Comment by sehansen
7 hours ago
Given that 15 has already been factored using Shor's algorithm on a real quantum computer, I think we can.
7 hours ago
Given that 15 has already been factored using Shor's algorithm on a real quantum computer, I think we can.
No you really can't. Being able to factor 15 but not 21 with Shor's algorithm is normal. I know it sounds absurd, but it really is that way. Because factoring 21 is about 100x times harder than factoring 15.
See https://algassert.com/post/2500 for details.
My point was that the comparison with nuclear explosions is wonky, since we (in the world of that analogy) already have seen a tiny nuclear explosion 15 years ago. And we kept being told that explosions 100 times larger are just around the corner, but explosions 25% larger are way too hard to expect.
I get that there's a lot of R&D going on to make larger quantum computers a thing and that there's been very definite progress, but factoring 21 is just too hard to expect for now. But that also pushes the date where pre-quantum cryptography is broken further into the future. If we still struggle to factor one of the smaller 5 bit numbers, factoring the 128 bit numbers necessary to break elliptic curve cryptography seems quite far away.