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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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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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 ...
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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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Baek and Zheng’s Threshold Cryptosystem - limit on threshold?

I have just completed an implementation of Simple and Efficient Threshold Cryptosystem from the Gap Diffie-Hellman Group by Baek and Zheng and am hitting a problem with high values of the threshold. ...
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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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Distributed Shamir's secret sharing

Wikipedia on its page for Shamir's secret sharing scheme provides a python implementation that applies the idea. This algorithm will generate a (k, n) threshold scheme so for example we could split a ...
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Is this a good way of splitting a private key into a 2 of 3 scheme?

Basically the idea is to split a key into three parts ($key_a, key_b, key_c$) of which any 2 of the 3 parts can be used to recreate the original key $key_a$: a random number smaller then our original ...
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Security of Shamir secret sharing with regards to the threshold

Consider Shamir Secret Sharing Scheme (SSSS). This is completely unfounded, but my intuition tells me that the threshold k we set (AKA the number of shares required ...
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What is definition of adversary ? And what they do?

Currently I am writing my last assignment about secret sharing. But I don't get clearly about adversary. I know this seems so basic understanding in secret sharing. But I couldn't get references that ...
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Shamir Secret Sharing GF(p) or GF(2^8)

I'm implementing Shamir's Secret Sharing Scheme, but I've hit a conceptual roadblock. In Shamir's paper "How To Share A Secret" he creates his shares an a finite field of order p, where p is some ...
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Is splitting AES ecrypted data safe?

Say I have a key, an iv and an AES/GCM/NoPadding encoded string and I want to split this information between three people such that only jointly can they reveal the ...
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Reed Solomon secret sharing and as a one-time symmetric key?

Shamir's Secret Sharing is just a special case of Reed-Solomon where only one coefficient is used to store the secret instead of the entire polynomial. Sarwate however, suggests that the latter can ...
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Is gfcombinefs - a filesystem for n-of-m Shamir secret sharing - fundamentally read-only?

With a view on using a tool similar to fgcombinefs in cloud situations, I would need a writable n-of-m Shamir secret sharing filesystem. As a matter of routine security, I do not want the cloud ...
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895 views

Shamir secret sharing: calculate rest of shares when you know secret and one share

Using Shamir secret sharing, one is starting with a secret and end up with a number of shares based on a polynomial. For example: INPUT: secret: 123456 Shares:4 ...
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General-purpose non-interactive multi-party computation protocol

Most of general purpose multi-party computation protocols are highly interactive. Especially the ones with Shamir's secret scheme, as there is a degree reduction step in multiplication that needs the ...
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Lagrange Interpolation for finite field GF(2^8), for Secret Reconstruction

I'm using Lagrange's Interpolation technique to reconstruct the secret from a set of point pairs (x,y). Since I only need the secret, not the whole polynomial, I have simplified the reconstruction ...
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How to generate a random polynomial of degree $m$?

I am trying to do a homework in which implement a variation of this paper and I don't know how to generate a polynomial of degree $m-1$. This polynomial is used to generate the $y_0$ and $y_1$ values. ...
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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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Multisignature or Multi-password File

I want to create a file that I could give to 3 trusted friends, and allow any two of them to decrypt it when together (or in sequence when not physically in the same place). This is similar to a ...
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Distributing shares in a particular monotone access structure

Consider 6 people, $A,B,C,D,E,F$ and a secret. Construct a scheme which enables the following subsets of people to retrieve the secret: three players from the set $\{A,B,C,D\}$ two players from the ...
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Some terms related to secret sharing: Optimality, What does it mean?

In any secret sharing scheme we have to develop step by step. After constructing such scheme we need to reduce share size. Why? e.g. Robust secret sharing scheme is modified Shamir secret sharing ...
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Shamir's Secret Share [duplicate]

I'm not quite sure the benefits of working over a prime modulus in Shamir's secret share- but doesn't limiting the numbers you pull from make the secret easier to guess? Instead of being over the real ...
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Relation between Threshold Cryptosystem and Secure Multiparty Computation ?

Is there any relation between secure multiparty computation and threshold cryptosystem ?
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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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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 $𝑃$ is a ...
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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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How can I generate large primes for Pedersen commitment?

