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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How is sum of two share of (2,n) shamir scheme equal to the secret?

I am refering to Privacy Aware Incentive Mechanism to Collect Mobile Data While Preventing Duplication https://ieeexplore.ieee.org/document/7357616. They claim to split secret $X$ into $X_s=\{x_0,\...
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Is there three-party protocol for Secure Equality Test (a.k.a Socialist Millionaire problem)?

Secure Equality Test is an important building block in Secure Multi-Party Computation (MPC) with respect to Secure Comparison, also known as Socialist millionaire problem. A similar question was ...
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Looking for multi-party key exchange/shared secret algorithm with specific requirements

I'm looking for the ability to create a SINGLE CONSTANT shared secret amongst two or more users (a group) AND if a new user is added to such a secured group the new user should also be able to learn ...
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Why are binary extension fields preferred for Shamir secret sharing?

It is known that Shamir's secret sharing works over any finite field but I don't get it why binary extension fields are preferred?
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Correcting threshold in multi-party computation

I am currently reading the paper Graceful Degradation in Multi-Party Computation. The paper mentioned something about correct structure, denoted C = {C1, . . . , Cl}. On page 10 the paper reads: ...
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A question about masking input then share

I am confused about a simple input-sharing schema. The schema: a party that holds an input x, and generates a random variable r. That party secret share r as [r], then distribute it to other parties. ...
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"shared" variant of 1-out-of-N oblivious transfer

In the traditional 1-out-of-n OT, we suppose Alice has an array $A=\{x_1,{\cdots},x_n\}$ and ...
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Giving a continuous fractional (e.g. irrational) part of a secret to someone

In secret sharing schemes, we usually give rational fractional parts of a secret out. E.g. Alice gets 4/10ths of the secret, Bob gets 7/10ths, Charlie gets 5/10ths, David gets 1/10th, etc., and you ...
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Public-key/asymmetric encryption where you can only leak the decrypted message by leaking your password

A bunch of friends are using public-key encryption to send encrypted messages to each other using an open public forum. I.e. each friend has a public key (which you can use to encrypt messages for ...
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What are the uses of shared cipher texts and signatures?

In Distributed Key Generation(DKG), why is there a need to actually create a master secret which can then derive into a single public and private keypair(for signatures) and a secret key(encryption)? ...
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Tools/libraries to protect private keys using shamir secret sharing / multi-party computation?

here is the scenario. I want to use the concept of shamir secret sharing (or other multi-party computation methods) to store my private key in the public-key encryption. For example, I use RSA to ...
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Problem with Shamir secret sharing degree reduction in multiplication gate

The process of Shamir secret sharing degree reduction in multiplication gate is explained in the following link Now, based on the secret sharing that done by a degree one polynomial, we must be able ...
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Question about round complexity of secure multiple party computation based on secret sharing

I am reading Fast and Secure Three-party Computation: The Garbled Circuit Approach And in the introduction section it said that: the round complexity of these protocols is proportional to the ...
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How could this scheme work?

When we use a secret sharing scheme we usually want to reconstruct the polynomial function $p(x)\in\mathbb{Z}_q[X]$ with the Lagrange interpolation method and then compute $s=p(0)=a_0$. However, the ...
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How can I use a secret sharing scheme when the secret is not a number but a statement?

I want to use a secret sharing scheme, where every player $i\in N$ has to share a pair of secrets $(l_i,\nu_{l_i})$, where $l_i$ is a unique code (positive integer) for every player, but $\nu_{l_i}$ ...
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Is it secure to do Shamir key split on a key in blocks and recombine?

Yesterday I made a PR to a python crypto library to support key sizes larger than 16 bytes for Shamir secret sharing scheme. Currently it supports 16 bytes, as follows: $$ K = \{ 0, 1 \}^{128} $$ $$ ...
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What could a_0=s in Shamir's secret sharing scheme represent?

What could $a_0=s$ in Shamir's secret sharing scheme represent? As we already know in a $k$ out of $n$ secret sharing scheme, a secret is split in $n$ parts however only $k=t$ parts (of a polynomial ...
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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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2 votes
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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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