[kevvok]

> But I'm not sure if it works the same way against elliptic curves - or at least you'd probably need a bigger computer to attack the same level of security.

Elliptic curve cryptography is also based on the difficulty of computing discrete logarithms, which makes it vulnerable to Shor’s algorithm. Unfortunately, while the increased difficulty of brute forcing ECC with a classical computer allowed it to use smaller key sizes to achieve security equivalent to older algorithms like RSA, the smaller key sizes make ECC attackable with fewer qubits.