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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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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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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Committing to a secret shared value

Suppose I run a multiparty protocol. At the output stage, I have the function output in a secret shared manner among all parties. Now I want all the parties to commit to their value of the secret ...
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Explanation of part of a visual cryptography algorithm

I have been working on a project involving visual cryptography and I am stuck with the following problem. My question is related to this paper, AN IMPROVED VISUAL CRYPTOGRAPHY SCHEME FOR SECRET ...
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Secure Secret sharing

I'm trying to come up with a new way to do oblivious transfer that is faster and requires less computation than existing methods. The basis of my method is shamir secret sharing. Below is an example ...
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Secret sharing - no dealer, modifiable, verifiable

I need to find a secret sharing scheme with these properties: The scheme is set up by all participants, ie no single entity called the dealer The parameters of secret sharing need to be modifiable,eg ...
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Could the multisignature scheme in bitcoin alternatively also be implemented by means of a Shamir Secret Sharing Scheme?

When I first came across the Bitcoin multisignature scheme, I wondered that it remarkably looked similar to what Shamir Secret Sharing does (SSS), but then by using facilities in the bitcoin scripting ...
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Majority encryption algorithm?

Assume that I want to leave an encrypted message to a group of $n$ people in a way that they can only decrypt it if they work together in the following sense: For some fixed $k < n$ every sub-...
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566 views

How to prove that a commitment hides the decryption of an ElGamal ciphertext?

I've decided to remove a previous unanswered question of mine and break it down into smaller pieces so it's not such a loaded question. For this question I need to prove that I've committed to a ...
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Reference for additive secret sharing

Regarding the secret sharing schemes, I am wondering if there are any academic references for the Additive Secret Sharing and its variations. Is there any textbook or article which has specifically ...
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What is difference between Unipartite Secret Construction, Bipartite Secret Construction and Multipartite Secret Construction

In this paper authors extend Asmuth–Bloom and Kaya schemes to bipartite access structures and further investigate how SSSs realizing multipartite access structures can be conducted with the CRT. The ...
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Verifiable secret sharing - Benaloh scheme; some doubts not answered earlier

I reviewed the paper "Secret sharing homomorphisms: keeping shares of a secret secret" by J.C. Benaloh yesterday and I had some difficulty understanding his version of verifiable secret sharing to ...
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Threshold signature without revealing id of signers to the recombiner

I want a threshold signature t out of n algorithm where set of t signers are not known before hand and want to remain anonymous after signing. How is recombination possible if id of signer is not ...
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Are there any information-theoretically secure verifiable secret sharing protocols with t=n?

Disregarding matters such as efficiency and round complexity, can verifiable secret sharing be done in a way such that the secret cannot be decoded unless you have all n shares, and that this ...
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Ecash - Probability of catching a user using secret splitting who duplicates the coin

For detecting double spending, secret splitting is used. If a user duplicates the coin, then there will be two different transaction items in transaction list. What is the probability of catching a ...
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How does threshold decryption with secretly shared exponents actually work?

Imagine the case where you have a sufficiently large finite field (or any multiplicative field for that matter) $\mathbb{Z}_{p}$ where p is some large prime. Now, I have a number $g \in \mathbb{Z}_{p}...
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Can you explain “k out of n” from the VCS paper by Naor and Shamir

I am new to visual cryptography. I’ve just read the paper “Visual Cryptography” by Moni Naor and Adi Shamir and I'm stuck on the chapter about the “$k$ out of $n$” construction. I am aware that, on ...
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Signing integers and UUIDs and restoring them from a third party server without tampering

I'm educating myself about cryptography. I know this is a long one, but please, bear with me. :) Now I have a scenario in my mind and I'd like to ask if what I've thought is sound (enough), what more ...
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Threshold signatures vs. certificate authority+voting verification

Perhaps a silly question, but I am wondering what the advantages are of threshold signatures. Let's consider the following two signature schemes: $(t,n)$-threshold signature with a trusted dealer, i....
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How to go about distributed private/public key pair generation?

I'm trying to implement a protocol in which two parties generate a private/public keypair, where both know the public key, but each party has only one part of the private key and cannot derive the ...
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Asymetric encryption, multiple recipients, traitor must share private key

Is there an Asymetric encryption scheme, or public key encryption, where multiple recipients are able to access the data but in order for one of the recipients to leak the key to the data they would ...
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What is the motivation of multipartite secret sharing?

In this thesis chapter 3.1 A multipartite secret sharing scheme is a scheme in which the set of participants is divided into several parts and all participants in the same part play an ...
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How can I calculate the feasibility of brute-forcing missing secret shares against the secret checksum?

Secret sharing has the problem of player cheating, where a forged share $s'_i$ can be sent to generate a fake secret $m'$ during reconstruction (and the cheaters can even collude to generate the real ...
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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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Purpose of the ZKPoPK in the original SPDZ protocol

What is the purpose of ZKPoPK in the SPDZ paper? And will the following can detect the active adversaries in 2 party spdz excluding ZKPoPK step? Each party sends a commitment on his MAC key ∆_i ...
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How does the user check whether $y < M$ without knowing all shares?

