[tzs]

> Before you start worrying about it though consider that RSA has held up for 47 years of active cryptanalysis so far

True, but is there much overlap between the set of people who actively do cryptanalyses on RSA and the set of people who actively research integer factoring?

As far as I know the skills needed to make progress on integer factoring are not really needed for anything in cryptography other than that specific problem and include a bunch of other skills that have nothing whatsoever to do with cryptography and take a long time to master. It's also been an open and important problem long enough that if it is solved it is likely to be by someone who is a world class expert in it, similar to how Fermat's Last Theorem was finally solved.

Similarly the skills needed for anything in cryptanalysis other than trying to break RSA by factoring are useless for working on integer factoring. The result is that very few, if any, people have the time and ability to become both cryptanalysts and world class integer factoring researchers.

Thus I'd expect nearly all of the 47 years of active RSA cryptanalysis has been on finding and fixing the numerous mistakes that can be made when implementing RSA that allow it to be broken without factoring.

I'd guess it is also similar with the P = NP problem. A solution to that has implications for cryptography but I doubt many cryptanalysts are working on the P = NP problem. Also maybe same for the Riemann hypothesis (I'm not sure if that one has implications for cryptography).