scrovy

@danielstreit The problem that you face is that $x^8 + x^4 + x^3 + x + 1$ is irreducible over $F_2=\lbrace0,1\rbrace$ but not a primitive polynomial. Indeed implement $GF(256)$ as...

As far as I know it's a non crucial issue, especially for a large number of bits. Typically `bits=8` is used. But in principle yes, you should allow $0 \in...

What you're saying is that if all the coefficients $a_1, a_2, \ldots, a_k$ are identically zero, then your polynomial is constant hence the share is equal to the secret for...