CRT-based Verifiable Secret Sharing Scheme In this paper, section 4 Verifiable Secret Sharing Scheme, the dealer phase and the combiner phase are as follows: Dealer Phase To share a secret $d \in ...
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Confirmation signature - Improved Feldman VSS

I am working through the implementation of A Distributed Private-Key Generator for Identity-Based Cryptography. In the paper (Figure 1, page 8) the validation of a share by a node says that once ...
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Differential privacy and Shamir's scheme

I have been unable to find any proofs (for my own reference) that demonstrate that Shamir's secret sharing scheme does (or does not) satisfy the definition of $\textbf{differential privacy}$ as ...
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PCI DSS requirement 3.5.3

3.5.3 Store secret and private keys used to encrypt/decrypt cardholder data in one (or more) of the following forms at all times: ............ As at least two full-length key components or key shares, ...
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Private Key Sharding - How is it Secure in a Distributed Network?

In a Distributed Network in order for a private key not to be compromised sharding will have to take place off the network, correct? If so: Why is it when a Distributed Network shards private keys ...
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Is recursive secret sharing of practical value?

This paper describes recursive secret sharing. In one of their illustrations, a binary secret of length L, along with 3 other binary secrets of lengths shorter ...
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Preserving location privacy

What are cryptographic techniques that could be used so that if I wanna to enable a server to send message to certain nodes in a network with preserving the privacy location for them ??
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Optimized Random-OT Security in Standard Model

I was going through the paper - " Efficient Oblivious Transfer and Extensions for Faster Secure Computation" by Asharov et al. where the authors propose an optimized OT protocol along with a Random-OT ...
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283 views

Additive homomorphic secret sharing

I am new to cryptography esp, homomorphic encryption. I would like to know if the following is possible using something similiar to additive homomorphic secret sharing. Please apologize me if its too ...
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What SMPC protocols make use only of additive secret sharing?

In Appendix G of the Hawk paper, where it talks about financially fair SFE, it mentions that it's possible to run a SMPC protocol where, at the end, each party has a share of their own output y, and a ...
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relationship between share size and entropy in secret sharing

In an $(s,r,n)$-ramp scheme, we require that any subset of at least $r$ parties can recover the secret, while any subset of size at most $s$ cannot learn anything about the secret. In Bogdanov et al.'...
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Threshold encryption with threshold on encryption part

For a thought experiment I'm looking for a threshold encryption scheme where $k$ out of $n$ shares are needed to encrypt the data and everybody can decrypt the data. However, I only found schemes ...
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How share size is reduced in robust secret sharing?

THIS IS ROBUST SECRET SHARING SCHEME The dealer $\mathcal{D}$ wants to share a secret among the participants $\{P_1, P_2, \ldots, P_n\}$, where at most $t$ participants are malicious and $t<n/2$. ...
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Does using a verifiable secret sharing scheme ensure robustness of a protocol if it is secure under the semi-honest adversarial model

Consider a protocol $\pi$ which uses a linear secret sharing scheme like that of Shamir secret sharing. Further assume that the protocol $\pi$ has been proven to be secure (correctness and privacy) ...
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Weighted secret sharing scheme?

Is there a secret sharing scheme where secrets can be weighted, and that you need a total weight of $1$ to unlock the secret? I know that you could, of course, just figure out every subset that has ...
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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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How to distribute symmetric key between $n$ entities?

If there are $n$ servers for broadcasting a symmetric key in such a manner that following holds: No server alone can find the key $K$ alone. Any two servers can pass $k_i$ and $k_j$ such that $K=f(...
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Is anyone aware of Du atallah multiplicative secret sharing scheme for dot products for > 2 party scenario?

I am working on Du Atallah's multiplicative secret sharing scheme for more than 2 party scenario. Is anyone aware of its multiparty version (more than 2 parties). The paper for 2 party can be found ...
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Question about publication “Efficient (k,n) Threshold Secret Sharing Schemes Secure Against Cheating from n − 1 Cheaters”

In the paper on section "4 Proposed Scheme", I suppose that the scheme does not protect if an adversary has access to the $k - 1$ original shares, am I correct? If the adversary has $k - 1$ of both ...
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Explain the meaning of “$E_i = g^{F_i} g^{G_i}$ is uniformly distributed in $G_q$”?

In this paper[1] Qiong et al.’s CRT-based VSS} {Dealer Phase} To share a secret $ d \epsilon Z_{m_0} $ among a group of $n$ users with verifiable shares, the dealer does the following: <...
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Is my analysis regarding $M_3$ and $M_4$ correct?

In this paper authors gave the following equations for $M_3$ and $M_4$ in section $3.2$ of Share distribution phase: Shares Distribution To distribute $n$ shares of a secret $K$ among the set of ...
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When Shamir secret sharing used in one time pad scheme

In the following, all operations are defined over a finite field of prime order. Please note that what I'm explaining below is a part of a bigger protocol, however, to keep things simple I just ...
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Split TOTP/HOTP secret and generate pin without trusted dealer

Many site use time-based one time password (totp) as second factor auth method, such as aws. So we can split the totp secret and distribute each part to different party to achieve threshold login ( ...
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How can a node establish pairwise shared key with other nodes using its own polynomial share together with other's public values?

A server has a symmetric bivariate polynomial $ F(x, y) = \sum_{{i,j}=0}^{t-1}a_{i,j}x^iy^j$ $\in GF(p)[X, Y] $ of degree $t-1$. For simpliciy, $ F(x, y) = a_{0,0}+a_{1,0} x+a_{0,1}y+ a_{1,1}xy$ mod ...
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How space efficient is the Asmuth-Bloom scheme

This answer to another question states that shares in Asmuth-Bloom scheme are $n$ times larger than the secret. From my understanding of the scheme, the share space is defined by the largest modulo $...