the advantage is the ability to reach areas where random or sequential will never reach, and each base random number should be pass through transformations, that way is much more powerful
and that includes:
1) binary shifting(depending on the binary string length)
2) hex rotation(or in a binary format)
3) binary reversion
4) binary inversion
this are the 4 basic transforms that perform in nested loops and that no collision and give unique results
you cannot hit the target directly, but you can reach its transformed form
What do you mean by areas that the sequential method can never reach?
in a huge space, there are places where random never reaches....or will reach in a hundred years...
if you do tests, you will see what i am talking about
Damn. Seemed kinda cool until you said that. You lost me there buddy. Please explain.
Its not like flipping a coin, expecting close to a 50/50 EV and not accounting for it landing on its side.
lets say we search a private key of "1abcdef555"
we can go random, and at some point randomize a hex private key like "2bcdef0666"
and we do a rotation downwards
--------------------------
2bcdef0666
|
v
1abcdef555
--------------------------
so each hex char have 16 options from 0 to F
there are 16 different private keys, hitting one of them we do a 16 times rotation of each char and hit the target private key hex
so:
1 A B C D E F 5 5 5
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
2 B C D E F 0 6 6 6
3 C D E F 0 1 7 7 7
4 D E F 0 1 2 8 8 8
5 E F 0 1 2 3 9 9 9
6 F 0 1 2 3 4 A A A
7 0 1 2 3 4 5 B B B
8 1 2 3 4 5 6 C C C
9 2 3 4 5 6 7 D D D - and here we hit the private key we search for
A 3 4 5 6 7 8 E E E
B 4 5 6 7 8 9 F F F
C 5 6 7 8 9 A 0 0 0
D 6 7 8 9 A B 1 1 1
E 7 8 9 A B C 2 2 2
F 8 9 A B C D 3 3 3
0 9 A B C D E 4 4 4
1 A B C D E F 5 5 5 ← back to original
so i call this a
"mirror" of a private key
we can also reverse the hex and do the same
16 vertical rotations + 16 reversed vertical rotations = 32 different private keys hitting which we hit directly the private key hex
this is on vertical
its easy to understand, but how about if we do the same on a "horizontal" shift, depending on the hex length we do a shift by 1 hex char in a cycle so:
abc -> bca -> cab -> abc
this gives us another amount of mirrors (depending on the private key hex length)
so there are "vertical" and "horizontal" mirrors
but wait, how about if we reverse them and do the same? even more mirrors
oh i almost forgot...if we do a binary inversion and repeat the process this doubles the amount of "mirror" keys
do you think by doing this kind of "operations" there is a tiny chance of hitting something?
so i combined all of these in a nested loops
I did a simple python script on CPU to understand this:
https://github.com/puzzleman22/Bitcoin-puzzle-transformations-CPUalso a GPU implementation:
https://github.com/puzzleman22/Bitcoin-puzzle-transformations-CPUits not so fast, because of the transformation operations that create a big divergence between threads on GPU, but it does the "thing"
you can try to use this idea on full range or on bitcoin puzzles
its not random, its not sequential, its a 3D search in the whole space, by applying full transformations
and with enough computational power this can be quite effective
in a binary format its even more accurate, cause it can hit tiny pieces
on hex format is faster, but less flexible
YOU CANNOT HIT THE PRIVATE KEY DIRECTLY, BUT YOU CAN HIT ITS "MIRRORS"