# Could anybody help by applying a secure multiparty secret sharing scheme?

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.

• @moderators I have totally re-edited my question, is there a choice where I can re-post it? Commented Jan 10, 2022 at 8:59
• @JAAAY I almost totally re-edited my question Commented Jan 10, 2022 at 9:10
• I would recommend you to read arxiv.org/pdf/1806.07197.pdf but an answer has to be given here also. Commented Jan 10, 2022 at 13:17
• @JoãoVíctorMelo seriously, the way that they write, all of those who are doing research in cryptography is quite non-efficient. For example, we know in general that $x\underbrace{\to}_{f} y$, which means that $f(x)=y$, but instead they are using an inverse arrow, $x_i\rightarrow inv(u_i)$ totally a mess. Especially when instead of inv you have a function like $VSS_{put}(s)=...$, well this function $VSS_{put}$ must have some properties what are they? None clarifies them. And the latter, they all say that $P_i$ shares $s_i$ among $N-\{i\}$ or $(n-1)$ agents.... Commented Jan 10, 2022 at 15:07
• Yes, in science sometimes to show some things you have to hide others. Commented Jan 10, 2022 at 15:39