What can you do with a sufficiently complex quantum computer against Elliptic Curve Cryptography?

I’ve heard that a modified version of Shor’s algorithm can “break” ECC. But what does this mean specifically? What are all the things you can do with this algorithm? Can you:

decrypt messages encrypted with the private key?… Continue reading What can you do with a sufficiently complex quantum computer against Elliptic Curve Cryptography?