[meta_AU]

I'm not really following the trapdoor reasoning. Both RSA and elliptic curves are based on having a system where 'exponentiation' commutes and the 'logarithm' is computationally difficult. RSA only needs the two generator primes to make finding the 'inverse' of the e exponent computationally tractable, once that is done the 'trapdoor' isn't used any more. There isn't an equivalent of that in elliptic curves in my understanding of them.