# 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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### 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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### Inside attack (attack from participants) in secret sharing

I have considered a $(t,n)$ secret sharing scheme with $n$ secret, say $a1,a2....an$. It's third party secure, but it has inside adversaries. While reconstructing secrets, a group of $t$ qualified ...
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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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### 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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### 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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### 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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### 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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### Why is a number of shares that is greater than a threshold required to construct a secret?

In this paper of Asmuth–Bloom threshold SSS, the algorithm is as follows: Shares Distribution To distribute n shares of a secret $K$ among the set of participants $P = \{ p_i : 1 ≤ i ≤ n\}$, the ...
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### Asymmetric encryption, multiple recipients, traitor must share private key

Is there an asymmetric encryption scheme, or public-key encryption, where multiple recipients can access the data, but in order for one of the recipients to leak the key to the data, they would need ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Secure Secret Sharing to a Distributed Key

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 ...
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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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### 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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### 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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### 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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### 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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### 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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### Running time of Shamir's secret sharing scheme

Let $p>n$ be a prime number. The key steps in the $(t,n)$ Shamir's secret sharing is as follows: Steps of dealer: Choosing $s \in \mathbb{Z}_p^*$ Selecting $b_i \in \mathbb{Z}_p^*$ for polynomial ...
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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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### 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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### How do I multiply two points on an elliptic curve?

Tell me if there is a way to multiply two points on an elliptic curve? For example, as in secp256k1 ...
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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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### Computational Complexity Of Breaking Information Theoretic Security

Wikipedia mentions that Shamir's secret sharing(SSS) for example, has information theoretic security. While I understand the concept that the adversary would just not have enough information to break ...
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### Generating and distributing a secret without trusting the source

I have multiple entities (servers) that all share a private secret already. Those servers need a rotating secret (TTL a few hours). All servers must have the same set of secrets at all times. I have ...
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I wasn't certain how to title this request/problem, but here goes: I'm A, and I want to send a message that is received by B, C, D. Each receiving entity here is part of some set of domains D1, D2, D3:...