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Slightly tangential but how significant is O(sqrt(n)) speed up? Fast algorithms are slightly faster but intractable algorithms are still intractable?

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It makes memory, not compute, the limit.

It halves the exponent on the number of operations. 2^128 - reasonably secure by todays standards! 2^64 - horribly insecure.

(CAVEAT: where the speedup is applicable, which is often hard.)

2^64 is hardly horribly insecure. Its on the edge of what a gigantic compute cluster can do. So its not secure, but hardly horribly insecure. Especially even if you can get a quantum computter working, its not going to be on the same level of operations that a million dollars in AWS credits will get you. At least not for a very long time.

Besides,in most places where that is an issue, its trivial to switch to 256bit algorithms

> (CAVEAT: where the speedup is applicable, which is often hard.)

Grover's algorithm has pretty wide applicability. Its the exponential speed ups like shor's algorithm that have super limited applicability.

I think the point is it lowers security by a factor of 2 in the exponent. Going from 2^64 to 2^63 lowers the amount of time to bruteforce a key by half.

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