5 ms·

What exactly is the application for cyber security? How does this affect cryptography?

zitterbewegung 8y ago
Nothing because it doesn’t show a method about the distribution of prime numbers but it says that given the Riemann hypothesis is true then the leinhoff problem is true .
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 ago
  So, people hire you to break into their places... to make sure no one can break into their places?
  - deleted 8y ago
    [deleted]
  - dmichulke 8y ago
    AKA pentesting
  - zinckiwi 8y ago
    A Sneakers quote. Worth watching for Hollywood's take on the early 90s version of our current social media/social engineering quagmire.
- QML 8y ago
  We 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 ago
    While 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 ago
  No, 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.
popcorncolonel 8y ago
Pretty much all of the relationship to practical stuff in papers like this related to the RH are "it gives us information about the prime numbers, and those are used in cryptography". It's really just about getting people to perk their ears up rather than true implications about crypto.
myWindoonn 8y ago
I can't point exactly to any particular thing, but I can tell you how to identify them! The magic words are "Assuming the Riemann Hypothesis..." Any time you see somebody say "We assume RH," or "assuming RH," then any stepping stone to RH makes this assumption more reasonable/likely/anticipated. At this point many working mathematicians will hold opinions like "RH is true" or "RH is true or there's a Siegel zero" so this is kind of like assuming plate tectonics in a seismology paper, or assuming human interference in the atmosphere in a climatology paper. In cryptography, the only times I can recall having seen it, they meant only "assuming the primes are remarkably well-behaved in their distribution." The primes are empirically remarkably well-behaved, including in the neighborhoods of typical RSA keys. So this is not surprising or unexpected, and improvements on RH should only reinforce our confidence in our empirical techniques.

Nothing because it doesn’t show a method about the distribution of prime numbers but it says that given the Riemann hypothesis is true then the leinhoff problem is true .

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 ago
So, people hire you to break into their places... to make sure no one can break into their places?
- deleted 8y ago
  [deleted]
- dmichulke 8y ago
  AKA pentesting
- zinckiwi 8y ago
  A Sneakers quote. Worth watching for Hollywood's take on the early 90s version of our current social media/social engineering quagmire.
QML 8y ago
We 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 ago
  While 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 ago
No, 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.

popcorncolonel 8y ago

Pretty much all of the relationship to practical stuff in papers like this related to the RH are "it gives us information about the prime numbers, and those are used in cryptography". It's really just about getting people to perk their ears up rather than true implications about crypto.

myWindoonn 8y ago

I can't point exactly to any particular thing, but I can tell you how to identify them! The magic words are "Assuming the Riemann Hypothesis..." Any time you see somebody say "We assume RH," or "assuming RH," then any stepping stone to RH makes this assumption more reasonable/likely/anticipated. At this point many working mathematicians will hold opinions like "RH is true" or "RH is true or there's a Siegel zero" so this is kind of like assuming plate tectonics in a seismology paper, or assuming human interference in the atmosphere in a climatology paper. In cryptography, the only times I can recall having seen it, they meant only "assuming the primes are remarkably well-behaved in their distribution." The primes are empirically remarkably well-behaved, including in the neighborhoods of typical RSA keys. So this is not surprising or unexpected, and improvements on RH should only reinforce our confidence in our empirical techniques.