Questions tagged [secret-sharing]

Secret sharing refers to splitting a secret among multiple parties so that together they can reconstruct it. All parties, or just a threshold number of them, can be required for reconstruction. If fewer than the required number of parties participate, no information should be leaked about the secret.

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An equivalent definition for shamir secret sharing?

Taking into account this paper I will write here a definition that the authors provide. $\textbf{Definition:}$ (linear secret sharing scheme). A $(t,n)$ secret sharing scheme is a linear secret ...
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How many combinotaion of all $n$ players are needed to reconstruct the secret in a $(k,n)$-treshold secret sharing scheme?

In a $t+1$ out of $n$ secret sharing scheme where there is a network of $n$ players, in order to reconstruct the secret $t+1<n$ players are needed to share their parts $(x_i,f(x_i))$ so as the ...
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Secret sharing questions

I would like to make a few questions about Shamir's secret sharing scheme and. To begin with, I am starting with the next theorem that determines the intuition of the whole theorem. $\textbf{Theorem:}$...
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How to define a cryptosystem when the encryption-decyrption scheme is based on Shamir's secret sharing scheme?

I would like to make a parallelism between Shamir's secret sharing scheme and how to define a cryptosystem where the encryption scheme is based on secret sharing. To begin with I do not know if there ...
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Could we use permutation polynomials for Shamir's secret sharing scheme?

Could we use permutation polynomials for secret sharing scheme like Shamir's? The say that they induce a bijection over $\mathbb{Z}_p$ what does this mean and how does it helps?
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Is this a well defined sharing scheme to propose

A proposed secret sharing scheme: Suppose that $p:S\times Y\to X$, with $|Y|\geq|S|$ is a cipher where, $y\in Y$ is the key and $x\in X$ the code, $p$ is bijective, namely $(x,y)$ is associated with ...
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Secure multi-party computation made simple - questions

The scheme that I refer to is from this paper. A secret $s\in D$ is obtained by splitting s into a random sum. We have (actually linear) for any $k$ this $k$-out-of-$k$ secret-sharing scheme: Select $...
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Could you provide the proof of a secure multi - secret sharing scheme that fulfils the requirements of correctness and information-theoretic privacy?

Suppose that we have a multi-secret sharing scheme and let $I$ be the a set of agents. 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 $...
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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)\...
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Is the Secret sharing scheme thresholds of variable of interest shared related with the entropy of the variable?

Is the $t$ out of $n$, namely $(t,n)$, threshold in the secret sharing scheme related to the entropy of the random variable that is shared according to the scheme? What changes in the secret sharing ...
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Could this scheme work for multiparty computation secret sharing?

Suppose that there are $5$ players and each of them learns a secret that is a coordinate of the random vector $s=(s_1,s_2,\cdots,s_5)$, such that $s$ is a uniformly distributed over the field $V$. ...
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Secret sharing scheme combined with probability theory results?

As a sequel of my previous post I am writing a new one with respect to the secret sharing scheme. I will only cite here the answer because I want to make a question on it. $\textbf{Answer:}$ To be ...
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How to design such a secure multiparty computation scheme with the players using a majority rule

Suppose that $y$ is a uniform random variable that is defined over the field (or group or abelian group) $Y$. Let us suppose that there are $N=\{1,2,\cdots,i\cdots,N\}$ agents and only one of them, ...
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Could this be a secure multiparty secret sharing scheme?

Suppose that $y$ is a uniform random variable that is defined over the field (or group or abelian group) $Y$. Let us suppose that there are $N=\{1,2,\cdots,i\cdots,N\}$ agents and only one of them, ...
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Secure multiparty scheme in key (splitting) distribution among the players

Suppose that we have a game with $I$ players and each of them has a private secret say $e_i$. Every player wants to share her secret with the rest of the players but in such a way that she will not be ...
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How can I enrich this mechanism of communication to become more efficient and secure?

Suppose that we have a Bayesian game, where $t_i\in T_i$ denotes the type of player $i$. Say that we have a communication game (communication equilibrium). The players do send each other an encrypted ...
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How to design such a protocol that the agents could replicate the mediator by themselves?

