For the really smart people out there...I had read somewhere that a pubkey may have 2 X coordinates, maybe 3 X coordinates, can't really remember.
Each pubkey has only 1 X coordinate and 1 Y coordinate. And only 1 private key.
There are 2 pubkeys that share the same X coordinate (for each valid X coordinate) but they have different Y coordinates:
if A = (X,Y) then B = -A = (X, p-Y)
(p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1)
There are 3 pubkeys that share the same Y coordinate (for each valid Y coordinate) but they have different X coordinates:
if A = (X,Y) then B = k*A = (beta*X, Y) and C = k*k*A = (beta*beta*X, Y)
(k = 0x5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72
and beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee)
There are about 2^256 points on secp256k1, (to be precise n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141) and Fp (the field of the coordinates X e Y) has about the same size;
that means that about 1/3 of the all possible values of Y are valid Y coordinates (are coordinates of a point/pub key) and about 1/2 of all the possible values of X are valid X coordinates.
That's all.
So within the Kangaroo program, with a Tame file:
4308F55406236F06FBBB5A328499E9F2787C64AC7779FD387BFBD803C0000000 00000000000000000000000000000000004448E8FD4C2B40AAF6E5C2D6A8A1E5
Are neither one of those the X coord? I read somewhere in this thread, that the above 4308F55406236F06FBBB5A328499E9F2787C64AC7779FD387BFBD803C0000000 was an X coord (034308f55406236f06fbbb5a328499e9f2787c64ac7779fd387bfbd803c0000000). Is that not true?
Because what I was saying, is that I have found the same exact private key, with different tame and wild coords/distances.
Meaning, if I was searching for private key 0x17A57BE2, using the Kangaroo program, I solved with different tame and wild files, example:
first solve tame:
4308F55406236F06FBBB5A328499E9F2787C64AC7779FD387BFBD803C0000000 00000000000000000000000000000000004448E8FD4C2B40AAF6E5C2D6A8A1E5[
first solve wild:
4308F55406236F06FBBB5A328499E9F2787C64AC7779FD387BFBD803C0000000 00000000000000000000000000000000000008E8FD4C2B40AAF6E5C2D6A8A1E5[
second solve tame:
DDD6055558606CB730B603F4ECF20B497A709FECF23671612A742FFBC0000000 000000000000000000000000000000000058D5A2BF77F6FA6D631B606B604BCE
second solve wild:
DDD6055558606CB730B603F4ECF20B497A709FECF23671612A742FFBC0000000 0000000000000000000000000000000000000002BF77F6FA6D631B606B604BCE
those are examples, not the actual wild and tame files I solved the one private key with.
