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Path: euryale.cc.adfa.oz.au!newshost.anu.edu.au!newshost.telstra.net!act.news.telstra.net!psgrain!usenet.eel.ufl.edu!newsfeed.internetmci.com!bloom-beacon.mit.edu!senator-bedfellow.mit.edu!lola-granola.MIT.EDU!ghudson From: ghudson@mit.edu (Greg Hudson) Newsgroups: comp.os.linux.misc,comp.os.linux.development.system,comp.os.linux.networking,comp.unix.bsd.bsdi.misc,comp.unix.bsd.netbsd.misc,comp.unix.bsd.freebsd.misc Subject: Re: need secure OS to entrust millions to Followup-To: comp.os.linux.misc,comp.os.linux.development.system,comp.os.linux.networking,comp.unix.bsd.bsdi.misc,comp.unix.bsd.netbsd.misc,comp.unix.bsd.freebsd.misc Date: 11 Mar 1996 04:54:03 GMT Organization: Massachvsetts Institvte of Technology Lines: 52 Message-ID: <4i0blb$g2m@senator-bedfellow.MIT.EDU> References: <4gi6t6$3h9@lace.colorado.edu> <nc0453Dn96w6.93F@netcom.com> <4hhp71$cv9@senator-bedfellow.MIT.EDU> <4hsun4$d3h@park.uvsc.edu> NNTP-Posting-Host: lola-granola.mit.edu X-Newsreader: TIN [version 1.2 PL2] Xref: euryale.cc.adfa.oz.au comp.os.linux.misc:91033 comp.os.linux.development.system:19114 comp.os.linux.networking:31313 comp.unix.bsd.bsdi.misc:2613 comp.unix.bsd.netbsd.misc:2434 comp.unix.bsd.freebsd.misc:15277 Terry Lambert (terry@lambert.org) wrote: : Your definition is predicated on the obscurity of a fast-factoring : algorithm. : Is it your claim that such an algorithm is impossible? No. Factoring is a problem theorized to be hard, but there's not currently any proof of this. Of course, there's nothing special about factoring as a mathematical problem, except that it's been heavily analyzed by the academic community. Coming up with an IDEA secret key given a known plaintext is also a mathematical problem, which hasn't been analyzed nearly as much. : I refer you to Godel's Theorem. You're confused. If you think you're not confused, please explain the relevance of Godel's First (or Second) Incompleteness Theorem to this problem. You may assume that I'm familiar with the theorem. : Typical "security through obscurity" is hiding a key in a : search space, but not securing the location of the key itself. If you honestly believe that that is the common definition, then I'd appreciate it if you'd provide a reference. Certainly, it is not what the poster I responded to was referring to by "security "security through obscurity." : You see, I believe the NSA already has fast-factoring : capability based on the questions Robert Morris Senior (formerly : of the NSA) posed at a recent security conference. I'm happy that you know how to speculate. I can speculate that the NSA has a way to break any cryptosystem you come up with except one-time pads. : All that's required to crack RSA is massive parallelism and a : willingness to epend the effort, and that's assuming nothing : more than a brute-force attack. If, as the key size increases, the effort required to break a cryptosystem expands sufficiently faster than the effort required to use the cryptosystem legitimately, then there will always be a key size which will defeat an arbitrarily amount of parallelism and time. Back-of-the-envelope calculations suggest that a 1024-bit product of two primes would require absurd amounts of time to factor even if every particle in the known universe were a supercomputer. Of course, if you speculate that the NSA has arbitrarily good factoring algorithms, you will never find a satisfactory key size.