great discovery in the field of elliptic curves cryptography?

Question

Prof. Adi Shamir says in The Cryptographers' Panel 2016:

i think that NSA has made a great discovery in the field of elliptic curves cryptography and NSA wants to avoid the increased use and growth of ECC, so the NSA's argument of the quantum computer would be a smokescreen.

i know that ECC is faster and better than RSA but my questions:

1. is ECC resistant against quantum computer? i know that RSA isn't!
2. what could be great discovery? is it on implementation?
3. professor shamir says that quantum computers aren't risk for cryptography nowadays(in the near future) but i read in internet that the rate of progression in quantum computer is faster than what was predicted for it. am i true?

note:my main question is 2 ;in another words which aspect of ECC can be a great discovery that this aspect is not clear and known for cryptographers? what does professor shamir talk about?

Answer 1

ECC is not resistant against quantum computers.

Quantum complexity for breaking RSA and ECC are $O(\frac{s^9}{{(\log (s))}^5})$ and $O(s^3)$ respectively. Which $s$ is security level $(80-96)$.

So as SEJPM mentioned in comments, "ECC is less resistant against quantum computers than RSA".

One of newest post quantum cryptographic schemes is isogeny based cryptography, and best known quantum complexity for breaking such schemes is exponential.

Also scientists believe that nowadays, providing such enormous quantum gates is very hard and may be infeasible . So 'quantum computers aren't risk for cryptography nowadays".