What about Shor's algorithm? Is this not at least in theory a easy way to break RSA. Only the practical barrier of building a quantum computer capable of cracking practical encryption remains.
Shor's algorithm was found/invented after RSA so for close for two decades there was no known theoretical solution. That did not mean that it was not possible however.
Many of the people who thought it was impossible to break RSA in polynomial time were arrogant, they thought they understood the world much better then they actual did. Many of the people who thought that it was obvious that RSA would one day be solved in polynomial time were also arrogant. You are right it is not possible to decide the answer one way or another, nature can not be bullied. It is however often necessary to take actions before you can not for sure one way or another. So your colleague probably internally transformed his best guess in to a 'fact' so he could act on it. Or maybe it transformed from guess in thought to an utterance of fact out of subconsciousness tendency because it sounds more convincing to most of the audiences he/she has talked to.
To my knowledge Shor's algorithm is currently accepted as correct the exact requirements for a practical quantum computer that can solve today's RSA encryption is still being explored.
Many of the people who thought it was impossible to break RSA in polynomial time were arrogant, they thought they understood the world much better then they actual did. Many of the people who thought that it was obvious that RSA would one day be solved in polynomial time were also arrogant.
Could you quote some of those people? I'm not aware of a lot of knowledgeable people making unwarrantedly strong assertions.
So, the FBI allegedly arranged for a number of backdoors to be built into the OpenBSD IPSEC stack. I don't really know how credible this claim is, but it sparked a discussion in my office about digital security, and encryption in general. One of my colleagues said something to the effect of it only being a matter of time before they found a way to easily break RSA.
It was at about this moment that time stopped.
I responded with something I thought was quite lucid, but there's only so much lay interest that can be held in a sentence that includes the phrases "fact about all integers" and "solvable in polynomial time". The basic thrust of my argument was that it wasn't something he could just decide an answer to, but I don't think he'll be walking away any the more enlightened.
This got me wondering: do arguments that sit on cast-iron facts (or lack thereof) about number theory feel any different when you're making them, compared to arguments that sit on facts about the world you're just extremely confident about?
If I have a discussion with someone about taxation it has no more consequence than a discussion about cryptography, but the tax discussion feels more urgent. Someone walking around with wonky ideas about fiscal policy seems more distressing than someone walking around with wonky ideas about modular arithmetic. Modular arithmetic can look after itself, but fiscal policy is somehow more vulnerable to bad ideas.
Do your arguments feel different?