I have a question regarding the operations performed on an elliptic curve, specifically related to point doubling and point addition. I am trying to understand whether it is possible to determine the order in which these calculations were performed in order to obtain the x and y values of a public key.
To provide some context, in elliptic curve cryptography, point doubling refers to the operation of taking a point on the curve and finding another point on the curve that lies on the same line. This operation involves doubling the coordinates of the point and performing some additional calculations to obtain the new coordinates.
On the other hand, point addition involves taking two points on the curve and finding a third point that lies on the same line. This operation involves adding the coordinates of the two points and performing additional calculations to obtain the new coordinates.
Now, my question is whether there is a way to determine the chronological order in which these calculations were performed
based solely on the resulting x and y values of a public key. In other words, can we determine whether
point doubling or
point addition was performed last to obtain the given x and y values?
Any insights or references to relevant research papers or resources would be greatly appreciated. Thank you in advance for your help!