# 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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### 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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### 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 ...
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### RS Erasure Coding and Shamir's Secret Sharing

So I was trying to understand the basic difference between erasure coding and secret sharing, and I found this paper (that you can find here or here). For what I understand, it states that Shamir's ...
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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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### 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 ...
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### Why only one secret value with Shamir's secret sharing? [duplicate]

Shamir's Secret Sharing works by sharing data points on a curve, whereby when you have the required number of data points, you can find the function of the curve and find out the secret, which is ...
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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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### 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, ...
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### Can I pre-define the points in Shamir's Secret Sharing algorithm

With Shamir's secret sharing is it possible to pre-define the points returned by the algorithm? For simplicity if I have (k, n) where k=2, and n=4, and I have the points X,Y,Z, and Q. Can I create ...
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### Secret sharing scheme with ability to add or update share number

I would like to have a secret sharing scheme with the following properties: Generate secret $S$ a split it to $N$ shares $(s_1, s_2, ..., s_N)$ Require $k$ of $N$ shares in order to reconstruct ...
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### Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme

Shamir's original paper (PDF, 197kb) describing a threshold secret sharing scheme states: To make this claim more precise, we use modular arithmetic instead of real arithmetic. The set of ...
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### K out of N encryption

A friend just showed me how to combine padlocks to achieve a lock that opens when k out of n people turn their keys. I was ...
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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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### 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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### How can we distribute Shamir's secret sharing scheme shares without a dealer?

Let's say $k$ users have shares to a $(k,n)$ secret sharing scheme, and they want to issue new shares. How can they do this without collecting the shares together? In particular, no set of $k-1$ ...
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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 ...
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### When all shares of a secret are given to adversary as a permuted matrix

Suppose we have a secret $\sigma$. The secret comes from a universe in which the elements are not necessarily distributed uniformly. We split $\sigma$ into $n$ shares $[\sigma_1,...,\sigma_n]$ (...
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### Secure multi-party computation for digital signature

Is there any practical algorithm that will allow to use public key cryptography (RSA or ECC) in the following way There are N parties. Up to M are malicious adversaries (were trusted, but got taken ...
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### 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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### How are one-time pads distributed?

It seems that OTP encryption is unbreakable. I have read some articles (Wikipedia, Blogpost, etc.), but I could not find any information about how they are used. If I wanted to create a messenger ...
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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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### An electronic voting system

This semester I am taking the course Cryptography. I will have a presentation about the topic "Voting Scheme". I am preparing myself by reading from the book “Cryptography : an Introduction” by N....
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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 ...
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### Threshold Signatures for RSA and DSA

I have a few questions relating to threshold signatures: a scheme where $n$ participants hold a key share and any $t$ of them can conduct a protocol using their shares that results in a valid RSA or ...
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### How many polynomials are used in Secure Multiparty Computation?

Secure Multiparty Computation based on Samir Secret sharing methods rely on Polynomials. Imagine corpus of data should be outsourced to bunch of untrusted servers for any computations. Now the data ...
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