Re: Joint encryption?

[John Richard Moser <nigelenki () comcast net>]

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Casper.Dik () Sun COM 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

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