Shamir's secret sharing scheme is a threshold secret sharing scheme based on polynomial interpolation over a finite field.

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Many single-time use keys encryption scheme (not Shamir's Shared Secret)

I'm looking for encryption scheme with the following properties: There's a sequence of keys that can be used to decrypt the message Strictly only one key from the sequence is required to decrypt the ...
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A variant of Shamir secret sharing

Suppose implement the Shamir secret sharing as following: we select a degree $d$ polynomial $P$ with a zero coefficient of 0, and all other coefficents selected randomly from $Z_p$; and to this ...
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Roots of polynomial in Shamir secret sharing

I need to know whether one can obtain any roots of the polynomial in Shamir secret sharing if he possesses less than threshold shares. For instance in (t,n) if he has t-1 shares can he obtain any ...
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Checking the share membership in secret sharing schemes

I was thinking of this since yesterday. Imagine, a secret is split into its respective shares (using any secret sharing scheme) with threshold $t$ and total $n$. Can we find out given any random ...
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Recover from compromised shares with Shamir Secret Sharing

He is a quote from Wikipedia page for Secret Sharing: If the players store their shares on insecure computer servers, an attacker could crack in and steal the shares. If it is not practical to ...
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How come Shamir Secret Sharing uses Lagrange interpolation?

I've read that Newton polynomials have better computational complexity, but Shamir's uses Lagrange polynomials instead. Does anyone know if there are particular reason why Newton polynomials aren't ...
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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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(n,n) Shamir secret sharing [duplicate]

In (n,n) Shamir secret sharing if n shareholders do not have the public values (X values) can they still obtain the secret with only Y values?
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Shamir's secret sharing scheme - type of channels

For information theoretic security in Shamir's [m,m] secret sharing scheme, do i need both authentic and confidential channels? Another related query is ;is it true that if the channels are only ...
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Shamir's Secret Sharing of modular inverse

Given a secret $K \bmod q$ which is shared among entities $E_1,…,E_n$ using polynomial Shamir's Secret Sharing, how can the inverse of $k$ be shared without revealing $k$ and $k^{-1}$?
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Back up an information as $n$ pieces and require exactly $n-1$ to recover it

Let $X\in \Bbb F_2^p$ be some information. How do I create $Y_1,\dots,Y_n \in \Bbb F_2^q$ so that having less than $n-1$ of the $Y_i$s gives you no information on $X$ but having $n-1$ of them allows ...
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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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Diffusion in Shamir's secret sharing scheme

The popular command line utility ssss implements the classic Shamir's secret sharing scheme over the generic field $GF(2^q)$ with $8 \le q \le 1024$. When $q>=64$, the constant coefficient ($c_0$) ...
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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, ...
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Secret Sharing 1 Required

Devise a scheme so that a message M can be shared among X, Y and Z in such a say that the only way of recovering the message is when X is present with either Y or Z. When X isn't present or each is ...
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199 views

Can I use Shamir's secret sharing scheme for multiplicative homomorphism for secure multiparty computation?

I would like to perform a dot product operation among $m$ parties using Shamir's $(m,m)$ secret sharing that is used for Secure Multiparty Computation. I am aware that Shamir's $(m,m)$ scheme is ...
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Third-party security issues with Shamir's secret sharing scheme

In Shamir's secret sharing scheme, we are trusting a third party who generates the secret polynomial. How can we ensure security here when we are involving a third party?
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Does Runge phenomenon affect Shamir's secret sharing scheme?

Lagrange interpolation seems to be affected by the so-called Runge phenomenon when one tries to interpolate polynomials of high degree from a set of equidistant points. Lagrange interpolation is ...
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Shamir Secret Sharing Modular Reduction

Say players use Shamir's secret sharing to share a value $k$ such that each player now holds $k_i$, a share of $k$. How can they securely compute $k \bmod m$ for some $m$. Of course they can ...
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Secure degree reduction for Shamir's secret sharing

I understand the basic Shamir Secret Sharing protocol, and when two shares are multiplied, the degree of the polynomial increases. I've seen in a number of papers a reference to a degree reduction ...
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Coefficients in Shamir's Secret Sharing Scheme

Sorry if this is a stupid question, but: in Shamir's scheme, we construct a polynomial and make our secret $S$ the zero-th coefficient $a_0$. What, if anything, necessitates this - in other words, can ...
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Elliptic Curve Verifiable Secret Sharing

I'm reading this paper, which on page 3(Section IV.C) presents a Jointly Random Verifiable Secret Sharing Scheme for Elliptic curves. The algorithm makes sense to me save for this part: "Each ...
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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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How does secret sharing solve the partial exposure problem?

I have been trying to understand how secret sharing methods like Shamir's secret sharing solve the problem of a share revealing information about the secret. I guess there are some random numbers ...
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Threshold cryptosystem with a required share

I am trying to find an implementation or variant of a (k, n) threshold cryptosystem (as described here Shamir's Secret Sharing) where we can fix at least one of the k key parts, i.e., instead of ANY k ...
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How to Distribute the Shares using Secret Sharing for arbitrary Monotone Access Structures

Consider 4 people, $A$,$B$,$C$,$D$, & a secret $s\in\{0,1\}^k$. Construct a scheme which enables the following subsets of people to retrieve the secret $\{A,B\}$, $\{A,C\}$, $\{B,C,D\}$. I know ...
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Shamir's Secret Share Over the Reals

What about using Shamir's secret share over the real numbers leaks information? I know there is a problem with random number generation, and someone suggested it leaks the parity of the polynomial, ...
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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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Shamir's secret sharing with passwords

I'm trying to design an extension to Shamir's Secret Sharing that would allow the participant to specify a password instead of remembering/storing a large integer or binary data. So far, I have two ...
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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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Why does Shamir's Secret Sharing Scheme need a finite field?

I read ampersand's question "Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme", where he asked why Shamir's Secret Sharing Scheme uses arithmetic in a ...
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715 views

Implementing secret reconstruction in Shamir's Secret Sharing

I am trying to implement Shamir's secret sharing in C++. I have got the generation of shares working. However, I am very confused with the reconstruction of shares. I get the part on how three users ...
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Addition with Shamir secret sharing

When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$. I believe this would be the correct solution (correct me if I'm wrong): Each party ...
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Is there a way to use Shamir Secret Sharing with updatable data?

I want to divide a system that maintains these properties, based on Shamir's Secret Sharing: A secret key is split up to N pieces, where T of them are enough to reconstruct the key. The original key ...
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How do you find a cheater in Shamir Secret Sharing?

If there are 4 people involved, and every two of them should be able to know the secret (the polynomial is just a line) and you are given f(x) and x for each of those people, and you know one of them ...