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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.

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.

For some of the more common implementations of Secret Sharing, see or this answer.

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How do you find a single 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 exactly one of them is a cheater, how do you find the…
user784756
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Practical examples of Threshold Secret Sharing?

Threshold secret sharing is pretty cool, but unlike, say, public-key cryptography, I haven't really heard about it "in the wild". It appears to be confined to discussions of theoretical scenarios, as I have not found any real-world software that…
Logan R. Kearsley
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Is multiplicative secret sharing secure?

I suggested mulitiplicative secret sharing in an answer to another question, but noted that I wasn't sure if it was even secure and was hoping someone would comment on the security. Since no one did, I thought I'd ask it as a separate question. Fix…
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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, but I can't see very many other problems.
user8632
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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 used in some secret sharing schemes like Shamir's…
LRM
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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 enrollment, disenrollment, change of access…
Muhamad Jafarnejad
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$(k, n)$ threshold secret sharing to $(k+k', n + n')$ without reissuing all shares

Given a $(k,n)$ threshold secret sharing used to back up a secret (meaning that the dealer has access to the secret at all times), is it possible to update it to a $(k+k', n+n')$ threshold secret sharing without reissuing all shares (in fact, the…
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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 change the secret, the uncompromised (Shamir-style)…
xavierm02
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Threshold Secret sharing - How to create a shared secret from pre existing secret parts?

In usual $(t, n)$ secret sharing schemes, a secret $S$ is split into $n$ parts so that any $t$ out of $n$ parts reconstruct the original secret. So, suppose that there is a group of $n$ participants each one has a secret $x_i$ ($x_i$ may be its…
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Simplified Lagrange interpolation formula inside Shamir's secret sharing scheme

I originally posted this question in the math stackexchange, but I then thought that it might be more appropriate in this section. I am currently studying Shamir's secret sharing scheme, which uses Lagrange's interpolation formula to reconstruct a…
user1301428
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Determining the Shamir's secret sharing scheme for the following problem

I'm having trouble solving the Shamir's Secret Sharing scheme for the following problem that states: Problem: A certain military office, which is in control of a powerful missile, consists of six generals, five colonels, and four desk clerks.…
KonoDDa
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Secret Sharing: Is this simplification secure?

I am a mathematician with no background in crypto or security. For work, I had to read up Chap.13 "Secret Sharing Schemes" in Stinson's Cryptography (3rd ed). My question is about a simplification of the so-called Monotone Circuit Construction. In…
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Shamir secret sharing where some specific people are required to participate

By using SSSS we distribute the key to "N" people where any "k" (N>=k) are required to participate to unlock the code. But what if I wish to have the people "x" and "y" always be part of "k". Any provisions for that??
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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 "Share conversion, pseudorandom secret-sharing and…
Fedma
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$t$-out-of-$n$ Secret Sharing over $\Bbb Z_2$?

Is it possible to construct a $t$-out-of-$n$ secret sharing scheme over $\Bbb Z_2$? Shamir Secret Sharing allows for an arbitrary threshold $t$ and an arbitrary number of participants $n$, but requires the field to have at least $n$ elements. Is…
Daniel
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