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I try implement Shamir Secret Sharing.
In this video: https://www.youtube.com/watch?v=j7Ngtl1cCpY is example.
But for another three share holders is can't reconstruction secrete.
For example:
a)
a(1) = 15
a(2) = 6
a(4) = 10
b)
a(1) = 15
a(2) = 6
a(5) = 6
But for another three share holders is can't reconstruction secrete.
Sure they can.
In the field $GF(17)$, we have:
$$\frac{43}{3} = \frac{9}{3} = 3$$
because $43 = 9 \pmod {17}$, and $3$ is the value that, when multiplied by 3, gives us 9 modulo 17.
And, we have:
$$\frac{23}{2} = \frac{6}{2} = 3$$
beause $23 = 6 \pmod {17}$, and $3$ is the value that, when multipled by 2, gives us 9 modulo 17.
Remember that, when we work in a finite field, division isn't exactly the same as it is when we're working with in $\mathbb{R}$; for example $\frac{1}{2}$ is not 0.5 (which is meaningless in $GF(17)$, but instead it is 9.
