> i wonder why anyone thinks open problems in number theory are a sound means of crypto The short answer is that the numbers are so large that with current sta

> i wonder why anyone thinks open problems in number theory are a sound means of crypto The short answer is that the numbers are so large that with current state of the art means (which I'm sure you know a lot about), factoring a 2048 bit number takes around 1000 years and 4096 bit keys takes about 2^32 times more years. Even if computers get faster every 10 years, you can see that it won't improve much. That's why we use number factoring for crypto; because it takes so long to break. However, as you've pointed out, since the problems are open, the calculations are meaningless. And of course all this analysis goes out the window with quantum computers. But the unfortunate truth (the "biggest embarrassment of computer science" as Dan Boneh calls it) is that we don't actually have any proof that security exists. All crypto is built on open problems. So better choose open problems that's been open for a long time.