-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Casper.Dik@xxxxxxx wrote: >>The case where N = 1 is simple authentication; the case where N = M is >>an easily solvable problem in the scope I'm looking at. I'm interested >>in the case where N > M and the data is encrypted. >> >>- Key is fragmented >>- Fragments are indpendently encrypted >>- Each user who can authenticate can decrypt PART of the key, but not >>all of it >>- M of the N users are needed to decrypt enough of the key to access >>the key in total > > > When you fragment the key as you propose, there's a danger of making > the remaining fragment bruteforcable by "M-1" users as they're > left to guess only 1/Mth of the key. > > I'd argue the best way is to give each of the M users a bit > vector the length of the key and XOR the M vectors to get > the key vector. This way, the security of the key is as strong > whether you have 1 , 2 .. upto M-1 fragments. (Of course, > you should also require each of the users to decrypt their > key vectors) > Yeah I noticed that on the wikipedia :) http://en.wikipedia.org/wiki/Secret_sharing > Effectively, none of the users know any key bits by themselves. > > >>The problem is that I need a guaranteed way to create data for any valid >>N and M where N >= 3 > M >= 2 in which access to M fragments of the key >>(each fragment is encrypted) can be used to gain access to the rest of >>the fragments, which in turn allows any selection of M users to >>authenticate and gain physical access to the key. > > > Exponentional might not be bad if you know that the numbers > will be small; in O(N^M) space a solution is trivial. > I actually was looking around and found secret sharing and shamir's scheme, which look interesting. :) I understand the math behind it vaguely, which is good; how exactly to do finite fields and generate polynomials I can regress of any arbitrary degree 1..+inf uhh. Bearing in mind I have no practical use for this, it's still interesting. > Casper > - -- All content of all messages exchanged herein are left in the Public Domain, unless otherwise explicitly stated. Creative brains are a valuable, limited resource. They shouldn't be wasted on re-inventing the wheel when there are so many fascinating new problems waiting out there. -- Eric Steven Raymond -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.2.5 (GNU/Linux) Comment: Using GnuPG with Thunderbird - http://enigmail.mozdev.org iD8DBQFCFy5FhDd4aOud5P8RAlz2AJ0aitdjpF6vNAFIWqiNTphiabd6MQCeIPhQ XBKiKVWK6B0+s56JVvD13eM= =hTx9 -----END PGP SIGNATURE-----
