Suppose we use $(t,n)$ Shamir secret sharing as follows:
We share the secret $\beta$ as $S=[s_1,..., s_n]$, where $X=[x_1,...,x_n]$ are the public values. For the sake of simplicity, lets assume that $n>100$ and $t=2$.
We permute the elements in the vector $S$.
Question 1: Given the permuted vector, can an adversary associate each share to the corresponding $x_i$ values? if yes/no why?
Question 2: What if we mix the shares with some dummy values and then we permute all, and give them to the adversary?