Some stuff about Diffie-Hellman (and more :-)

[hughes@ah.com (Eric Hughes)]

>Indeed, a paper has been published on how to break Sun Secure RPC
>based on the idiotic decision by someone at Sun to standardise the
>modulus used. 

It wasn't standardization that was the problem.  The Sun modulus was
just too small.  My take on the idiocy was that the designers were
assuming that because they didn't know how to break such a large
modulus, that no one else did either.

>The suggestion by Mr. Cain to use a
>single generator and modulus for all traffic is astonishingly naive.

It's not naive (as such), it's just that any such modulus must be chosen with
extreme care.

Here are some very basic rules of thumb:

-- Don't use a 2^k modulus.  In addition to the exponentiation taking
place faster, they're much easier to break.

-- Use a single large prime p for the modulus of size > 600 bits.

-- Make sure that you can prove that your generator actually generates
the group.  This requires knowing the factors of p-1.

Burt Kaliski told me that he picked a D-H modulus by searching for a
pair of primes < q, p=2q+1 >.  It took a _long_, _long_ time, but it
was then easy to show that the element 2 generated the group.  It may
be that there is a clever attack based on the generator 2, but I
haven't seen one published.

Eric