I know add or substract a point to another (different or equal) but i can't divide a point by any number if i only have the x and y coordinates.
If it's possible can you show me how divide this point by 2 for example ?
you shouldn't think in terms of "divide by 2" but in terms of "multiply by 2
-1" and 2
-1 is defined this way in modular arithmetic:
find x such that 2*x ≡ 1 (mod prime)
the important distinction here is that when you compute (1/2 * point) you are NOT cutting the private key in half. in other words P=(10*G)*2
-1 =/= 5*G
this is all because of how 2
-1 is defined and its value is 57896044618658097711785492504343953926634992332820282019728792003954417335832
(note that the number posted above by @keelperu which is copied from SE which ends with 169 is wrong)
so when you are computing P*2
-1 you are computing P*57896044618658097711785492504343953926634992332820282019728792003954417335832
x = 72488970228380509287422715226575535698893157273063074627791787432852706183111
y = 62070622898698443831883535403436258712770888294397026493185421712108624767191
P(x,y)*2
-1=R(x',y')
x'= 106810878386822850692156427210294299673332011179144735775923143050877434444445
y'= 88851644022983211264145162774930138405176896058716012182199091704714043860842)