The x coordinate and y coordinate are both binary numbers in the range 2256.
the max is also a little bit less than 2
256 but unlike private keys the max is defined by P (the prime) not N (the curve order)
For the curve used for Bitcoin public keys it turns out that for every x coordinate there are two possible y coordinates.
that doesn't depend on which curve is used, as long as it is an elliptic curve it will be symmetrical about the x-axis so for each x there are 2 y values. which is due to the formula being y
2=...
A compressed public key give you the x coordinate and the sign of the y coordinate so in order to convert it to a full public key you have to calculate the correct y coordinate from the x coordinate.
that is not exactly the "sign", the first byte being 2 or 3 indicates if y is even or odd respectively.
we don't actually use any signs in elliptic curve calculations since we are using modular arithmetic. for example if prime is 7 then we have
4 ≡ 11 ≡ 18 ≡ -3 ≡ -10 (mod 7)
by a "contract" we only use the smallest positive number meaning "4"
Thanks, I was trying to be a little less technical for zeilar since he is a total noob - I did not want to overwhelm him.
You points are all well taken. Very good information for the more technical savvy in the audience.
Thank you very much! I do not yet understand, however, where these values consisting of more than 150 SAME numbers come from. Converting hex to dec gives me a string of 77 characters. I could transform the logic to combine the DEC result from the first and the second and it will come out just right :-) but it probably does not work, because these strings usually also appear twice.
I have absolutely no idea how to decipher your post so I cannot help you. Good luck!