Quote from: vjudeu on Today at 11:00:47 AM

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Therefore, there is probably a different "infinity" point for each pair (-k*G, k*G), which is in accordance with the fact that addition of x-axis symetrical points forms parallel lines.

No, the point is the same. For every public key Q you have nQ=O, where O is the infinity point (0,0). If you have different results, then (as _Counselor mentioned) "you should check your calculations". For two points, where you have d and (-d), your y-value of the public key after addition should be equal

Aditions of the pairs (-k*G, k*G) gives each time a different (x,y) result, so please don't add entropy to the discussion.

Maybe the zero infinity point is just an abstract notion and therefore we are not allowed to calculate (-k*G + k*G) as a normal addition.

Yet, having -1*G + 1*G = N*G could help finding a relationship with -k*G + k*G that gives a point with arbitrary-looking cooridnates. An example was given with k=2.
Any help is welcome after verification.