How to judge a determinant equals non-zero in cryptography?
For linear system $Ax = \beta$ with a vector on $n$ unknowns $x$, $A$ is the Vandermonde matrix, produced with powers of $c_i$. For such a matrix, determinant is a product of $(c_i - c_j)$, and so is non-zero for different $c_j$ in the set of field elements.