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[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] 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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