4 ms·
I think it's because any information we gain about the Riemann Hypothesis (Lindelöf hypothesis is implied by RH) gives us information about the distribution of
by robertelder 8y ago
I think it's because any information we gain about the Riemann Hypothesis (Lindelöf hypothesis is implied by RH) gives us information about the distribution of prime numbers. Any time you gain information about the distribution of prime numbers you immediately gain information that can be applied to any form of cryptography that makes use of prime numbers. You could use this information either to break existing forms of cryptography faster, or apply it to building newer and stronger cryptography.
- hsienmaneja 8y agoSo, people hire you to break into their places... to make sure no one can break into their places?
- QML 8y agoWe already have polynomial-time algorithm for primality testing [1]; not sure if a proof of the Riemann Hypothesis will affect cryptography by that much. [1] https://en.wikipedia.org/wiki/AKS_primality_test https://en.wikipedia.org/wiki/AKS_primality_test
- mtzet 8y agoWhile I agree that a proof of the Riemann hypothesis is unlikely to matter for cryptographical purposes, neither does the AKS primality test. As with many asymptotically efficient algorithms, the constants are simply too large for it to be practical.
- Ar-Curunir 8y agoNo, this is not true. Before this conjecture was proved, you could just assume it was true and see if it would lead anywhere. People already do that with the GRH. If it did have consequences, people would use the resulting algorithm regardless of whether the conjecture was true, because we believe to be almost certainly true. But even if you didn't believe that, you could see if the algorithm was effective by applying it to real world instances.