# 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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### 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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### Are the shares of Shamir secret sharing uniformly distributed random numbers?

Let $t$ be a threshold in the Shamir secret sharing (SSS) scheme. Assume we know $t'<t$ shares. Assume we are given some random values picked uniformly from the same field as the one used in SSS. ...
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### Centralized orchestration of Secret Shares for SMPC

With regards to SMPC with additive secret sharing, the protocol I am using involves a centralized node(the querier) orchestrating the share creation at client end via setting their random seeds. Now ...
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### Secret sharing such that all shareholders obtain access to the secret (one shareholder can't just run off with the shares)

Say, using something like Shamir's polynomial scheme, you split a secret $x$ among $n$ people (each given a "share" of the secret) such that you need all $n$ shares to recover the secret. ...
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### Which contemporary programming language is apt for implementation of algorithms in cryptography?

I am a researcher in cryptography. Most of the time I generally do theoretical/Mathematical work only and not doing the implementation part. I am not able to get the feel about the time complexity of ...
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### What is the reason for Shamir scheme to use modulo prime?

In Shamir's secret sharing scheme, Dealer performs the following steps Choose a prime number $q$ such that $q > n$ Choose a secret $s$ from finite field $\mathbb{Z}_q$ Choose $t-1$ degree ...
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### Product of secrets in multi-secret sharing schemes (aka packed secret sharing schemes)

The question is related to the multi-secret sharing scheme described in the following paper: [FY92] Matthew K. Franklin, Moti Yung: Communication Complexity of Secure Computation (Extended Abstract). ...
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### How to create (n, t) secret splitting from (n, n) secret splitting?

Given a secret splitting scheme $(n ,n)$ that creates $n$ shares from secret $s$. In this scheme all shares must be combined to create $s$. How do you create a secret splitting scheme $(n, t)$? Of $n$ ...
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### The security level of secret share compared to homomorphic encryption

I want to compare additive secret share to Paillier encryption. However, I haven't found out how to set the parameters in such a way that the security level is consistent. Additive secret share (...
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### What security does the BMR protocol offer against corruption?

I've been conducting some research into general-purpose MPC protocols and have been unable to pinpoint the exact security offered by the BMR protocol. The reference I've been using for the majority of ...
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### Shamir secret sharing in automated verification tools

Can Shamir secret sharing scheme (SSS) be verified using automated verification tools such as AVISPA? I read in the HLPSL manual that we cannot use arithmetic or relative operations such +,-,< ......
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### Splitting an AES-256 key into two?

I understand there are already few question here which are similar but mine is a bit different in that I want to split AES 256 bit into two 128 bit key and then use a different AES key of 128bit to ...
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### Detailed running time analysis for Shamir secret sharing scheme

I am successfully working on Shamir's secret sharing scheme for few months. But the only issue I am facing is the calculation of theoretical time complexity. Since I am from algorithmic background, I ...
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### Identifying the cheater in (3,5)-Shamir's secret sharing

The problem I'm trying to solve: Identifying the cheater in (3,5)-Shamir's secret sharing when we can see only the 3 shares that were given to the system in the secret reconstruction process, and we ...
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### Gennaro & Goldfeder Key Generation Protocol

As I am going through the “Fast Multiparty Threshold ECDSA with Fast Trustless Setup” paper by Gennaro & Goldfeder, 2018, I am stumbled by the key generation protocol (Sect. 4.1, p.10): In Phase ...
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### SS/HE/GC/OT secure integer comparison

I have been reading some papers to find a 'faster' way to compare two integers without revealing their real values. But I think I'm a bit lost in those papers due to my limited knowledge in ...
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### Proof of theoritical security of Shamir's secret sharing

community ! I'm looking for the proof of theoritical security of Shamir's secret sharing. I found some articles saying that it's assimilable to the halting problem, which implies that there is no ...
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### Time complexity of a brute force attack on Shamir's Secret Sharing SSS

I have searched everywhere in academic papers about time complexity of a brute force attack on a Shamir's Secret Sharing key. I'm confused between if it is $O(p^k)$ or $O(p)$, such that $p$ is the ...
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### Are Shamir shares independent?

Assume we have a secret $s \in Z_p$. We generate the set of secret shares $\{ (x_i, s_i) \}_{i=1}^{N}$ according to a $(N,k)$ Shamir's scheme. The evaluations are generated according to the following ...
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### Transparent Voting and Advance Secret Code

In the book "Introduction to the Theory of Computation", Michael Sipser writes The field of cryptography, as this area is known, now extends well beyond secret codes for private ...
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### Is the dealer a volunteer in Shamir secret sharing scheme?

In this Paper, Shamir secret sharing scheme there is one dealer and n players. The dealer gives a share of the secret to the players, but only when specific conditions are fulfilled will the players ...
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### Understanding multiplication of Shamir secret sharing during threshold (EC)DSA signing

I have been looking at the threshold (EC)DSA schemes for honest majority by Gennaro et al. https://www.sciencedirect.com/science/article/pii/S0890540100928815. In the scheme, there are steps where we ...
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### Multi-Linear Secret Sharing vs. Shamir Secret Sharing

I hope someone can help me. I read several papers including the original paper, "Multi-linear Secret-sharing Schemes," by Beimel et al., and watched the following video https://www.youtube....
Setup There are two groups, $A$ and $B$. Each group is in a Shamir's secret sharing scheme ($t_A$ of $N_A$ and $t_B$ of $N_B$). Each group has a public key that is associated with the identity of the ...