i have only one missing part to understand the complete picture.
G is a point on the curve with two coordinates(X,Y), how can you multiply the with a number and end up with a single number(public key) and not with a new point?
What you get is a new point, which is your public key.
There are two possible ways to represent your public key. Either the long one with
04 + x_coordinate + y_coordinate
or (the compressed way) if y is even
02 + x_coordinate
and for odd y
03 + x_coordinate
Your public key is a point in the field. It is just represented in the way I described above. And you can always calculate the x and y coordinates from the compressed format too.
from the public key you can calculate your address, and for that you have to take SHA256 and Ripemod160 hashes. And add a few check bytes to the end...
Thanks for the explenation
when i multiply G with my secret key i get astronomical number, which is not the public key, what am i doing wrong consider those params?
var Gx = 79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
var Gy = 483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
var private key = 845ADD761F80CD7BA8AD296B262939D6191370D286D29D4F06A4F1C9A8DE4E4B
i get this public key which is not the right one
C532FC9C12D71842216394CD94771F9B72302CABD0C5D4CCCF1585131548378D1B9F08218A4E3A0
F5E06D981D74720B8F59235385F25AECE75E6FFA787AF3988DD1D215B39C94994D0600D31C1971E
88CF8623AC07DCB72279CD66038AD281049F0E028D31C40417FDD97364A8D6664AEB3437740CE41
D37928CF956E64E61E8