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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Advantage of Asmuth-Bloom secret sharing scheme with polynomial over integers?

Currently, I am studying the Asmuth-Bloom secret sharing scheme and want to learn more about its polynomial version. What are the exact reasons to use polynomials over integers for this scheme?
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Is there a secure multi-party computation (SMPC) scheme that doesn't use secret sharing?

According to the Wikipedia article about SMPC: Secure MPC is closely related and builds on to the problem of secret sharing, and more specifically verifiable secret sharing (VSS), which many ...
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How to implement a Hybrid cryptosystem via GnuPGP?

I would upload some file on the cloud and share to my friends (more than one), securly. Reading on wikipedia I found an explication on how it works, but I have doubs, because I don't understand if I ...
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Inside attack( attack from participants) in secret sharing

I have considered a ( t,n) secret sharing scheme with n secret , say a1,a2....an. its third party secure but it having inside adversaries. Now while reconstructing secrets a group of t qualified ...
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Shamir's Threshold Scheme (Theory Part, Need some help understanding a term that I can't find online)

What does the max(S, n) part mean, and what am I supposed to do with it? I somewhat understand, but it is still confusing. I don't know what it exactly represents. Can you help me please?
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Pseudorandom zero-sharing: how does it work?

TL;DR How can the shares of the PRZS protocol proposed in [CDI05] reconstruct the "secret" $0$? Is the number of shares required to reconstruct $0$ equal to $2t + 1$? Long question The paper "...
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Secret sharing scheme WITHOUT Shamir Secrete Sharing

I am planning to use the following XOR scheme to divide a secret into only 2 shares (I do not want to use Shamir Secret Sharing for different reasons that are beyond the scope of this post). Here's ...
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What kind of operators should I perform on 4-qubit state $|\psi\rangle_A|GHZ\rangle$ to get expression like $|\Psi\rangle_4$?

I'm reading the paper "Quantum secret sharing" by Hillery, Bužek and Berthiaume (Phys. Rev. A, 1999; preprint on arXiv) and I have a question about it. Let's say Alice wants to send Bob qubit in ...
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Function Secret sharing and sharing a truth table

I was reading a paper (Function Secret Sharing by Boyle, Gilboa and Ishai, PDF) on Function Secret Sharing and in that the author talked about a naive construction of a p party DPF wherein the truth ...
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ECDSA Private Key from SSS

I have all of the Shamir's secret shares required to Lagrange-interpolate f(0), which represents an ECDSA private key. The field of this object is ...
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BGW Multiplication: Linearizing the polynomial

I have some trouble understanding the linearization of the degree 2t polynomial generated by multiplication in BGW. It would be great if someone could decode this ...
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BGW Multiplication: How does it work?

I could not understand how multiplication is carried out in the BGW protocol for 3 parties. Reference: https://crypto.stanford.edu/pbc/notes/crypto/bgw.html I've understood that in multiplication, we ...
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Secret-sharing scheme that can be “audited” without auditing code?

I am designing an app that allows (among other things...) users to divide a secret into 2 shards and was planning to use Shamir Secret Sharing (SSS) to do so. However, I want to allow users of my ...
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basic Shamir's secret sharing scheme

I have tried to look online in various sites and texts and tried to use several youtube tutorials but I still cannot grasp it correctly. could someone please help me understand a simple case ...
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Using an alternative to shamir's secret sharing

I was wondering about the following as an alternative to secret sharing(shamir): Assuming that in order to gain access to some theoretical system, we'd be saving secrets on the system and we will ...
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GMW Multiplication AND for 2 parties

I am looking into the GMW protocol's evaluation for multiplication in 2 parties. I have referred to different materials on it but I didn't exactly understand how $a_i b_j + a_j b_i$ is calculated in a ...
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Practical examples of Threshold Secret Sharing?

Threshold secret sharing is pretty cool, but unlike, say, public-key cryptography, I haven't really heard about it "in the wild". It appears to be confined to discussions of theoretical scenarios, as ...
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Can we use fixed Beaver's multiplication triples many times?

