Encryption & Prime Numbers

Mark Brownell gizmotron at earthlink.net
Mon Sep 6 20:23:11 EDT 2004

from here:

> The Riemann hypothesis would explain the apparently random pattern of 
> prime numbers - numbers such as 3, 17 and 31, for instance, are all 
> prime numbers: they are divisible only by themselves and one. Prime 
> numbers are the atoms of arithmetic. They are also the key to internet 
> cryptography: in effect they keep banks safe and credit cards secure.
> This year Louis de Branges, a French-born mathematician now at Purdue 
> University in the US, claimed a proof of the Riemann hypothesis. So 
> far, his colleagues are not convinced. They were not convinced, years 
> ago, when de Branges produced an answer to another famous mathematical 
> challenge, but in time they accepted his reasoning. This time, the 
> mathematical community remains even more sceptical.
> "The proof he has announced is rather incomprehensible. Now 
> mathematicians are less sure that the million [prize-see full article] 
> has been won," Prof du Sautoy said.
> "The whole of e-commerce depends on prime numbers. I have described 
> the primes as atoms: what mathematicians are missing is a kind of 
> mathematical prime spectrometer. Chemists have a machine that, if you 
> give it a molecule, will tell you the atoms that it is built from. 
> Mathematicians haven't invented a mathematical version of this. That 
> is what we are after. If the Riemann hypothesis is true, it won't 
> produce a prime number spectrometer. But the proof should give us more 
> understanding of how the primes work, and therefore the proof might be 
> translated into something that might produce this prime spectrometer. 
> If it does, it will bring the whole of e-commerce to its knees, 
> overnight. So there are very big implications."

I fail to see the relationship between a 32 bit word, bitXOR, and 
random padded cypher block chaining having to do anything with Prime 
Numbers. As far as Blowfish goes there doesn't look like there are any 
connections to prime numbers. Perhaps AES openSSL 128 bit encryption is 
based on random prime numbers. Any guesses as to how the above 
information can be considered useful beyond the scope of it being a new 
internet urban legend?


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