Re: What's the latest in factoring? (fwd)

Forwarded message:

> Date: Mon, 09 Feb 1998 13:40:03 -0800
> From: Bill Stewart <bill.stewart@pobox.com>
> Subject: Re: What's the latest in factoring?

> Remember that factoring difficulty is roughly exponential;
> adding logn bits about doubles the cracking workload 
> (depending on which factoring method is being used).  
> Factoring a 1024-bit number is _much_ harder than factoring a 512-bit
> number, and factoring a 2048-bit number is well into age-of-the-universe 
> difficulty level.  The practical level of factoring right now
> is about 512 bits, for either a distributed internet effort or
> an NSA internal one; in the unlikely event that Moore's law lets
> us double processing power 100 times in the next 150 years,
> that means a 1500-bit key could be crackable.  So 2048 bits
> is certainly more than enough for _your_ lifetime.

That depends on what current and near-future medical technology can do
to extend the lifespan of humans. If your assumption is that most folks
younger than about 50 will be dead in 75 years I suspect that you're in for
a nasty surprise. The reason I posted those cc:'s regarding such research is
enough that current estimates of key strength based on human life times need
to be re-evaluated. It is my suspicion that within 10-15 years it will be
possible, as a matter of course in regards employer medical insurance, to
have ones biological clock reset such that the lifespan will be extended 3-4
times with the main limiting factor being cancers. Under those conditions
key strength lifetime computations need to be re-evaluated.



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At 07:05 PM 2/9/98 -0600, Jim Choate wrote:
...
>> an NSA internal one; in the unlikely event that Moore's law lets
>> us double processing power 100 times in the next 150 years,
>> that means a 1500-bit key could be crackable.  So 2048 bits
>> is certainly more than enough for _your_ lifetime.
>
>That depends on what current and near-future medical technology can do
>to extend the lifespan of humans. If your assumption is that most folks
>younger than about 50 will be dead in 75 years I suspect that you're in for
>a nasty surprise. 

That is my assumption, and being wrong would be a highly pleasant surprise.

>The reason I posted those cc:'s regarding such research is
>enough that current estimates of key strength based on human life times need
>to be re-evaluated. 

If Moore's law plus algorithm improvements can give us a 2**150 increase
in processing power over the next 200 years, and I'm around to see it,
I'll be very surprised.  (Or I'll be posthumously surprised, if I'm 
not around.)  On the other hand, if that's true,
we'll be in something like the nanotech singularity, where
eavesdropping will make up for any remaining difficulty in key cracking,
as I'd also discussed.
				Thanks! 
					Bill
Bill Stewart, bill.stewart@pobox.com
PGP Fingerprint D454 E202 CBC8 40BF  3C85 B884 0ABE 4639