I am using this https://github.com/gburca/ssss-js Shamir implementation. I generated 4 shares from secret (threshold of 2).

I am wondering if I can recreate (interpolate) original polynomial from these shares (polynomial which was generated from random numbers) and base on it create a new point (share). In normal cases (not GF(2) fields) is will be an easy task, because after I get pair of points $(x,y)$ I can easily interpolate linear function.

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    $\begingroup$ In a word, yes. $\endgroup$ Feb 7, 2019 at 2:09
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    $\begingroup$ Generally, after interpolating the polynomial, instead of evaluating it for $x=0$ to get the secret, you evaluate it for $x = rand()$ and distribute the result as a new share. Just make sure to not use a value for $x$ that was already used for another share. If your question is specific for this implementation, it might be best to ask the author on Github. $\endgroup$
    – Ceriath
    Feb 7, 2019 at 8:45


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