
Sharing secrets and distributing passwords - dwwoelfel
http://datagenetics.com/blog/november22012/index.html
======
cypherpunks01
The ssss unix utility does this, it's fun to use.

Docs at <http://point-at-infinity.org/ssss/>, demo at <http://point-at-
infinity.org/ssss/demo.html> and it can be installed on ubuntu through the
'ssss' package, listed as ssss - Shamir's secret sharing scheme
implementation.

~~~
ryan-c
Here's one I wrote that wraps the algorithm with passwords
<https://github.com/ryancdotorg/threshcrypt> and you can set the same password
multiple times to accomplish the second 'advanced scenario'.

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dexter313
It explains how a password can be cut up in pieces and distributed so that
each piece individualy can be used to reveal the secret.

Skip to >>Shamir’s Algorithm<< section to get to the most interesting part.

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xk_id
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?

~~~
lucas-beyer
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.

~~~
xk_id
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...](http://www.had2know.com/academics/cubic-
through-4-points.html), but atm I don't remember why matrixes are connected
with equations.

~~~
joshzayin
There's a more general proof at
[https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:...](https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:nm.mathforcollege.com/mws/gen/05inp/mws_gen_inp_bck_introduction.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESg6HcId-
jvRg7Ihh3dMF3DGTmBUCUOukBjCH1SunBJxGZFV3gri-
zWyN91qUSinDMFJ3lvexKfgAvN3xewN2mWfG6idDKfHutuAcb62pH-
UHJJXLUnbo3dCjt12NyTTYiZHuqDR&sig=AHIEtbSO9AURkaDNywKJ62dsSWklsecAEw) that
looks reasonable at a skim.

~~~
xk_id
Awesome!

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cprussin
<https://en.wikipedia.org/wiki/Threshold_cryptosystem>

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snprbob86
This is an extremely interesting and well written article. More like this
please!

