A riddle wrapped in a curve
As a mathematician (though not a cryptographer), I have a great deal of difficulty trusting cryptographic protocols which have a mathematical basis. Whether they are based on factoring, elliptic curves, or any other mathematical concept, they always "smelled" sketchy to me for the very simple reason that they are easy to formulate in terms of mathematical ideas, hence naturally lend themselves to the thought process of an algebraist or a number theorist. In short, these problems look like precisely the sort of questions a mathematical genius would find tractable. Without any solid proof that they are actually computationally hard to break, it seems like they are inherently dangerous to rely upon because they look like fair game to the next Ramanujan.I'll also go out on a limb here and also say that I think the technology community has a bias towards thinking something like "math == hard" is true, so gives added weight towards using these same protocols. I know many people here have deep knowledge of both cryptography and software development, so I'd be very interested to hear other people's thoughts on these issues. Can anyone speak about options to math-based public key algorithms, or ways to inject some skepticism into the tech community about these algorithms, so perhaps alternatives can start being implemented? A public key algorithm which doesn't lend itself easily to algebraic analysis would feel much safer to me.