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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 |
- |
- |
- |