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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Threshold schemes

I am looking for a reference that lists all major $(n,k)$ secret sharing schemes. Can anyone help me get such a reference?
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Black-box secret sharing schemes

My question is about black box secret sharing schemes (BBSSS). Do these schemes have any advantages over the better known secret sharing schemes like Shamir’s?
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Noisy secret sharing

I am looking for a secret sharing scheme that is robust against noise, the shares are going to be noisy. We do not want to reconstruct the secret perfectly and a noisy reconstruction with a bound on ...
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What are the consequences of Diffie Hellman problem in P?

Computational Diffie Hellman problem wants to know $g^{ab}$ given $g^a$, $g^b$ and $g$ while the discrete logarithm problem wants to know $x$ from $g^x$ and $g$. The latter resolvable in polynomial-...
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Secret Sharing Domain Questions

all, I have a very fundamental question on Secret Sharing schemes such as SPDZ families. As far as I can see for now, SS schemes always assume a certain variable range. For example, suppose the bit ...
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Shamir secret sharing with no dealer

Suppose we have a set of $N$ parties. I am looking for a scheme to generate shares of a random secret $s$ where any subset of the participants with size $k$ can recover the secret similar to Shamir's ...
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Shamir's Secret sharing for Key encryption

I have studied Shamirs Secret Sharing(SSS) scheme. Now my doubt is to how to apply this in real time applications. I have an application which receives encrypted data from server and decrypts the data ...
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Can you have perfect secrecy with countable message/key spaces by dropping countable additivity?

This classic paper by Chor and Kushilevitz shows that if the key space and the message space are both countably infinite, then it is impossible to have a perfectly secure private-key encryption scheme....
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How (generally) do modern schemes deal with an adversary with the capacity to either instantly, or over time, corrupt a majority of parties

I'm curious about the honest minority case and what cryptographers have and are currently using to get around this. My motivation is primarily the MPC space, but I'm sure there are other subfields ...
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Looking for an algorithm to encrypt with a single key and decrypt with a lot of keys without consuming too much space

Is it possible to have an encryption scheme that could be encrypted with a particular key, then decrypted with a large amount of keys without massively inflating the size of the final result? I am ...
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Using XOR to derive a data key for ECIES

I have been thinking about a rather simple enhancement for (EC)IES / RSA-KEM. The scheme would allow you to encrypt data while the calculation of the session / data key can be performed afterwards or ...
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Why does verifiable secret sharing with an honest majority require a broadcast channel?

In the information-theoretic model with active adversaries, it seems to be well-known that no protocols with exact reconstruction of the secret exist for the task of verifiable secret sharing (VSS) ...
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Which are the current solutions to the illegal values in the homomorphic secret sharing?

There is a usual example about homomorphic secret sharing, focused on e-voting. Supposing we use Shamir's scheme for the Secret Sharing system, a participant generates a polynomial whose a0 is +1 (yes)...
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What is the fundamental difference between multipartite and multilevel secret sharing?

According to this paper , Multipartite secret sharing scheme is a scheme in which the set of participants is divided into disjoint parts and all participants in the same part play an equivalent role ...
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Is there a way of sharing a key without anyone knowing what the key is initially?

I started learning about key sharing and Shamir secret sharing, I'm wondering whether you need someone who knows the key initially and then distributes it, is this step necessary or not? In my case I ...
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How to convert from small field to large field

If I have number $2$, which is additively shared into $3+4 \bmod 5$. Now I need to change the filed to a large one, like $500$. How to convert the shares, so that I can have a new number or shares $a+...
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Calculate share for a specific value of $x$ in Shamir's Secret Sharing scheme

I am currently reading the book Cryptography: Theory and Practice (4th edition) by Stinson and Paterson and going through the exercises. I have reached the Threshold schemes section and am currently ...
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In a secret image sharing scheme, what are the advantages of Galois field $\mathrm{GF}(p^m)$ over finite field $ F_p$?

Shamir's Secret Sharing Scheme uses arithmetic in a finite field of prime order. In a secret image sharing scheme, what are the advantages of Galois field $\mathrm{GF}(p^m)$ over finite field $ F_p$?
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Non-interactive proof of value in MPC

Does it exist? Specifically using Shamir secret sharing based MPC and looking for a (non-)interactive way to prove that the secret value is valid. A value is valid if it is part of a set for example $[...
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Simplified Lagrange interpolation formula inside Shamir's secret sharing scheme

I originally posted this question in the math stackexchange, but I then thought that it might be more appropriate in this section. I am currently studying Shamir's secret sharing scheme, which uses ...
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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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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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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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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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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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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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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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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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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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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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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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