[quote author=joseperal link=topic=1306983.msg63924019#msg63924019 date=1712688187]
Also talking about ID's. I realized the puzzle pieces are alternatively Compressed-02 and 03 only.
[/quote]
It's not like the 02 or 03 were chosen arbitrarily. It's stupid to check for a collision by doing
both 02 and 03. Just stick to the correct parity of the actual Y of the point.
Why? Because if
k is the private key of some point, then the key of its Y-symmetric point is
-k ==
N - k. So the keys of all those other points is in the range [2^256 - 2^66 .... 2^256 - 2^65] which is always outside the interval of interest.
Another short cut is you don't need to calculate the Y value of all the subsequent keys (unless you are scanning for uncompressed keys) this may double the speed of the calculations.
Another short cut is endomorphism (This don't work on small puzzles) but it can multiply your speed up to 6 times for a general search.
Is there some trick to compute the X value of P + G if you don't know P.y? I'm curious to know.
Endomorphism will not work for any puzzle, not just small ones. Same reason as above. Multiplying the key by lambda or lambda^2 instantly lands your key into 256-bit space, no matter what interval you were working on. Even for 160-bit puzzle, the chance that k*lambda or k*lambda^2 ends up back into a 160-bit space is 1 / 2^96.