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 ...

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Elliptic Curve Crypto, is a distributed signing method possible using Shamir's Secret Sharing?

Note: A distributed signature scheme exists for RSA: Practical Threshold Signatures, Victor Shoup. Is it possible to adapt such scheme for ECC? A centralized signing machine is vulnerable to ...
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Secure Secret sharing

I'm trying to come up with a new way to do oblivious transfer that is faster and requires less computation than existing methods. The basis of my method is shamir secret sharing. Below is an example ...
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(n,n) Shamir secret sharing [duplicate]

In (n,n) Shamir secret sharing if n shareholders do not have the public values (X values) can they still obtain the secret with only Y values?
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Send a symmetric key generated by one user to other users (more than two) using a server

I am developing a software in which I am using AES for encrypting messages shared in a group. The key is generated by one user, the admin of the group and needs to be shared with other members. How ...
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338 views

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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68 views

Encrypt HDD with keyfile and password and allow backing up the keyfile with secret sharing

I want to: Encrypt my whole HDD with a keyfile and a password (meaning that both are required to decrypt it), Be able to back up pieces of the keyfile in several distant locations using Secret ...
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93 views

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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92 views

Numeric combination of passwords

Pls I need explanation on How i can design a Cryptography that use multiple passwords or passphrase to open a safe(Lock). For example, if i need five people to unlock a secured device whereby all the ...
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170 views

Diffusion in Shamir's secret sharing scheme

The popular command line utility ssss implements the classic Shamir's secret sharing scheme over the generic field $GF(2^q)$ with $8 \le q \le 1024$. When $q>=64$, the constant coefficient ($c_0$) ...
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Is anyone aware of Du atallah multiplicative secret sharing scheme for dot products for > 2 party scenario?

I am working on Du Atallah's multiplicative secret sharing scheme for more than 2 party scenario. Is anyone aware of its multiparty version (more than 2 parties). The paper for 2 party can be found ...
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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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53 views

Secret Sharing 1 Required

Devise a scheme so that a message M can be shared among X, Y and Z in such a say that the only way of recovering the message is when X is present with either Y or Z. When X isn't present or each is ...
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Can I use Shamir's secret sharing scheme for multiplicative homomorphism for secure multiparty computation?

I would like to perform a dot product operation among $m$ parties using Shamir's $(m,m)$ secret sharing that is used for Secure Multiparty Computation. I am aware that Shamir's $(m,m)$ scheme is ...
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130 views

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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144 views

Do deterministic secret sharing schemes exist?

Are there algorithms for secure secret sharing such that the algorithm depends solely on the value being secured, relying on no randomness in its calculations. If there aren't, is such an algorithm ...
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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 ...
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Shared secret: Generating Random Permutation

-- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ...
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How do you distribute secret shares without knowing who to first distribute them to?

Figure 1 on page 1249 of the “Multiparty Computation Secure Against Continual Memory Leakage” paper shows $m$ committees are elected in step 1 and then later in step 3 are each given a secret share. ...
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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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140 views

How can Shamir's method for secret sharing work in the GF(256)?

I have been reading about Shamir's secret sharing, and maybe i completely misunderstand something, but the field is meant to be a prime. However, when i look at the implementations of this algorithm, ...
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129 views

Secure function evaluation

Consider 3 parties, Alice, Bob and Charlie. Suppose each party has a bit as input, i.e. Alice, Bob and Charlie hold $a, b, c \in \{0, 1\}$ respectively. Show how construct a scheme with which ...
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113 views

How does secret sharing solve the partial exposure problem?

