Suppose we have a secret $\sigma$.
The secret comes from a universe in which the elements are not necessarily distributed uniformly.
We split $\sigma$ into $n$ shares $[\sigma_1,...,\sigma_n]$ (using Shamir secret sharing). So the order of shares matters.
We know given all the shares in the right order one can recover the secret.
We permute all the shares in a matrix (see below). We fill the empty indices with some dummy (or random) values $d_{i,j}$ \begin{matrix} d_{11} & \sigma_{n} & \sigma_{2} & \dots & d_{1,m} \\ d_{21} & d_{22} & \sigma_{i} & \dots & d_{2,m} \\ \dots \\ d_{k,1} & d_{k,2} & \sigma_{3} & \dots & \sigma_{1} \end{matrix}
Question: Given the matrix, can the adversary recover the secret with a high (or non-negligible) probability?
I emphasis that $\sigma$ may have very greater distribution probability than the other elements of the universe and the adversary knows that probability.
Please note that the values $k$ (number of rows) and $m$ (number of columns) are independent of the number of shares $n$ and we can increase them if it's needed.
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Edit: Newly added:
Suppose we have two permuted matrices one contains shares of secret value $\sigma$ and dummy values; and the other matrix contains shares of $\gamma$ and random values. We give away the two permuted matrices and one-to-one mapping of the elements to the adversary. The mapping tells the adversary that value in $i,j$ position in one matrix corresponds to value $k,l$ position in the other matrix.
Question: Would the adversary learn the secret values $\sigma$ and $\gamma$ with a non-negligible probability.