From: "John Smith" <jsmith58@hotmail.com>
Date: Tue, 26 Aug 1997 00:39:03 +0800
To: cypherpunks@cyberpass.net
Subject: Re: PGP5i supports RSA keys?
Message-ID: <19970825162815.1328.qmail@hotmail.com>
MIME-Version: 1.0
Content-Type: text/plain



>TWAK!
>
>Barring a _severe_ breakthrough in the entire nature of computing, >you 
still
>need at least 1 atom to store one bit of information.  It would take 
>more
>computing power than all the atoms in the world, with the ability to 
>store 1 bit
>on a atom and other dazzling feats of miniaturization, to crack a >2048 
bit key
>barring algorithmic breakthrough.

TWOK!  Au contraire, mon ami...

Breaking a 2048 bit key is approximately 1E16 (10 to the 16th power)
harder than breaking a 512 bit key.  The RSA-129 factoring effort
broke a key of approximately 430 bits using about 6,000 MIPS years.
That is about 2E17 instructions.  Some estimates are that with
current algorithms, a 512 bit key could be broken with not too much
more work.

If so, the total work to factor a 2048 bit key would be roughly
1E33 instructions.

Eric Drexler estimates that with nanotech, it should be possible
to create a 1 GHz processer that fits in 1/8 of a cubic micron.
It would take 1E24 such processors to factor a 2048 bit number.
If we wanted to factor that 2048 bit key in 1E6 seconds, a couple
of weeks, we would need 1E18 processors, which would fit in a cube
100,000 microns on a side.  This is 10 cm on a side, about the
volume of a soccer ball.  A far cry from the whole earth, no?

"John

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