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-From: stewarts@ix.netcom.com (Bill Stewart)
-Newsgroups: sci.crypt
-Subject: Re: Diffie-Hellman key exchange
-Date: Wed, 11 Oct 1995 23:08:28 GMT
-Organization: Freelance Information Architect
-Lines: 32
-Message-ID: <45hir2$7l8@ixnews7.ix.netcom.com>
-References: <458rhn$76m$1@mhadf.production.compuserve.com>
-NNTP-Posting-Host: ix-pl4-16.ix.netcom.com
-X-NETCOM-Date: Wed Oct 11  4:09:22 PM PDT 1995
-X-Newsreader: Forte Free Agent 1.0.82
-
-Kent Briggs <72124.3234@CompuServe.COM> wrote:
-
->I have a copy of the 1976 IEEE article describing the
->Diffie-Hellman public key exchange algorithm: y=a^x mod q.  I'm
->looking for sources that give examples of secure a,q pairs and
->possible some source code that I could examine.
-
-q should be prime, and ideally should be a "strong prime",
-which means it's of the form 2n+1 where n is also prime.
-q also needs to be long enough to prevent the attacks LaMacchia and
-Odlyzko described (some variant on a factoring attack which generates
-a large pile of simultaneous equations and then solves them);
-long enough is about the same size as factoring, so 512 bits may not
-be secure enough for most applications.  (The 192 bits used by
-"secure NFS" was certainly not long enough.)
-
-a should be a generator for q, which means it needs to be
-relatively prime to q-1.   Usually a small prime like 2, 3 or 5 will
-work.  
-
-....
-
-Date: Tue, 26 Sep 1995 13:52:36 MST
-From: "Richard Schroeppel" <rcs@cs.arizona.edu>
-To: karn
-Cc: ho@cs.arizona.edu
-Subject: random large primes
-
-Since your prime is really random, proving it is hard.
-My personal limit on rigorously proved primes is ~350 digits.
-If you really want a proof, we should talk to Francois Morain,
-or the Australian group.
-
-If you want 2 to be a generator (mod P), then you need it
-to be a non-square.  If (P-1)/2 is also prime, then
-non-square == primitive-root for bases << P.
-
-In the case at hand, this means 2 is a generator iff P = 11 (mod 24).
-If you want this, you should restrict your sieve accordingly.
-
-3 is a generator iff P = 5 (mod 12).
-
-5 is a generator iff P = 3 or 7 (mod 10).
-
-2 is perfectly usable as a base even if it's a non-generator, since
-it still covers half the space of possible residues.  And an
-eavesdropper can always determine the low-bit of your exponent for
-a generator anyway.
-
-Rich  rcs@cs.arizona.edu
-
-
-