How Riemann hypothesis would break internet security?

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Discussion Overview

The discussion revolves around the implications of the Riemann hypothesis on internet security, particularly in relation to cryptographic systems like RSA. Participants express curiosity about how the hypothesis could potentially affect security protocols and share their understanding of the topic.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants reference a TV show, "Numb3rs," which suggests that if the Riemann hypothesis is true, it could undermine internet security.
  • One participant argues that the Riemann hypothesis is practically accepted as true since no one has succeeded in falsifying it, implying that if it could break internet security, it would have already happened.
  • Another participant expresses skepticism about the portrayal in the TV show, suggesting it is more of a myth or oversimplification rather than a factual representation of the implications of the hypothesis.
  • A participant explains the connection between prime numbers and the zeros of the zeta function, noting that the Riemann hypothesis posits that these zeros have a real part equal to 1/2.
  • It is mentioned that RSA encryption relies on the difficulty of factoring large numbers, and proving the Riemann hypothesis would not necessarily aid in finding prime factors of RSA numbers.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the claims made in the TV show. While some accept the premise that the Riemann hypothesis could impact security, others challenge this notion, suggesting it is an exaggerated or incorrect interpretation.

Contextual Notes

There are unresolved assumptions regarding the implications of the Riemann hypothesis on cryptographic security, particularly concerning the RSA algorithm and the nature of prime factorization.

Avichal
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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
 
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Avichal said:
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

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.
 
FredericGos said:
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.

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
 
Avichal said:
Ah, why would they show such a thing? I got so excited!

Because it sounds cool. ;)
 
Avichal said:
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

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:

\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

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.
 
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