I'm not convinced on the first part. That it won't be broken by improvements to prime factorization. https://www.ams.org/notices/199612/pomerance.pdf https://w

I'm not convinced on the first part. That it won't be broken by improvements to prime factorization. https://www.ams.org/notices/199612/pomerance.pdf https://www.ams.org/notices/199612/pomerance.pdf has a great writeup on the history of the work around this. Essentially when you see improvements in complexity of the form Old best: Quadratic Sieve: exp(c(log n)^1/2(log log n)^1/2) New best: General Number field sieve: exp(c(log n)^1/3(log log n)^2/3) I can't help but feel that's an exponent there that we've moved to 1/3 that could be moved further. Sure we don't know how and we've been stuck here on the current best for just over 25 years but i just feel that if you give me two methods and one moves a term like that there's a good chance there's a way to reduce that term further. It'd be weird for that complexity statement to stay as is. That's telling me "the universe doesn't allow factorization any faster than a term that's raised to a power of 1/3rd" and i'm asking "why is 1/3 so special?". So i'm not convinced that there's not more here. I don't have a clue how of course. But the history of RSA going "256bits is secure" to 512bits to 1024bits to 2048bits being needed has me worried about the safety of prime factorization.