Re: Are 2048-bit pgp keys really secure ?

-----BEGIN PGP SIGNED MESSAGE-----

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

-----BEGIN PGP SIGNATURE-----
Version: 2.6

iQBVAwUBLwGdahnMLJtOy9MBAQGolwIAzZFbwVx0pqLV3MgQrBYOWELISIsVgj5g
BywmOcdqDZiqPAi+gTqR4C/zZQnHgLnnsxDH45OBcaVDHv8D4uSvjQ==
=6YIb
-----END PGP SIGNATURE-----

On Dec 28, 12:04pm, Hal wrote:
> 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!

Just a mostly-irrelevant aside...

A somewhat disturbing trend has appeared in the low-end cost-sensitive PC
SIMM market.  Some supposedly 9-bit SIMMs are actually 8-bit SIMMs plus
a parity generator.  This means that the parity checking is essentially
subverted, because the parity bit is generated from the stored contents
of memory at read time, rather than the stored contents when it was
written to.  As such, NO bit errors are detected.

These SIMMs are almost all being produced in Taiwan, and many have the
parity generator marked so that the chip appears to be another DRAM.
It is worth watching out for.

Why are they doing this?  Well, parity generators are much cheaper than
the extra DRAM, and so the manufacturers are saving 15-20% on the production
price.

							Ian.

> 
> A somewhat disturbing trend has appeared in the low-end cost-sensitive PC
> SIMM market.  Some supposedly 9-bit SIMMs are actually 8-bit SIMMs plus
> a parity generator.  This means that the parity checking is essentially
> subverted, because the parity bit is generated from the stored contents
> of memory at read time, rather than the stored contents when it was
> written to.  As such, NO bit errors are detected.
> 
> These SIMMs are almost all being produced in Taiwan, and many have the
> parity generator marked so that the chip appears to be another DRAM.
> It is worth watching out for.
> 
> Why are they doing this?  Well, parity generators are much cheaper than
> the extra DRAM, and so the manufacturers are saving 15-20% on the production
> price.
> 
> 							Ian.
> 
	There is, or was a couple of years ago, another reason for this. 
One of the major SIMM patents is for SIMMs with parity and does not
apply to SIMMs without (a matter of how the claims were phrased), so
companies that don't want to pay royalties to Wang in the US (the owner
of MOST SIMM patents) have used this trick not primarily to cut product
cost but to aviod paying royalties (something like 5%).