# Tagged Questions

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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### Does revealing shares of the result reveals shares of the inputs?

Suppose Alive and Bob have shares of two polynomials $P,Q$, say, Alice knows $P_A,Q_A$, Bob knows $P_B,Q_B$ s.t. $P=P_A+P_B$ and $Q=Q_A+Q_B$. They perform some operation $f$ over the shared values, to ...
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### Difference between hierarchical and multi level secret sharing

In this paper, the definitions are simply as follows. Multi-Level secret sharing: Higher level participants can help lower participants to get the secret. Compartmented secret sharing: Each level ...
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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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### Multiplicative sharing of 1

Let R be a ring. Is there a known/standard way for N parties to perform some exchanges, such that at the end each party holds an element $r_i\in R^\ast$ and $r_1r_2\dots r_N=1$ (and each party $i$ ...
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### In Shamir's (t, n) secret sharing scheme why don't use infinite field? [duplicate]

Well, we use finite fields to select shares. What happened if we use infinite fields.then will the scheme be vulnerable? Easy to break? Or share generation and reconstruction will be difficult? ...
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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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### How share size is reduced in robust secret sharing?

THIS IS ROBUST SECRET SHARING SCHEME The dealer $\mathcal{D}$ wants to share a secret among the participants $\{P_1, P_2, \ldots, P_n\}$, where at most $t$ participants are malicious and $t<n/2$. ...
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### Santa Claus' secret permutation

This December, $N$ friends play secret santa: they select a random permutation $\sigma$ of $N$ (without fixed point). For Santa Claus, everyone has to bring a gift to the next person in the ...
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### Is Shamir's Secret Sharing Scheme insecure for larger field? [duplicate]

According to wikipedia, if you are using shamir's secret sharing scheme with a field of order $p$, "High values of $p$ are risky because Eve knows that the chance for $f(x)\pmod{p}=f(x)$ increases ...
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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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### 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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### Shamir SS: To associate shares to the public values $x_i$, when the shares are permuted [duplicate]

Suppose we use $(t,n)$ Shamir secret sharing as follows: We share the secret $\beta$ as $S=[s_1,..., s_n]$, where $X=[x_1,...,x_n]$ are the public values. For the sake of simplicity, lets assume ...
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### Could we share a secret key using the Birthday problem?

I stumbled upon this code on-line, it seems obvious to me that generating all 2^40 keys in trivial time can always be achieved as can hashing each and everyone of them, using the SHARED Salt that "Eve"...
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### Should the secret key of Shamir's secret-sharing algorithm be interpreted byte by byte?

Should the secret message of Shamir's secret-sharing algorithm be interpreted and processed byte by byte? Interpreting it byte by byte makes it easier to process, but in case one of the shareholders ...
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### Problem in understanding Blakley's Secret Sharing Scheme

I need to implement Blakley's Secret Sharing Scheme. I have read below mentioned two research papers but still unable to understand how to implement it. Safeguarding cryptographic keys Two Matrices ...
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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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### Security guarantees of Shamir's secret sharing when some co-efficients are zero

Shamir secret sharing techniques rely on polynomials for splitting and reconstructing. It's security properties are very good, i.e. it is impossible to reconstruct the secret when $t-1$ shares are ...
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### How secure is Shamir's Secret Sharing for password sharing when attacker has t-1 shares?

I am designing protocol to share a random generated n long password between k parties using Shamir's Secret Sharing. I know that share alone does not reveal much information about the original ...
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### How do we solve Shammir 2,3 sharring scheme where arithmetic is modulo?

I am trying to get secret S and I have 3 values (2,2)(6,3)(4,9) and know that modulo is 13. I tried using Lagrange basis polynomial and got 8 but I am not sure if that is right and also I cannot find ...
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### Secret only known on consensus

Does a method exist where a secret is generated so that is is unknown until 3 or more people (predetermined) reach consensus that it should be revealed?
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### Explanation of part of a visual cryptography algorithm

I have been working on a project involving visual cryptography and I am stuck with the following problem. My question is related to this paper, AN IMPROVED VISUAL CRYPTOGRAPHY SCHEME FOR SECRET ...
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