I have been trying to understand how secret sharing methods like Shamir's secret sharing solve the problem of a share revealing information about the secret. I guess there are some random numbers ...
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63 views

How to pass an arbitrary signature to a certificate

I am trying to sign certificate (X509) using secret sharing. That is shareholders combine their signatures to produce the final signature which will be in this case the signed certificate. However ...
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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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79 views

secret sharing of product of 2 numbers

Does evaluating the products of shares $a_jb_j$ give a secret sharing of $ab$? I think it's a no, but I am not sure on how to prove it.
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How to Distribute the Shares using Secret Sharing for arbitrary Monotone Access Structures

Consider 4 people, $A$,$B$,$C$,$D$, & a secret $s\in\{0,1\}^k$. Construct a scheme which enables the following subsets of people to retrieve the secret $\{A,B\}$, $\{A,C\}$, $\{B,C,D\}$. I know ...
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225 views

XOR secret sharing scheme

I was wondering how we can get a secret sharing of $a+b$ from the sharing of secrets $a$ and $b$ themselves by using an XOR secret sharing scheme, where $a_1,...,a_n$ and $b_1,...,b_n$ are the shares ...
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Safety when disclosing hashes of secrets used to calculate other secrets

In my application, I am generating a big random number and publishing a SHA256 hash of it. After the hash it published (but not the secret), anyone can submit any number, and the system will calculate ...
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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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post-quantum threshold secret sharing

I am looking for a references for post-quantum threshold secret sharing schemes. I am especially interested in knowing whether any one based on one-way compressor functions or cryptographic hashes ...
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126 views

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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171 views

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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51 views

Algorithm for sharing secret information with redundant keys [duplicate]

I have an information that I would like to encrypt and give it to someone else. I would like to encrypt it using N separate passwords (say 5) and give each password to some other persons. However the ...
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174 views

Shamir's secret sharing with passwords

I'm trying to design an extension to Shamir's Secret Sharing that would allow the participant to specify a password instead of remembering/storing a large integer or binary data. So far, I have two ...
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General-purpose non-interactive multi-party computation protocol

Most of general purpose multi-party computation protocols are highly interactive. Especially the ones with Shamir's secret scheme, as there is a degree reduction step in multiplication that needs the ...
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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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209 views

Secret sharing scheme with possibility to change the secret

Here's a scenario I want to handle with a secret sharing scheme: Alice wants to share the secret $S$ with Bob, Charlie and Dave. Alice generates private shares based on $S$ for Bob, Charlie and ...
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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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152 views

What's efficient MPC protocol for determining if sum's bigger than y?

My secure multi-party computation (MPC) in need is simply to determine if a sum of two private variable is bigger than a given value $y$, as $f(x_0, x_1) = [(x_0 + x_1) > y]$ in which the value ...
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116 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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144 views

Is this a sensible cryptographic protocol intending to reduce the impact of compromised security?

I'm in the process of designing a cryptographic protocol which will reduce the impact an attacker will have if they gained root access to a server storing data. The basic crux of it is that keys ...
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592 views

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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237 views

Requiring a “supervisor” key pair and a “user” key pair to decrypt multiple-recipient messages

I've been toying with some encryption scenarios recently. One of the hard ones I came across is a multi-party system. So we have Bob -- The person who sends the message (and knows it's recipients) ...
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190 views

Addition with Shamir secret sharing

When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$. I believe this would be the correct solution (correct me if I'm wrong): Each party ...
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135 views

How to obtain a one-value share in Shamir's secret sharing

This is a trivial question, but I had to ask: since each generated share in a Shamir's secret sharing scheme initially consists of a pair of values (representing the coordinates of a point on the ...
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289 views

Understanding Feldman's VSS with a simple example

I'm trying to understand Feldman's VSS Scheme. The basic idea of that scheme is that one uses Shamir secret sharing to share a secret and commitments of the coefficients of the polynomial to allow the ...
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534 views

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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208 views

How to generate a random polynomial of degree $m$?

I am trying to do a homework in which implement a variation of this paper and I don't know how to generate a polynomial of degree $m-1$. This polynomial is used to generate the $y_0$ and $y_1$ values. ...
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Does zero-padding the secret in Shamir's sharing scheme increase security?

When performed in binary Galois fields $GF_{2^n}$, Shamir's threshold secret sharing scheme produces shares that are each the same bit-size as the secret. Though the scheme is "perfectly secure" in ...
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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 ...