A problem in game theory is that of communication. Taking into account the classic approach of Myerson and Forges, the agents communicate each other, however indirectly, through a communication ...
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How secure is it to share "Passwords" using Shamir Secret Sharing given a way to verify if password is correct?

Lets say you have a order $n$ finite field which you are using to create $k$ shares for a password using Shamir Secret Sharing. Assume that the attacker gets $k-1$ shares. Is it possible that the ...
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Could anyone provide any idea of such a protocol?

Could anybody provide the seminal paper and/or every specific manual in mathematics that describes a secure multiparty computation procedure, where the players will exchange encrypted messages (...
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Sharing information scheme of cryptography - operations in modular arithmetic

Taking into account my previous question here and the answer about the proposed encryption-decryption scheme. I am trying to understand how to make possible operations in modular arithmetic for a ...
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Classic secret sharing schemes vs Homomorphic secret sharing schemes

What is the difference between the classic secret sharing schemes that are used in the protocols of Ben-or and Rabin, Ben-Or, M., Goldwasser, S., Wigderson (that is the Shamir's secret sharing scheme) ...
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No-dealer secret sharing scheme that prevents anonymous collaboration to reconstruct the secret

Is there a no-dealer secret sharing scheme that allows a threshold $k$ of $n$ parties (where $k<n$) to collaborate to reconstruct a secret, but in such a way that none of those $k$ parties are able ...
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Split prvate key without Private Key Holder knowing the key shards?

Is is possible to split a private key into shards and distribute the shards to Key Holders such that (1) k of n key shards are required to recover the private key and (2) the private key holder does ...
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How to convert the secret sharing modulus?

Assume $c$ is a secret number in $Z_p$ and $c = a + b$. Alice has $a$ and Bob has $b$. Is there any methods to convert the modulo $p$ to some $q$, ($c<q$, $c<p$)? That is to say, $c = a' + b'$ ...
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Can we encode with the set of $\{0,1\}$ and its Boolean operations any finite or infinite domain?

Can we encode with the set of $\{0,1\}$ and its Boolean operations any infinite domain that is subset of the real numbers $\mathbb{R}$ or the whole set of real numbers? For example can we encode the ...
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Shamir Secret Sharing and replacement for Lagrange interpolation

Shamir Secter Sharing in standard version (paper version) works pretty good with Lagrange Interpolation to generate more shares. Problems arise when you generate more pairs (xi, yi) and you try to ...
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Shamir Secret Sharing and recover polynomial function from shares

I've got working first part of SSS scheme so I can use some secret number as an input and generate some random polynomial function and create simple shares as pairs (xi, yi). The task is how to get ...
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Can anybody explain the proof of Rabin and Ben-or of secure multiparty computation?

Can anybody explain the proof of Rabin and Ben-or of secure multiparty computation? The idea is that every player $i$, of $N<+\infty$ players, holds a secret say $s_i$. All of them want to share ...
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Rational secure multiparty computation with permuatation secret sharing scheme?

Taking a look in this economic paper they use cryptographic tools to implement correletaed equilibria in the case of two plaeyrs. They use permutations for the exchange of information between the ...
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Overflows in classic Shamir Secret Sharing Scheme

I've implemented classic Shamir Secret Sharing Scheme which looks like this: get password as input (any length) convert password text to big integer generate polynomial coefs (an ... a1) generate ...
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Why do we need to mod in Shamir's Secret Sharing algorithm [duplicate]

I'm looking into Shamir's Secret Sharing algorithm and it's clear to me how it works but I don't understand the exact reason why we need to find a prime number and do modulo arithmetic using that ...
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Secure protocols by implementing cheap talk instead on a centralized mediator to compute any function $f(s_1,...,s_n) = (y_1,...,y_n)$?

Based on this paper a protocol is secure if and only if it satisfies secrecy and resiliency. Most of the papers in ecnomic and computer since deal with the following problem. They consider the case ...
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Is it possible to have a shared secret without any party knowing all the parts?

