[serendipitous]

The mathematics of Shor's algorithm have been known for decades. The challenge is in building the hardware, not in the math.

There are tens of billions of dollars worth of abandoned Bitcoins in addresses with exposed public keys. It would be trivial to get those if you can break ECDSA. Yes, there is much more outside of Bitcoin but I don't see why someone who had this capability wouldn't go after the easy targets first.

[dheera]

Yes, Shor's algorithm would be a feat of quantum computing hardware.

I was referring to if it was possible to break encryption using classical computers in polynomial time -- that would be a feat of mathematics, if it were even possible, and would likely have implications about P vs. NP.