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[Andy Brown]

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On Mon, 31 Jul 1995, Dr. Frederick B. Cohen wrote:
> I wrote:
>> On Fri, 28 Jul 1995, Dr. Frederick B. Cohen wrote:
>> 
>>> How (specifically) do you know that this is true?  Key generation is
>>> very tricky stuf, and very subtle changes can have very profound impacts.
>>> I doubt that Zimmerman's original was truly perfect at this either, but
>>> how do we really know?
>> 
>> Because I've succesfully run the primes that PGP generates through the
>> primality tests in other mathematical packages, most notably Arjen
>> Lenstra's FreeLIP package.  The remaining steps to generating an RSA
>> keypair are very easy to follow, and the result simple to check by
>> verifying that the components PGP comes up with satisfy
>> ed=1 mod(p-1)(q-1).  rsagen.c is pretty easy to follow if anyone wants to 
>> check for themselves.
> 
> But that doesn't guarantee there aren't weak keys at all.  For example,
> primes of the sort 2^N+1 would pass the primality tests and be very
> weak keys.

As I'm sure you know, PGP picks its primes by choosing a random starting 
point and testing each odd number upwards until it gets a probable 
prime.  The random number generator used to seed this search is mixed 
using MD5 which gives a uniform 1/0 distribution.  I'd hazard a guess 
that the chances of a start point having so many contiguous 1's as to be 
close to 2^N is so vanishingly small that it's more likely a 
non-prime would pass the probabalistic tests!

I suppose if I were really paranoid I'd feed in fixed starting points
for the search to MIT PGP and PGP 2.6.2 to make sure that they come out 
with the same keys.


- - Andy

+-------------------------------------------------------------------------+
| Andrew Brown  Internet <asb at nexor.co.uk>  Telephone +44 115 952 0585    |
| PGP (2048/9611055D): 69 AA EF 72 80 7A 63 3A  C0 1F 9F 66 64 02 4C 88   |
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