I want to make a commitment on Shamir's Secret Sharing, based on the work of Pedersen, "Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing". To implement the commitment ...
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Secret sharing over reals - Difficulty with Computer implementation

I asked a question recently regarding the paper "Secret Sharing Over Infinite Domains" - B. Chor and E. Kushilevitz which describes a secret sharing scheme for real numbers in the interval $[0,1]$. I ...
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Multi-secret sharing (Packed secret sharing) - Some questions

In the publication - "Communication complexity of secure computation", I have encountered a small problem - on page 5 of the literature under the heading "Theorem 1" they have ...
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Shamir Secret Sharing Scheme - some doubts not answered earlier

my first question on here. I've gone through some examples of Shamirs Secret Sharing Scheme, but I have 2 rather pressing doubts - i. Why do we choose the co-efficients of the polynomial from the ...
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266 views

How does one construct a 27x27 tabula recta for 2-of-3 secret sharing?

In the answer to this post at security.stackexchange, someone describes how, using pencil and paper, one can do 2-of-3 secret sharing with a tabula recta. But I don't understand how he created his ...
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201 views

Question regarding reconstruction vector in LSSS

Suppose we have a policy $A \wedge ( D \vee (B \wedge C))$ with attributes ${\{A,B,C,D}\}$. The set of subsets of attributes which satisfy this policy is ${\{{\{A,D}\},{\{A,B,C}\},{\{A,B,D}\},{\{A,C,D}...
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461 views

Reverse Shamir's Secret Sharing Algorithm?

Shamir's Secret Sharing algorithm works by breaking a single secret to multiple parts. While it is trivial to implement the reverse in a $n$-out-of-$n$ scheme, how would one implement an $m$-out-of-$n$...
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531 views

AES encryption using MPC SPDZ protocol

I'm reading the article about SPDZ protocol for secure multiparty computation (and also improvements for offline phase like MASCOT). However I'm thinking about practical application of SPDZ for AES ...
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Can we use Shamir secret sharing conversely?

In Shamir secret sharing scheme, we have a secret and then the shares are generated based on the secret. The question is can we generate the shares before knowing the 'secret' (which is uniformly ...
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296 views

Combining Shamir's schemes

I am learning about Shamir's secret sharing scheme and I've come across this problem: Let's suppose we have a combination of a (3, 6) and (1, 2) Shamir's schemes, where participants $P_1$ and $P_2$ ...
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164 views

Require x of y possible passwords to decrypt

Is there a way to set up encryption so that a certian number (x) out of a total (y) number of users/passwords are required to do the decryption? Background: This is mostly a thought experiment, and ...
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Numeric combination of passwords

Pls I need explanation on How i can design a Cryptography that use multiple passwords or passphrase to open a safe(Lock). For example, if i need five people to unlock a secured device whereby all the ...
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620 views

Shamir's Simple Sharing Scheme - preventing partial recovery of data

In SSSS, if you recreate the original secret with one of the decoder inputs being slightly damaged (e.g. one or two chars incorrect), you receive a slightly damaged version of the original secret. So ...
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Safety when disclosing hashes of secrets used to calculate other secrets

In my application, I am generating a big random number and publishing a SHA256 hash of it. After the hash it published (but not the secret), anyone can submit any number, and the system will calculate ...
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Trying to find an algorithm to share portions of a key with multiple people

Sorry if this question's a bit basic, but I don't know of any way to ask it concisely enough for a search... What I'm looking for is a proven means of doing the following: Create x number of strings ...
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471 views

Multiparty key exchange for end-to-end encryption

I need to make end-to-end encrypted messaging between 2 and more parties without trusting a server. Each party has it's secret and private keys. The obvious solution is to make ECDH between all of ...
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216 views

Reconstruction vector in Linear secret sharing schemes

Suppose we have a policy $A \wedge ( D \vee (B \wedge C))$ with attributes ${\{A,B,C,D}\}$. The set of subsets of attributes which satisfy this policy is ${\{{\{A,D}\},{\{A,B,C}\},{\{A,B,D}\},{\{A,C,D}...
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Number of possible access structure with $n$ person

I want to count number of possible access structures in closed form(if possible) as a variable of $n$,the number of share holder. I have tried in several ways. Still no good progress. It is very hard ...

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