112-bit prime ECDLP solved

james hughes hughejp at mac.com
Thu Jul 16 20:51:09 EDT 2009

On Jul 14, 2009, at 12:43 PM, James A. Donald wrote:

> 2033	130
> Subsequent expansions in computing power will involve breaking up  
> Jupiter to build really big computers, and so forth, which will slow  
> things down a bit.
> So 144 bit EC keys should be good all the way to the singularity and  
> a fair way past it.

"Prediction is very difficult, especially about the future".

I have researched the possibility of 50 or 100 year key sizes. All we  
have to do is look back 50 years to the (unbreakable) Enigma, and 30  
years to the famous Sci.Am article by Rivest that said it would take  
40 quadrillion years to break the challenge, which actually took 25,  
or more recently, or FEAL, or RC-4 (WEP), or MD-5, or SHA-1, or, or  
need I say more?

If we assume that all knowledge to be discovered has been discovered,  
and all mathematical insight humanity is capable of has been achieved,  
you are correct that 144 bit EC keys are "good all the way to the  
singularity" (which actually depends on the Hubble constant, but I  
digress) and that "everything that could be invented has been invented."

I believe it is folly to suggest that 144 bit keys will never be  
broken. Frankly, I hope to see the day.


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