Does a solution to the Riemann hypothesis render RSA encryption obsolete? [pdf]

http://phys.lsu.edu/~fmoxley/fieldsMedalSymposium.pdf

by padic • 9 years ago

2 4 9 years ago

phys.lsu.edu

padic• 9 years ago

A very major threat to RSA encryption would be a solution to the Riemann hypothesis. If a solution is found, prime numbers would be too easy to find, and RSA would fall apart. Undoubtedly, much more sophisticated algorithms than RSA will continue to be developed as mathematicians discover more in the fields of number theory and cryptanalysis.

godelmachine2• 9 years ago

Hi, I read on Wikipedia entry of "P versus NP problem" - if its proved that P=NP, then any kind of encryption can be broken. How true is that? Thanks.

YomiK• 9 years ago

This is incorrect.

"prime numbers would be too easy to find" -- they're already really easy to find. Factoring large semiprimes is currently hard. Primality testing and finding primes for RSA keys is very easy. If the RH was proven true, it wouldn't speed that up in any practical way either.

As an experiment, assume the Riemann Hypothesis. Does that make factoring easier? No. Do we have any currently known methods of weakening RSA if the RH was true? No.

For some actual consequences of the RH: https://mathoverflow.net/questions/17209/consequences-of-the...

godelmachine2• 9 years ago

A small note to future viewers - This PDF does not mention anything about solution being a threat to the RSA encryption. It provides a mathemetical proof for something which I couldn't comprehend.

Also, on a quite unrelated note - won't any kind of encryption be obsolete of it is proved that P=NP. I read this two days ago on the Wikipedia entry of "P versus NP problem" in the "Consequences" part.

Does a solution to the Riemann hypothesis render RSA encryption obsolete? [pdf]

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