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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?

Edit:

Question 2: What if we mix the shares with some dummy values and then we permute all, and give them to the adversary?

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  • $\begingroup$ Comments are neither for providing answers, nor for extended discussion; this conversation has been moved to chat. $\endgroup$ – e-sushi Jan 31 '16 at 19:22
  • $\begingroup$ As an aside: to clean up things, I’ve moved out conversation to chat too. ;) $\endgroup$ – e-sushi Feb 1 '16 at 11:49