In the secure computation based on GMW and SPDZ style approaches, we use multiplication triples to gain efficient online computation time. Can a same triples be used multiple times? Is there any need ...
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Is an implementation of blinded encryption/decryption mechanism exists?

I want to use 2 semi trusted servers, to decrypt a secret for a user but I don't want those servers to have access to the plain text. Those server need to be able to "partially" decrypt and let the ...
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How to backup a secret encrypted by multi parties without revealing the secret?

I'm searching for a way to backup a secret that only the end user knows the information with 2 trusted hosts. But trusted hosts shouldn't have access to secret at any time. First basic version : ...
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Example of a Two-party GMW Protocol

I have been looking for a concrete example of GMW protocol for two parties. I was trying with the following example for computing $XOR$ of two parties: A's secret bit is $a = 0$, B's secret bit is $b ...
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How modern messengers encryption keys can't be hacked [closed]

I dont know is this question more like reverse-engineering or cryptographic. Why governments are hunting for encryptions keys? Aren't they delievering by the network the same as the encypted messages? ...
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Publicly verifiable secret sharing scheme

In https://www.win.tue.nl/~berry/papers/crypto99.pdf, Schoenmakers proposes a publicly verifiable secret sharing scheme, that uses a non-interactive DLEQ proof to allow any participant to verify the ...
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Faster alternative to shamirs secret sharing algorithm

I recently discovered shamirs secret sharing scheme. Pretty interesting stuff. I noticed that a common case is to split a secret which is used to encrypt/decrypt something else. For example Vault is ...
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Encrypting text with AES and MPC

I'm thinking of implementing text encryption and decryption in my program using AES using key sharing thanks to MPC (the point is that the key should never be provided in full), however, all public ...
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Shamir's Secret Sharing of modular inverse

Given a secret $K \bmod q$ which is shared among entities $E_1,…,E_n$ using polynomial Shamir's Secret Sharing, how can the inverse of $k$ be shared without revealing $k$ and $k^{-1}$?
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How to forge a Shamir secret share?

On this website, we have a lot of questions and answers devoted to Shamir secret sharing. We make it clear that Shamir secret sharing does not guarantee integrity. When we want integrity, we need to ...
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Secret sharing scheme verifiability

This secret sharing scheme takes place in the polynomial ring over a finite field $F_p[x]$, $p$ being a large prime, in the following simplified way: The dealer chooses a private polynomial $f(x)$. ...
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Secret sharing in different groups; Rounding down of elements

I have the following problem: A secret $x \in \mathbb{Z}_q$ is secret shared (additive secret sharing) between $n$ parties, now is it possible to compute the secret shares of $y = \lfloor x \rfloor ...
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What does non-collusion assumption mean in server-aided protocol based on secret sharing?

Suppose $m$ clients split their own input into $n$ shares using additive secret sharing scheme (mod something). Then, each of the clients sends each share to each of $n$ external servers. After ...
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Secure multi-party computation for digital signature

Is there any practical algorithm that will allow to use public key cryptography (RSA or ECC) in the following way There are N parties. Up to M are malicious adversaries (were trusted, but got taken ...
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Share Conversion between Different Finite Fields

Let us have any linear secret sharing scheme (LSSS) that works on some field $Z_{p}$, where p is some prime or a power of a prime e.g., Shamir Secret Sharing, Additive secret Sharing. The problem at ...
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Difference between group key agreement, group key sharing, group key distribution and group key establishement

I am currently doing a survey on group key, and throughout my readings, I stumbled on these different terms: Group Key agreement, Group key Sharing, Group key distribution, and Group key establishment....
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Understanding a variant of Shamir's cryptosystem with authorization levels

I am having problems understanding this implementation of Shamir's secret sharing with confidentially levels (in this case 3). I will give the context and then my problem to make it more clear. ...
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ElGamal Threshold Cryptosystem

Suppose we have a threshold ElGamal cryptosystem $(t, n)$ over an Elliptic Curve $E_p$, $p$ being a large prime, with the following parameters: $G$ is a generator point of $E_p$ with order $q$ A ...
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PCI - Limit Key Injection Capabiltiy 3DES + DUKPT

Current Context: I'm using a Triple DES with a DUKPT Key Management Approach. I have two organization which have access to the BDK Key: Orgzanization 1 which acts as the Secure Decryption ...
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$X_ {i_1}, . . . , X_{ i_ k} $ are IID random variables or not?

