Discrete logarithm

They're single core, and they're single threaded when it comes to doing a job like a merge sort or something like that.

So the only thing it's really good at, which indeed is a magic trick, is going from exponential time algorithm, which is integer factorization or elliptic curve discrete log problem, which I want to mention a little later, shout out to the ECDLP problem, the quantum computers can do those in polynomial time, which is remarkable.

And to a nerd, that's the greatest, coolest magic trick ever.

But to a business person, unless you were in the business of factoring numbers, there's not a whole lot to be excited about here.

So the only thing it's really good at, which indeed is a magic trick, is going from exponential time algorithm, which is integer factorization or elliptic curve discrete log problem, which I wanna mention a little later.

Shout-out to the ECDLP problem.

The quantum computers can do those in polynomial time, which is remarkable, and to a nerd, that's the greatest, coolest magic trick ever.

But to a business person, unless you were in the business of factoring numbers, there's, there's not a whole lot, uh, to be excited about here.

But I think P equals NP is very unlikely, and intuitively it's much more likely that a mathematical object has exactly no exploitable structure, like hashes are intended to Then that a mathematical object has exactly about three forms of exploitable structure for elliptic curves, associativity, Shoof, pairings, and not some secret fourth form of structure we have not yet discovered that greatly degrades its security.

For elliptic curves, ECDLP and pairing security.

Similar for LWE, SVP, RLWE, and the zoo of lattice problems.

For this reason, we do not yet see any reason to worry and start padding the byte size of hashes.