An important point to note, that is not very obvious from the text, is that it is (very, very) difficult to retrieve ka from A=ka.P and kb from B=kb.P. For an attacker who has A and B, it's close to impossible to recover P and ka.kb.P
In the early days of EC you were able to pick a custom base point, and then it was found that this could leak information in various ways. Itβs not allowed in modern curves or implementations.
