Yeah, everything i said is in case the key IS even.
If there existed such method to determine whether point is even or odd that would break ecdsa security.
Or if there existed a method to know if a key is 'greater' than a certain key that would break ecdsa security.
If I search a key x in the range [1, ..., 2^80] and I know that the key x is greater than 2^79 too, then I can work only on range [2^79,..., 2^80].
Better: if I know that the key x is a multiple of 3 (it is divisible by 3), then I can remove 2/3 of the possible values.
where one can find your renowned ecc fast library code base?
"renowned"
?I wrote that library 5 years ago to have my version of vanitygen and BSGS.
It's a library tailored to generate a bunch of public keys with same distance very quickly,
like:
1G , 2G, 3G ,4G, ...
or
5G, 15G, 25G, 35G, ...
where G is the generator of the curve.
Each public key is an array of 4 x 64 bit. Each operation is mod p.
I have to clean the code before I can make it public. If I'll have time, maybe by the end of the year.