Date: Fri, 20 Jan 2012 06:20:17 +0100 From: Michael Niedermayer <michaelni@....at> To: oss-security@...ts.openwall.com Cc: valentino.angeletti@...l.com, bugtraq@...urityfocus.com, tytso@....edu Subject: Re: Re: pwgen: non-uniform distribution of passwords On Thu, Jan 19, 2012 at 11:34:12PM +0400, Solar Designer wrote: > On Thu, Jan 19, 2012 at 09:21:17AM +0100, valentino.angeletti@...l.com wrote: > > may ask you what software (and how it works brute force ecc) you used? > > John the Ripper, indeed - generating a custom .chr file (which is based > on trigraph frequencies) from a sample of 1 million of pwgen'ed > passwords and then using this file to crack another (non-overlapping) > sample of pwgen'ed passwords. My initial notification to oss-security > and Bugtraq included these links, which describe this in more detail: > > http://www.openwall.com/lists/john-users/2010/11/17/7 > http://www.openwall.com/lists/john-users/2010/11/22/5 > http://www.openwall.com/lists/john-users/2010/11/28/1 > http://www.openwall.com/lists/john-users/2010/12/06/1 > > However, as I wrote in a followup posting to oss-security 2 days ago: > > "I might update/revise my analysis on this issue in a few days. > > Specifically, I now suspect that a (large) part of the apparent > non-uniformity of the distribution was in fact an artifact of my > analysis approach. I only analyzed sets of 1 million of pwgen'ed > passwords, so I could not directly check the distribution of full > passwords (1 million is too little, even compared to the small keyspace > of these passwords), whereas JtR only uses trigraph frequencies. > > I am now generating 1 billion of pwgen'ed passwords, which should take a > couple of days to complete. [...]" > > http://www.openwall.com/lists/oss-security/2012/01/17/14 > > This has in fact completed by now: > > $ ./pwgen -1cn 8 1000000000 | dd obs=10M > 1g > 17578125+0 records in > 858+1 records out > 9000000000 bytes (9.0 GB) copied, 147496 seconds, 61.0 kB/s > > And I analyzed this larger sample briefly: > > $ time ~/john/john-1.7.9-jumbo-5/run/unique -v -mem=25 1gu < 1g > Total lines read 1000000000 Unique lines written 697066573 > > real 144m40.619s > user 142m8.727s > sys 0m39.645s > > So that's 697 million unique passwords in 1 billion, which for a uniform > distribution would correspond to a total keyspace size of 1.3 billion: > > $ ./solve 697066573 1000000000 > 1296935185 > > I've attached the solve.c program to this message. [ BTW, I verified > that there's no fatal precision loss in its expected_different() > function (despite of the risky expression) for the value ranges on which > it is called here. I did so by also computing the expected different > value with a different (much slower) algorithm - just not as part of > equation solving (which would be slower yet). ] > > However, let's see what numbers we get for smaller samples (actually, > subsets of the 1 billion sample above, but that's OK in this case): > > Total lines read 100000000 Unique lines written 89163247 > Total lines read 10000000 Unique lines written 9811335 > Total lines read 1000000 Unique lines written 997978 > > $ ./solve 89163247 100000000 > 427419891 > $ ./solve 9811335 10000000 > 261676022 > $ ./solve 997978 1000000 > 246946702 Its also interresting to note that some password lengths are a lot worse than others and that longer does not equal better in some cases $ pwgen -1cn 4 100000 | sort | uniq -u |wc -l 98385 $ pwgen -1cn 5 100000 | sort | uniq -u |wc -l 82589 $ pwgen -1cn 6 100000 | sort | uniq -u |wc -l 96693 $ pwgen -1cn 7 100000 | sort | uniq -u |wc -l 99524 $ pwgen -1cn 8 100000 | sort | uniq -u |wc -l 99954 lucky the default is not 5 [...] -- Michael GnuPG fingerprint: 9FF2128B147EF6730BADF133611EC787040B0FAB The real ebay dictionary, page 2 "100% positive feedback" - "All either got their money back or didnt complain" "Best seller ever, very honest" - "Seller refunded buyer after failed scam" Download attachment "signature.asc" of type "application/pgp-signature" (199 bytes)
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