Quote from: pooya87 on September 11, 2020, 06:09:32 AM

this is all because of how 2^-1 is defined and its value is 57896044618658097711785492504343953926418782139537452191302581570759080747169 because 2 * 57896044618658097711785492504343953926418782139537452191302581570759080747169 ≡ 1 (mod N)
it can be computed using Euclidean algorithm or the simplified 2^(prime-2) mode prime.
now multiplying that with the point we had returns the half point

x = 21505829891763648114329055987619236494102133314575206970830385799158076338148
Y = 98003708678762621233683240503080860129026887322874138805529884920309963580118

Quote from: j2002ba2 on September 11, 2020, 11:13:50 AM

Quote from: pooya87 on September 11, 2020, 03:00:02 AM

why not. private key will tell you how many times to add G to itself. but after you are done and have the value for k*G as point P then you can do whatever you want with that point. for example you can add another G to that point and compute Q=P+G or R=P-G and similarly you can multiply that point with any number like computing S=3*P (the same way you would compute 3*G).
2^-1 is just another number that your point (P or G or Q,...) is multiplied by. you just have to first calculate what integer 2^-1 is in congruence with. to do that you compute its modular multiplicative inverse as i explained above. there is also an example in my second comment with small numbers.

Hum! I'm clearly a noob and i can't get it working..
I'm ok with the concept of multiplicative inverse of 2 --> 57896044618658097711785492504343953926418782139537452191302581570759080747169
But how use this number to half a public key with x and y coordinates ?
I have a lot of difficulty doing research with my broken English, someone can clarify this for me, perhaps with a python code ---> how half public key (private key 10) to get public key (private key 5) Huh

It's now that I realize that mathematics is a profession ^^ lol

Thanks in advance