Re: Are 2048-bit pgp keys really secure ?

[Hal <hfinney@shell.portal.com>]

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One thing to keep in mind is that other things can go wrong than
Carmichael-like numbers in finding false primes.  You can get hardware
errors.  Here is my estimate of the chance of an undetected memory parity
error.

Let us suppose that a 8 MB PC uses parity protection per byte and gets
one parity error per year of operation.  This is just a guess but I have
occasionally seen parity errors on PC's and I certainly don't use them
full time 24 hours a day for a year!

So the chance of a particular byte getting a parity error in a particular
one-minute period (approximately the time for a key generation) is 1/(8M
* 365 * 24 * 60) or about 2E-13 (2 times 10 to the minus 13).  The
chances of 2 parity errors, which would then be undetected, would be the
square of this, or about 6E-26.  During key generation let us just look
at the data and say that there are about 256 bytes in the active working
set at any time, so the chance of an error in an important byte is about
1.4E-23.

So if your chance of the Fermat test failing is much less than about
10^-23 then you would do better to invest in a more expensive PC than in
improving the test.  And of course there are other hardware failure modes
as well, which should increase this threshold.

Hal

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