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    RE: IPS security draft: SRP groups (follow-up)



    Upon re-reading previous email on this subject I noticed the memo from Bernard Aboba showing the procedure Dan Simon  gave to find group generators when the moduli that define the group are of the form p-1=2q, q prime, as is the case for the IKE moduli (primes). 
    
    I also now understand that SRP simply requires a true generator (generates all elements of the group) whereas IKE allows the use of 2 which, though misleadingly called a generator, is not strictly speaking a generator. I thought SRP only allowed a subset of generators which made no sense to me. I now realize SRP requires a true generator and it is IKE that allows a non-generator. 
    
    In any case, using Dan Simon's procedure it is very easy to compute generators for any of the IKE moduli and thus I see no problem using IKE moduli as the primary moduli for SRP. The moduli are certifiably prime and the generators are easy to compute deterministically. I have verified that the generators I computed pass the two tests that Dan Simon gave. If there is interest in pursuing this approach I will compute generators for the rest of the IKE moduli.
    
    Vince
     
    
    |-----Original Message-----
    |From: CAVANNA,VICENTE V (A-Roseville,ex1) 
    |Sent: Monday, July 15, 2002 2:02 PM
    |To: 'ips@ece.cmu.edu'
    |Cc: 'tom@arcot.com'; CAVANNA,VICENTE V (A-Roseville,ex1); 
    |'Paul Koning';
    |'Black_David@emc.com'; THALER,PAT (A-Roseville,ex1); SHEEHY,DAVE
    |(A-Americas,unix1)
    |Subject: RE: IPS security draft: SRP groups (resend)
    |
    |
    |I previously hit the Send button when I had meant to hit the 
    |Save button. This is the message I had intended to send.
    |
    |I was unsuccessful at getting Mathematica to prove the 
    |primality of the SRP moduli.
    |
    |If we cannot prove the primality of our chosen moduli I 
    |thought why not use moduli, such as the well known groups from 
    |RFC 2412, whose primality has been proven. Tom Wu told me that 
    |would not be a problem provided we found generators other than 
    |2 (the generator that is given in RFC 2412), because 2 in not 
    |useful (for these moduli) in SRP (I don't know why such is the case). 
    |
    |Using Mathematica I have been able to find other generators 
    |for a couple of the well known groups. The 768-bit modulus 
    |from RFC 2412  has 7 as a generator. The 1024-bit prime from 
    |RFC 2412  has  5 as a generator. I have used the PrimitiveRoot 
    |function in the NumberTheory package of Mathematica. As a 
    |simple (incomplete) verification I have raised the generator 
    |to the power equal to one less than the moduli and have gotten 
    |an answer that is congruent to 1 as would be expected for any 
    |generator. What I can't tell from that simple verification is 
    |if I also get a number congruent to 1 when I raise the 
    |generator to some lower power - which would mean the 
    |"generator" is not really a generator.
    |
    |Vince
    |
    ||-----Original Message-----
    ||From: CAVANNA,VICENTE V (A-Roseville,ex1) 
    ||Sent: Friday, July 12, 2002 9:11 AM
    ||To: 'Paul Koning'; CAVANNA,VICENTE V (A-Roseville,ex1)
    ||Cc: Black_David@emc.com; ips@ece.cmu.edu; tom@arcot.com
    ||Subject: RE: IPS security draft: SRP groups
    ||
    ||
    ||Hi Paul,
    ||
    ||I suspected as much, since I don't have a supercomputer on my 
    ||desktop. Mathematica apparently also has the capability to 
    ||perform a mathematical proof of primality and to produce a 
    ||"certificate" using which Mathematica's results may be 
    ||independently and easily verified. When I attempted to perform 
    ||the proof on the smallest modulus (the one with 768 bits) my 
    ||computer was rendered useless for over 20 minutes which just 
    ||happened to be my threshold of tolerance for this morning. I 
    ||will try again when I leave the office tonight and if I get 
    ||any useful  results I will look deeper into the method.
    ||
    ||Vince
    ||
    ||
    ||
    |||-----Original Message-----
    |||From: Paul Koning [mailto:ni1d@arrl.net]
    |||Sent: Friday, July 12, 2002 7:15 AM
    |||To: vince_cavanna@agilent.com
    |||Cc: Black_David@emc.com; ips@ece.cmu.edu; tom@arcot.com
    |||Subject: RE: IPS security draft: SRP groups
    |||
    |||
    |||>>>>> "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
    |||
    ||
    |
    


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Last updated: Mon Jul 15 23:18:51 2002
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