Interesting thing this elliptic curve..
I didn’t think that there are even fractional points on the curve
For ex. if 7/2=3.5
-snip-
There are no fractional points. All points are integer. Your example with integer 7 divided by 2 is not the same in discrete group.
If you divide 7 by 2 you receive not 3.5, but you receive the following integer number:
invert(2) * 7 mod order = 57896044618658097711785492504343953926418782139537452191302581570759080747169 * 7 mod order =
57896044618658097711785492504343953926418782139537452191302581570759080747172So, if you divide
7 by 2 you will receive number 57896044618658097711785492504343953926418782139537452191302581570759080747172 or
0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a4 in hex, and it is
NOT 3.5If you double this number by module order, you will have your initial 7 number:
(0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a4 * 2) mod 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 = 7
The reason is easy. Numbers within the order are no infinite, they are limited to the order. That means they are repeating and could be considered as a
wheel.
Imagine huge wheel with all integers from 0 to 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 (order-1) marked on it. So you can roll it forever for infinite numbers, but all the results will be only within the order, and only integers. Not fractional numbers.