Suppose that we have a multi-secret sharing scheme as it is described in the literature
Let there be $I$ agents and say that $S$ is the space of the (uniform) random variables $s=(s_1,s_2,\cdots,s_I)\in S$ such that the share $s_1$ is known to $P_1$, $s_2$ is known to $P_2$ and so on. Could someone propose an appropriate multi secret sharing scheme? Every agent $i$ wants to share $s_i$ in such a way that it is not easy computable from a small group of players (I do not know if an $(|I|-1,|I|-1)$-threshold scheme can be applied)
Could anyone provide explicitly a proof? Maybe it seems easy, but I am a bit confused where to start or how to do the maths. I would appreciate it if it is convenient for him/her who could give a proof to use $+$ or $\otimes$ and $mod$ schemes from group theory instead of polynomial explanation because it seems more simple for my understanding.