Sharing secrets and distributing passwords

Re:Sharing secrets and distributing passwords by xk_id on Saturday November 03, 2012 @07:53PM (#4738321)

hmm.. the article says: "If we encoded our secret with a cubic function and distributed coordinate sub-passwords it would require any combination of four points to determine the intercept and the secret."

Maybe I'm missing something here, but, taking any of the cubic function diagrams as example, what if all four coordinates have their "x" between -10 and 0? Those four coordinates will not be enough to generate the whole curve, no?

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Re:Sharing secrets and distributing passwords by lucas-beyer on Saturday November 03, 2012 @08:36PM (#4738427)

No.

As soon as you have 4 points, these 4 points uniquely define a cubic. Even if those 4 points are "right next" to eachother.

If this is difficult to imagine, it is the same with a line. Wherever you place 2 points, they always uniquely define a single line.

Unless, of course, you place 2 points exactly on top of eachother.

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Re:Sharing secrets and distributing passwords by xk_id on Saturday November 03, 2012 @09:32PM (#4738570)

really? that's amazing! I'd love to see a formal proof of this.

edit: I suppose this counts as proof http://www.had2know.com/academics/cubic-through-4-points.htm..., but atm I don't remember why matrixes are connected with equations.

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Re:Sharing secrets and distributing passwords by joshzayin on Saturday November 03, 2012 @09:52PM (#4738618)

There's a more general proof at https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:... that looks reasonable at a skim.

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Re:Sharing secrets and distributing passwords by xk_id on Saturday November 03, 2012 @10:31PM (#4738715)

Awesome!

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