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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
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