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

Hunger Learn

5/9/23, 5:00 PM

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.

0 + 0

multiparty-computation

entropy

protocol-design

group-theory

secret-sharing

Hunger Learn

5/10/23, 8:59 AM

@moderators I have totally re-edited my question, is there a choice where I can re-post it?

Hunger Learn

5/10/23, 9:10 AM

@JAAAY I almost totally re-edited my question

João Víctor Melo

5/10/23, 1:17 PM

I would recommend you to read https://arxiv.org/pdf/1806.07197.pdf but an answer has to be given here also.

Hunger Learn

5/10/23, 3:07 PM

@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....

Hunger Learn

5/10/23, 3:08 PM

So what is that every other player $j$ leans form $i$ so as if all $j$ players do a computations they can compute $s_i$. None writes explicitly that for example, player $j$ learns $x_j$ and all of them exchange their $x_j'$s and compute for example $x_1\oplus x_2\oplus\cdots\oplus x_{n-1}=s_i$, namely $x_j'$s are the puzzle to reconstruct $s_i$

Hunger Learn

5/10/23, 3:14 PM

@JoãoVíctorMelo I do not mean to offend you. It is very nice that you have some kind of help to give. The problem is in the general with how all these in computer science write the maths...fully complex while everything could be simple

João Víctor Melo

5/10/23, 3:39 PM

Yes, in science sometimes to show some things you have to hide others.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

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

TH: ใครสามารถช่วยโดยใช้รูปแบบการแบ่งปันความลับหลายฝ่ายที่ปลอดภัย

RO: Ar putea cineva să ajute prin aplicarea unei scheme securizate de partajare a secretelor cu mai multe părți?

RU: Может ли кто-нибудь помочь, применив безопасную многостороннюю схему обмена секретами?

VI: Ai đó có thể trợ giúp bằng cách áp dụng sơ đồ chia sẻ bí mật nhiều bên an toàn không?

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