of crypto math, crypto knowledge

many formulas many functions talk by using simbol or short code I not sure what that mean
like "/" divide is divide multiplication  or  *G
sometimes I try to use python code for calculating by manual it not correct with normal math numbers
(I am not an expert to use segemath, I know it is a very good tool but it is difficult to use it)

someday in the future will expose this puzzle is a scam or real
like solve puzzle #115
when puzzle #120 transfers out will see what is key reveal
maybe scam maybe not

101 Blackboard Series on youtube can help explain in real work
try reading python code calculates it is helpful to know easy

from my understand
The first time I see   Q=k*G   look like some math but actually it is a process calculated a lot
multiply it is a one-way flip very long number over 300 time

https://www.youtube.com/watch?v=iB3HcPgm_FI&list=PLzctEq7iZD-7-DgJM604zsndMapn9ff6q&index=18

https://github.com/wobine/blackboard101/blob/master/EllipticCurvesPart4-PrivateKeyToPublicKey.py

I think you know answer, you smart
no, Naver

I am not expert
just test and play some have free time from busy works
waste time maybe better than losing from price crash down for now

It is possible to found key on other range?

my testing with puzzle#32 (32bit key)
all wide 31-32 bit can found key on many point collision

and it can found on 40bit range or higher that key
if on low bit key that pubkey*genpoint can collision on many point on 256bit range

but for puzzle #120 may be can found on range 121 bit or 160 bit

The problem is 120bit is too much wide
 

it is can possible to fine NONCE on R,S,Z value

I think puzzle #64 is NO PATTERN
brute-forcing is brute-forcing should brute-forcing all keys that is BitCrack
There it is can not find the position or rank range of key
ECDSA is chaotic, distribute key is disrupted and chaotic that can say no pattern

BitCrack is brute-forcing private keys
it calculates private key to address directly, so that means needs power to calculate by super fast for 256bitall key

today it is stopping BitCrack power at 64 bit
now it is stuck with the power of hardware

Way can crack the 64-bit key is
1. Use a GPU NETWORK of over 1 million GPU to calculate  (just for 64bit key) it can possible but it has a high cost not worth it
(forget for 120-bit key never can solve with 1 million GPU)
problem COST IS EXPENSIVE

2. Pool 64 bit, it is possible works but needs to have more members to join 1 million members
but the shared pool needs to change who runs GPU high number of the scan will get a high benefit share, need to change to who lucky will get that found to get all this way possible to have member join 1 million users in the same time and have much use run a long time or run high scan number until found key just and idea

(just dream, never happen for now)
3. develop new hardware BitCrack that power than GPU (like making ASIC bitcrack) no one waste time making it

4. Just Dream of BitCrack Quantum (not yet have anyone code BitCrack on Q# or qiskit quantum programming language)
(require basic code of ECDSA SHA-256 RIPEMD-160 Base58 in Q# or qiskit language) maybe waiting next your life

With VanitySearch  engine
Can anyone help to modify BTCCollider to can custom rank search?

https://github.com/JeanLucPons/BTCCollider

if possible I would like to custom start seed from random 256 bit start to any seed want
I would like to start seed from 63bit and 119 bit for both puzzle64 and puzzle120

Maybe, Are you have any script for collecting thousands rsz?
but the problem is it is a 256-bit key not easy and it needs to develop high advance to do
maybe try a test with some brainwallets

but I would like to understand lattice first and how BKZ reduction: block size = 15 , it is works
can possibly use million block size or brute force it
I would like to try to modify the lattice-like use of kangaroo with collision
if not yet understand how it works, can not use it.

What is this BKZ reduction : block size = 15
I test with 4-bit leak nonce and signature between 50-90 set
many key losses and some key can calculate with BKZ reduction : block size = 15 and next untile con recover (some)

I mean, How to know ECDSA has collisions like that?
know from any report/research? or who find out
just would like to know step by step develop on this forum before Pollard's kangaroo ECDLP release
the first version is that python script right and then develop c++ for use GPU with high speed calculate

I do not yet understand your method, maybe you are the next who can find a way to solve some puzzle

Did you try to divide with another number?

I try to find how to divide/sub/multiple/invest with a number under 32 bit for a found range of key (just range not key) but all faile
actually, we did not calculate with 256-bit number but truly we calculated with the number over 786 bit (or maybe 1024 bit level)
all numbers is not easy and can not use random to find a number that can solve it

Thank you WanderingPhilospher

Who can find out they have a collision? How did they find from some testing?

I had not been here when started the puzzle

https://github.com/JeanLucPons/Kangaroo
kangaroo calculate random both tame and wild right?
tame is multiplied with a random number with G
wild is multiplied by ADD PUBKEY(target) with a random number
if both results is the same X that is collision right?
How can control range random of tame?
How can control range random of the wild?
control on Kangaroo 2.2 (use GPU)
(in python kangaroo script I can modify it)



distinguished point (DP)
-d: Specify the number of leading zeros for the DP method (default is auto)
-d dpBit
What mean if use -d ?
-d 32 = distinguished point 32 bit
-d 64 = distinguished point 64 bit
-d 128  = distinguished point 128 bit
(I did not yet understand it)

Thank PawGo, NotATether
I try to use old PC I have it no cost, maybe buy new one cheap mainboard PCI-E 3.0 x16

Another ideas make a DIY eGPU for work with a laptop connect M2 port

Did BitCrack need fast speed for GPU with PCI-E 3.0 (x16)?
I would like to use with mainboard PCI-E 2.0
So, does it is effective to speed GPU or not?

Just in case someone wants to know RSZ more, may be your know already.


(python 2.7)
https://github.com/wobine/blackboard101/blob/master/EllipticCurvesPart5-TheMagic-SigningAndVerifying.py

https://www.youtube.com/watch?v=U2bw_N6kQL8&list=PLzctEq7iZD-7-DgJM604zsndMapn9ff6q&index=19