[texaslonghorn5]

> rising to the non-associative power indices ... in the last two decades has been analyzed and does not have a quantum polynomial algorithm that solves it. The problem is called Exponential Congruences Problem.

The author uses similar wording a couple times and it is a little ambiguous? Does "does not have" mean a superpolynomial quantum lower bound has been discovered for this algorithm (or is there a reduction to some other important conjectured complexity theorem)? Or is it just that a polynomial algorithm has not been discovered yet?

[jmount]

Yeah, knowing there is no poly-time quantum algo would be as big as showing P!=NP. If it is "no known" algo, it is well known not to use the stronger wording. Outside of oracle results an "at least this hard result" is a big deal.

[tromp]

There is indeed no excuse for saying "there is no" when they mean "there is no known"

It's almost as bad as saying that NP stands for Non Polynomial time.

[opheliate]

It’s probably worth remembering this is a pre-print of the paper. This is the kind of thing that would be corrected when actually published.

[cryptonector]

It could be a translation error. The author clearly does not speak English as a first language.