Please clarify the below doubt regarding EC point addition and multiplication:
$P$-Generator Point; $a$ and $b$ are integers; $X$ and $Y$ are EC points, defined as follows:
- $X = (a*P) + (b*P)$
- $Y = (a+b)*P$
- Are the points $X$ and $Y$ equal?
- Does computing $X$ take 1 scalar point multiplication (i.e. 0.5 + 0.5),
whereas computing $Y$ takes 0.5 scalar point multiplikations?
- Does $(a*b)*P$ take 1 scalar point multiplication?
- How can an EC-point computation be (equal to?) 1 or 0.5 scalar point multiplications?