Re: Someone had wikipedia open when they wrote that
No, apparently, YOU were the one with Wikipedia open--and you misread it.
Yes, the #1 rule of crypto is you don't role your own--but this applies to creating the primitives, not implementing them. As I've repeatedly mentioned here, however, if you're not using libraries, you better have a **** good reason.
And the prior poster mentioned libraries.
But secret sharing is actually one of the more simple primitives (and arguably less sensitive than encryption or hashing). I actually would not be too freaked out over an independent implementation.
If you want to share this secret among n people (with infinite storage) so that any three or more can know it, just translate the secret into a plane in R^3, and hand out random points on the plane.
Of course, we are finite beings, so you need to use finite fields instead of R--say, of order p^k. This in turn means that any two collaborators can "compromise" the secret to the point that only p^k possibilities remain. So, choose p^k to be as high as you need for your application, and you check that no set of three points end up on the same line.
If you want to require four to reveal, just step up the dimension of the affine plane (and "line") in question.
If you need to look up anything I just wrote, then use a ******* library.
The issue is application development. All of the usual issues apply here, but it's important to keep in mind that the secret is not known to the application until enough keys are provided--and the application properly combines them.