I believe with Shamir’s Secret Sharing Scheme, I can create an n-part secret and distribute each of those parts to n parties. ...
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Shamir secret sharing where some specific people are required to participate

By using SSSS we distribute the key to "N" people where any "k" (N>=k) are required to participate to unlock the code. But what if I wish to have the people "x" and &...
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Secure protocols with the dynamic programming solution concept?

Suppose that we have the usual problem of secure communication, where each of the $I$ agents have a private signal $s_1,s_2,\dots,I$ and they wish to compute any function $f(s_1,s_1,...,s_I)=(x_1,x_2,....
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Security of verifiable shamir secret share

Let us consider the following verification protocol based on Feldman. Assume, $c_0,\cdots,c_k$ represent the coefficients of the polynomial $p()$ in $\mathbb{Z}_q$. For verifying share $(i,p(i))$ and ...
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Linear operations on packed Shamir secret share

Suppose I have a k-dimensional secret $\langle x_1,\cdots,x_k \rangle$ which I share using a packed Shamir's secret share $(t,k,n)$ where $t$ is the threshold and $n$ is the number of shares as ...
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Fast implementations of verifiable Shamir's Secret shares

One way of verifying Shamir's secret shares is to use the technique by Feldman where $c_0,\cdots,c_k$ represent the coefficients of the polynomial $p()$ in $\mathbb{Z}_q$. For verifying share $(i,p(i))...
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Secret sharing is based in random variables that are uniformly distributed?

In Rabin and Ben-Or, their basic assumption is that each participant can broadcast a message to all other participants and that each pair of participants can communicate secretly. Hence, they design a ...
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Example of exchanging information

I am searching for a simle model that can simulate the following procedure. Suppose that $i$ and $j$ are two agents that each one obtains her state dependets signal $s_i(\omega)$ and $s_j(\omega)$. ...
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Reconstruction of shamir secret shares in the presence of malicious parties

Suppose we have a (t,n) Shamir-secret sharing scheme. A value of some computation is shared with n parties where at most $t-1$ parties are malicious. What is the best strategy to reconstruct the ...
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How to speed up Shamir secret share generation?

Let us say we have to generate Shamir's secret share for n data points. Is there a way to speed up the implementation apart from using Horner's rule for the polynomial evaluation?
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Secret Sharing in a decentralized network

Is there a method by which a secret can be split across multiple nodes, such that: No one node can learn the secret. An adversary can't learn the secret by bringing up multiple dummy nodes. ...
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Algorithmic game theory and protocol design for communication

There is a field of exchanging information that combines cryptography and game theory. I am interested in understanding this field, but it's a little complex for me. To begin with there is a paper of ...
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Different secret sharing schemes instead of Shamir's?

Are there any different secret sharing schemes instead of Shamir's Secret Sharing , that is not based in polynomial interpolation over finite fields? Or is it the most efficient than the others?
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BGW multiplication by Gennaro et al.: Why does H(x) have exactly degree t and why is $2t + 1 \le n$ necessary?

With this question I am referring to the BGW multiplication by Gennaro et al (PDF here). The multiplication is described on the 4th page. (Another source for me was "A pragmatic Introduction to ...
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Multisignature 2 of 3 cryptology

I want to put text into multisig cryptologic and store them in separate 3 locations with a fault tolerance of 1 but only 2 are needed to get the text. I think some people call is Shamir's Secret. So ...
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Protecting AES via Shamir Secret Sharing

This is about the paper Protecting AES with Shamir's Secret Sharing Scheme by Louis Goubin and Ange Martinelli which describes how to use Shamir Secret Sharing to obtain masked implementations of AES. ...
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Find the product of two sums via SMPC

I'm currently working on a distributed threshold DSA scheme that requires to find the product of two sums via secure multi-party computation. Specifically speaking, every one of $n$ parties $P_i$ ...
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fast encryption with one key and fast decryption with multiple keys sequentially

Is there such a encryption and decryption mechanism: Given an encryption C = E(K1, M), where K1 is the encryption key and M is plain text, it have to apply decryption with two keys K2 and K3 ...

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