> Perhaps we understand the fundamentals so well that we can truly say an algorithm today can hold up in a QC world - I have no idea, that certainly sounds bold, but we do already have purported 'quantum hard' algorithms.
We don't have any theoretical proof that we can even encrypt against classical computation. It's still technically an open problem if P=PSPACE (as well as P=NP). All encryption (quantum or not) would be broken if we could effectively solve PSPACE-hard problems.
So really, nobody can truly say any encryption can hold up anywhere. But we still usually have a good idea of the truth of things simply based on empirical evidence - we don't think anybody is proving P=NP, much less P=PSPACE. We don't think people are going to crack our best classical encryption without brute force.
There's not as much empirical evidence that our current quantum encryption will hold up, which is the point of the assertion "it's hard to predict what people will actually do [with shor]"
We don't have any theoretical proof that we can even encrypt against classical computation. It's still technically an open problem if P=PSPACE (as well as P=NP). All encryption (quantum or not) would be broken if we could effectively solve PSPACE-hard problems.
So really, nobody can truly say any encryption can hold up anywhere. But we still usually have a good idea of the truth of things simply based on empirical evidence - we don't think anybody is proving P=NP, much less P=PSPACE. We don't think people are going to crack our best classical encryption without brute force.
There's not as much empirical evidence that our current quantum encryption will hold up, which is the point of the assertion "it's hard to predict what people will actually do [with shor]"