From 3e4d8f433239c40311037616b1b8833a06651ae0 Mon Sep 17 00:00:00 2001 From: Arne Schwabe Date: Mon, 16 Apr 2012 19:21:14 +0200 Subject: Initial import --- openssl/crypto/dh/generate | 65 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) create mode 100644 openssl/crypto/dh/generate (limited to 'openssl/crypto/dh/generate') diff --git a/openssl/crypto/dh/generate b/openssl/crypto/dh/generate new file mode 100644 index 00000000..5d407231 --- /dev/null +++ b/openssl/crypto/dh/generate @@ -0,0 +1,65 @@ +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" +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 + + + -- cgit v1.2.3