RE: IPS security draft: SRP groups

[Paul Koning <ni1d@arrl.net>]

>>>>> "vince" == vince cavanna <vince_cavanna@agilent.com> writes:

 vince> Hi David, I can't prove so, but Mathematica from Wolfram
 vince> certifies as prime (in a matter seconds) all five moduli
 vince> specified in the iSCSI security draft for use in SRP! I used
 vince> the PrimeQ built-in function. PrimeQ first tests for
 vince> divisibility using small primes, then uses the Miller­Rabin
 vince> strong pseudoprime test base 2 and base 3, and then uses a
 vince> Lucas test. I have not explored the nature of these tests.

Miller-Rabin is a probabilistic test.  As for "Lucas" -- the Handbook
of Applied Cryptography lists "Lucas-Lehmer primality test for
Mersenne numbers".  That suggests that this test has no meaning for
numbers that aren't Mersenne numbers (such as randomly chosen
numbers). 

So I think you have a probabilistic primality test here, similar to
what Tom did.  That's certainly useful confirmation, but it doesn't
sound like we have the primality proofs yet.  (Unfortunately, HAC is
not sufficiently helpful in pointing to an algorithm to to so...)

    paul