The basic thrust of my argument was that it wasn't something he could just decide an answer to
If the question was whether prime factorisation was likely to become easy, then probably you'd be justified in saying, essentially, "you don't get to have an opinion!". But since RSA is only an implementation, not a pure essence of mathematics, it might be vulnerable in ways we don't know about yet. It wouldn't be the first time. (Of course your interlocutor might not have intended this interpretation.)
I think this is a good example of a common case, where our certainty concerning ideal objects like mathematics can blind us to the existence of uncertainty in the real world. If someone designs an AI tomorrow and provides a proof of its friendliness, should we implement it?
This question nicely straddles the dichotomy between taxation (which has policy consequences and is somewhat subjective) and modular arithmetic (which has no policy consequences, and "can look after itself").
To clarify, in the discussion in question I was trying to distinguish between software implementations of encryption and the underlying mathematics of those implementations. I am in doubt as to whether my colleague appreciated that distinction.
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?