# 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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### Shamir secret sharing with field 2^8

I want to split a message using Shamir's Secret Sharing by splitting each byte of it so the field I'm using is $2^8$. Assume $(2,2)$ scheme, i.e., splitting it into $2$ shares and both of them are ...
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### What is the significance of $\prod \limits_{i=1}^{t}m_i > p \prod \limits_{i=1}^{t-1}m_{n-i+1}$ in Asmuth–Bloom threshold SSS?

In this paper by Asmuth–Bloom on threshold SSS, the algorithm is as follows: Shares Distribution To distribute $n$ shares of a secret $K$ among the set of participants $P = \{ p_i : 1 ≤ i ≤ n\}$, ...
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### Two parties SPDZ Protocol Input sharing

Assume we have two computing parties for SPDZ protocol. The two parties are also the input parties. How can they share the MACs on their input shares assuming one party is the master who owns the MAC ...
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### Conditional $k,n$ secret sharing

I would like to know if there is a way to place a condition on $k$-out-of-$n$ secret sharing such that out of $k$ participants who can pool their shares to reconstruct a secret, one of them should ...
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### Can we share an n-bit string by using shamir's secret sharing n times?

For Shamir's Secret Sharing, with a secret of size $n$, instead of having a finite field of order $n$, can we just use Shamir's Secret Sharing $n$ times, once for each bit, using a field of order 2? ...
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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 ...
177 views

### Is there way to combine secrets first and later split them?

Shamir's Secret Sharing allows a secret to be split into multiple shares so that it can be reconstructed later. Is there a way to do the reverse? Can we combine a few secrets first and later split ...
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### How to compute secure sum using secure multparty computation?

Suppose there are three voters $P$, $Q$ and $R$, and each will vote only on one candidate out of $X$, $Y$ or $Z$, with a 6 bit vote vector corresponding to $X$, $Y$ and $Z$ respectively (with 2 bits ...
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### Private Information Retrieval with no server computations

Is there any way to perform Private Information Retrieval when no computations can be executed on the server-side? I would like to perform the computations on the client, and without having to ...
250 views

### Size of Parameters in Polynomial Key-Splitting Algorithm

I've seen the elegant way of splitting a key among different people so that only a certain number need to be present to re-compute the key, yet nobody has enough information to re-compute the key on ...
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### Whether ramp secret sharing possess additive homomorphism?

Ramp secret sharing replaces the random coefficients in original Shamir secret sharing with original data to be shared. In such a case, all the coefficients in the polynomial evaluation will be ...
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### Secret shared input for garbled circuit?

I’m curious about what the secret shared input for a garbled circuit is. Essentially, a garbled circuit is a two party computation framework where each of two players has each input as bit string. In ...
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### Shamir Scheme: Whats the problem of not using random x-coordinates?

i would like to know why there is a problem of not using random x-coordinates in shamir secret sharing schemes. I consider that after evaluating the points in a polynomial $f(x)$, the share is ...
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### Enforcing Randomness in Malicious Setting

I was going through some lecture notes where it said that if we have a 2-party protocol that requires both the parties to generate random integers during the course of protocol, then if we migrate the ...
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### ECIES: key derivation function and symmetric encryption scheme

I am using an elliptic curve library which provided me with a shared secret using my secret key and a foreign public key. Unfortunately an ECIES is not available in the programming language. I would ...
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### How can I prove that it is impossible to find a cheater in shamir secret sharing?

Three participants Quadratic polynomial, one cheater. The Cheater discloses a false (x,y) pair I need to prove that any one of the truth-telling participants can't tell which of the others is the liar....
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### Pre-determined points in Shamir's secret

I have distinct sets of pairs of values $(a_1, b_1), ..., (a_i, b_i)$. This set of pairs is ordered, and each $a_i$ and $b_i$ are related. I want to share the $a_i$ values publicly. I do not want to ...
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### Unleakable shared secret under realistic assumptions?

Can two devices share a common secret in a way that an adversary who compromises one of the two devices after deployment is unable to reconstruct the shared secret, under the following assumptions: ...
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### Two-way secret sharing for authentication?

Secret sharing, using methods such as Shamir's Secret Sharing allows for t out of n shares to recreate a secret. For authentication, the secret can be a user ID. A client with a logged-in user can ...
345 views

### How to implement oblivious transfer where probability of the receiver getting secret is exactly 1 out of 4? [duplicate]

As we know that oblivious transfer is done with probability of 1 out of 2. But how to implement it with probability of 1 out of 3 or 1 out of 4??
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### Public key of a split key without calculating private key

I am searching for a secret splitting scheme where the private key doesn't exist, since each party chooses their own secrets. The other parties should however still be able to calculate the public key....
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### Does Shamir's Sharing Scheme make sense if k=2 and n=2?

Given that I have a secret which I want to split into 2 parts (n=2) and require 2 parts to restore it (k=2), does it still make sense to use Shamir's Scheme or would a trivial scheme with XOR (...
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### Can Shamir's SSS be augmented so that having the secret as well as half the shares necessary to construct the secret is enough to reconstruct the key?

More generally, is it possible to construct a $(k,n)$ threshold secret sharing scheme (i.e. let than k shares leaks no statistical information about the secret) such that possession of the secret ...
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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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### 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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### Shamir's scheme secret sharing

Shamir's scheme for implementing an $(n, k)$ sharing of a secret $S$ involves a random polynomial $F$ of degree $k-1$ such that $F (0) = S$. Each of the $n$ shares of $S$ is a pair $(x, F (x))$ for $x$...