# Tagged Questions

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

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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 ...
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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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### 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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### 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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### Shamir's Secret Scheme : Knowing the threshold

If I am decoding a key by applying shares, is it possible to know when the threshold has been reached, and the secret revealed, without having to be told what the threshold is? Also, is it possible ...
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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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### 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'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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### 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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### 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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### 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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### Information theoretical security of an inefficient Shamir based access structure

I have studied Sharmir's scheme as well as the multiple assignment scheme proposed by M. Ito. My question is if anyone can tell me if the following scheme is theoretically secure: Terms: P = set of ...
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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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### Shamir Secret Sharing: Why cannot we recover polynomial's root if we have $t-1$ shares?

Imagine we have $t-1$ shares in $(t,n)$ shamir secret sharing. So at least $t$ shares are needed. Question: Why cannot we use $t-1$ shares to find a root of the polynomial and then recover the ...
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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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### Can you update a (k,n) scheme to a (k+t, n+t) scheme (assuming old keys can be deleted)?

I know that $(k,n)$ can increased to $(k+t,n-s)$ one, by generating a random polynomial $p(x)$ of degree $k+t$ with constant term $0$, and then ordering each agent $a$ to add $p(a_x)$ (where $a_x$ is ...
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### Recombination thresholds in degree reduction of multiplied Shamir shares

Shamir's secret sharing can be considered multiplicatively homomorphic, if one is aware of the fact that multiplying two shares of a (n,t)-threshold shared secret yields a share of the same secret, ...
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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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### 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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### 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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### 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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### Benefit of using random key in Shamir's Secret Sharing

I am implementing Shamir's Secret Sharing, and I find that in (t,n)-threshold scheme, the shares are just using 1,2,3...,n as the key to form the shares ...