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How Riemann hypothesis would break internet security?

  1. Jul 18, 2013 #1
    I saw this in one of the episodes of Numb3rs - (a T.V. show that describes how math can be used to solve crimes)
    It basically said that if Riemann hypothesis is true then it could break all the internet security. I want to know how.
    I couldn't understand Riemann hypothesis from Wikipedia and other sources so don't throw all the math at me.

    P.S. :- I don't know under which forum this thread belongs. I couldn't find a number theory forum
  2. jcsd
  3. Jul 18, 2013 #2
    It's a TV show. For all practical purposes, the Riemann hypothesis IS true. It just hasn't been proved to be. There are computers out there trying to falsify it 24/7, and they haven't succeeded yet.

    So if it could break internet security, that would have been done a long time ago.
  4. Jul 18, 2013 #3
    Ah, why would they show such a thing? I got so excited!
    Yes if it was true then it would have been broken a long time ago ... didn't think of that
  5. Jul 18, 2013 #4
    Because it sounds cool. ;)
  6. Jul 19, 2013 #5
    I believe this is a modern day math old-wives tale. It stems from the (beautiful) connection between prime numbers and the zeros of the zeta function:

    [tex]\psi(x)=-\frac{1}{2\pi i} \mathop\int\limits_{\gamma-i\infty}^{\gamma+i\infty} \frac{\zeta'(s)}{\zeta(s)}\frac{x^s}{s} ds[/tex]

    That's primes on the left and zeros on the right. Riemann conjectured that the conjugate zeros of the zeta function all have real part equal to 1/2 (Re(z)=1/2).

    Now, one of the most hack-proof security systems used today on computers relies on the RSA algorithm which involves factoring very large numbers: if you know the prime factors, you can compute the number but if you know only the number, very hard to find it's factors if it's a product of two very large primes.

    So that if the Riemann hypothesis is proven, someone will have shown indeed the conjugate zeros are all on the line Re(z)=1/2. However, this information will do nothing towards finding the prime factors of an RSA number.
    Last edited: Jul 19, 2013
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