[zitterbewegung]

Many people in the industry does not think that RSA is crackable due to the assumptions that the Riemann Hypothesis and also the distribution of prime numbers is such a hard problem with a long time of being unsolvable.

A possible mitigation for things like websites would be either ECC or even using the quantum resistant encryption systems (the industry would more likely avoid this due to the systems being very prototypical since we have just started researching this).

Since old bitcoin wallets can’t be moved off of RSA you can transfer the coins to your wallet and there is no mitigation.

[red_trumpet]

I don't see how proving the Riemann Hypothesis would help cracking RSA? If it helps, couldn't you just assume it is true and start cracking RSA today? If you ever hit a point where it doesn't work then BOOOM: Riemann Hypothesis disproven!

[tzs]

I think it is the other way around--disproving the RH might break some things.

Most mathematicians believe RH is true, and generally when doing industrial number theory people operate under the assumption that RH is indeed true and so if they need to use X to justify something and there is a theorem of the form "if RH is true then X" they use X.

Thus a proof of RH is not a problem. It just confirms that what people applying number theory already assumed was correct.

A disproof means that those X's might not be true and their use would need to be reassessed.

[AnotherGoodName]

RSA was once 128bits and today has to be 2048bits minimum to be secure because it was essentially broken multiple times. There used to be 128bit rsa encrypting hardware that now doesn’t work at all to protect data due to previous mathematical breakthroughs.

The congruence of squares equivalence to factorization demonstrated we need at least 500 bits and then the special number field seive that built on this push it to 1024. The general number field seive pushed it again to 2048.

Sure it’s not a log(n) break but it’s been broken. If you look at the complexity analysis of the special vs general number field seive the portion of the exponent going from 1/2 to 1/3 should give you thought. Can it be moved to 1/4? Could it be moved indefinitely to 1/x? The general number field seive is relatively recent. If someone comes up with a similar breakthrough again (and this has happened many times over with rsa) your 2048bit keys won’t be secure just as your 128bit rsa keys from the past are no longer secure.