In this paper secret sharing is to distribute information (the secret) over a set of participants such that the secret can only be reconstructed if certain authorized combinations of participants join ...
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Does the transposition cipher have a network application?

So I'm reading a chapter in my networking book, and it talks about substitution and transposition ciphers. I know that most network security uses public key or symmetric encryption, but I wonder ...
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Does lagrange interpolation work with points in an elliptic curve?

Defining the lagrange interpolation for $x=0$ as $\mathcal{L} = \sum_{i=1}^{t+1} y_{i} \cdot l_{i}$ with $l_{i}$ as the lagrange basis polynomials. Does this hold if we apply the elliptic curve ...
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In a shamir secret sharing scheme, why can't the secret be a middle coefficient and only the first or the last?

In the shamir secret sharing scheme, the Secret s is set as the constant in the equation $ y_p = s+ \sum_{i=0}^{i = t-1} a_i * x_p^i$ s can only be the constant term or the last coefficient or the ...
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Example of the $Ω$−partite

Consider the following definition from section 2.2 of this research paper We write $\mathcal{P}(𝑃)$ for the power set of the set $𝑃$. An $𝑟-$partition $Ω=\{𝑃_1,\cdots,𝑃_𝑟\}$ of a set $𝑃$ ...
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Encrypt data. Create 5 keys. Just 3 keys are needed for decryption

I would like to encrypt some data and create 5 keys. These keys are stored in different places. If I want to decrypt the data I just need 3 of these 5 keys. Is there a way to do this?
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Privacy of Multiplication of Shamir Shared Secrets with an Active Adversary Where Final Result is Revealed to a Third Party Over a Secure Channel

I have the following question related to the privacy of multiplication of Shamir Shared Secrets: Suppose we have two secrets, a and b, shared by a Shamir Secret Sharing Scheme in a (k,n) ...
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Literature question on secure multiparty computation

Consider $N$ players and assume that a private channel between each pair of players is available. Player $i \in \{ 1, \ldots,N\}$ holds a secret $S_i$, which is a sequence of $B$ random bits. The ...
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Distributed group signature scheme

Since there is only one group manager in group signature scheme, are there any scheme that have n group managers who pubilish the member private key or member credential together(or like threshold ...
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Which flaws does the following 2 out of 3 threshold secret sharing algorithm have?

Let's say the secret is an ordered set of two 8-bit integers — $\{a, b\}$. First, we generate additional entropy, another ordered set of random 8-bit integers — $\{c, d\}$. \begin{gather} a \oplus c ...
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How is Shamir's Secret Sharing better than this simple 2-password technique?

I'm looking for a solution to protect a message, such that both password1 (usually given to trusted person #1) and password2 (...
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Secret Sharing between $x$ parties

So for an unknown number of parties $x$, I make $x-1$ random $n$-bit strings represented by {$r_1, r_2,...,r_{x-1}$}. Where $s$ is the complete string split up between $x$ parties (yes?). I then ...
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Shamir Secret Sharing - How to reconstruction secret? Example

I try implement Shamir Secret Sharing. In this video: https://www.youtube.com/watch?v=j7Ngtl1cCpY is example. But for another three share holders is can't reconstruction secrete. For example: a) a(...
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Do I need verifiable shares?

I'm using Shamir's secret sharing in a 2:3 system. Thus a secret Key is split in 3 subkeys (KeyS:KeyC:KeyT) I've 3 entities at ...

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