Point addition which exceeds field

Let's say we set a secret key integer to be P itself and get the corresponding public point coordinates, X and Y.

Let's say we set another secret key integer to be 100 and also get the public point, X and Y

We can perform point addition on these points and get a resulting point, let's call it (X_res, Y_res). Working from this simple example, how can we get the integer value of the secret key that has (X_res, Y_res) as a public point?

For example, if we do a simpler point addition on the public points that correspond to the secret key integers of 5 and 3, we see that the resulting point is equal to the public point of the secret integer is 8. This agreement between integer space additions and X,Y coordinate point additions seems to not work when the secret key sum (in regular integer space) exceeds P.



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