They're closely related, ECC and RSA are both instances of the hidden subgroup problem.
It kinda does, it just uses them differently
The basis here is the discrete inverse logarithm in a specific group (elliptic curves over rationals or multiplicative group module n)
Hundreds of years ago, it was not unusual to publish an encrypted solution of some mathematical problem, in order to establish priority without disclosing the algorithm that was used.
Of course, at that time very simple encryption methods were used, for instance an anagram of the solution was published (i.e. encryption by letter transposition).
"God doesn't exist" is essentially incoherent. God is the perfect being, and if he didn't exist, he wouldn't be perfect.
I think the logical mistake is obvious.
People want AI to be able to do every good thing but no bad thing, which is impossible twice. First because false positives and false negatives trade against each other, so a general purpose AI which can do anything approximating all the good things is going to have the bias leaning heavily towards being able to do things in general and therefore being able to do many things that are bad. And second because "good" and "bad" aren't things that anybody can agree on and then some people will demand that it must do X while others demand that it not do X (e.g. "help the rebels win the war"), which means someone is inherently going to be unsatisfied and it's not a thing that can be sensibly regarded as everyone working towards a common goal.
... and the world could well have been unsafer. There is pretty strong reason not to release insights which could be used as an attack on public key cryptography. We already know the fix anyway, post quantum cryptography algorithms.
Sometimes scientific curiosity has to step back when it comes to potentially dangerous research. Scott Aaronson recently [1] compared this case to when scientists stopped publishing on nuclear fission research because the possibility of developing an atomic bomb became concrete:
> When I got an early heads-up about these results—especially the Google team’s choice to “publish” via a zero-knowledge proof—I thought of Frisch and Peierls, calculating how much U-235 was needed for a chain reaction in 1940, but not publishing it, even though the latest results on nuclear fission had been openly published just the year prior.