1aqp

I'd say: you are absolutely using the right tool. :-)

Hear! hear!

NO! It would not be cool.

I like programs to work on an off-line computer.

Sorry, I wrote that comment too quickly. It is close to impossible to recover ka, kb and ka.kb.P, even given A=ka.P, B=kb.P and P.

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