I always dreamed finding something unspent on those ID's (04-06-07).
I didn't know the existence of 06 and 07 public key prefix. I wonder where are those prefixes used?
Is there some trick to compute the X value of P + G if you don't know P.y? I'm curious to know.
Q = P+G
Well you need to know the value P.y in order to calcualte the next sequence of Q values but you you don't need to calculate the actual Q.y value, this sound a dubious but actuallly it works and faster than regular approach.
This work better for some array of Q values, if the array is 512 or 1024 items long you can skip the calcualtions of 512 or 1024 Q.y values
You only need to calculate one Q.y value for next group of items and repeat (This value need to be the center of the group becuse it use it use a property that P + i*G and P - i*G have the same deltax and same inverse value), this save alot of time.
It not only works for Q = P+G but for any Q = P+ iG
Its complex and painful but read the code but it worth the time to study and implement it, just to see how the speed increment, maybe i will publish an step by step explatnation for it, but if you want to take a look please check where i learned it:
https://github.com/JeanLucPons/BSGS/blob/master/BSGS.cpp#L189That implementation alone multiply the previous speed x4 times.