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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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 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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239 views

Terminology: differences between the terms “pre-master secret”, “master secret”, “private key”, and “shared secret”?

Both crypto.SE and security.SE have excellent Q&As about how TLS generates session keys (I have linked some at the bottom). In reading these threads I'm having troubles with terminology since the ...
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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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126 views

Verifiable, Distributed Secret Santa Assignments

My family was planning a secret santa and I thought about how I might write a little web app to dole out these secret assignments. But the downsides to this approach are obvious: there's no way for ...
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516 views

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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422 views

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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996 views

How to require two keyholders to decrypt a document?

I want to create a system to encrypt a document and store it with a 3rd party, but not have the 3rd party be able to decrypt it until some unspecified later date. It seems like the solution would be ...
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629 views

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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252 views

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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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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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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337 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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105 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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99 views

$(k, n)$ 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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790 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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370 views

Is there a secret sharing scheme which allows delegation/re-sharing without reconstructing the original secret?

EDIT: Ilmari Karonen's answer below well not exactly what I want, gives a very good idea of what I am trying to accomplish. Are there any known secret sharing schemes that allow new parties to be ...
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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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239 views

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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498 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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237 views

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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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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448 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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207 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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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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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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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 ...
3
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186 views

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 ...
3
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222 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, ...
3
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1answer
150 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 ...
3
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1answer
245 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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301 views

Security considerations for partially shared password databases

Programs like KeyPass and 1Password store password database files encrypted by a single password. If someone knows the protecting password ("Vault Key"), they can read the entire database ("secrets"). ...
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301 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 ...
3
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406 views

secure multiparty computation for multiplication

Suppose there are $N$ parties $p_j$, each with a binary $b_j\in{\{0,1\}}$. The problem needs to compute the multiplication of number of ones times that of zeros, that is, ...
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Image sharing without data overhead

The idea is to share $n$ images among $n$ persons so that all images can be reconstructed by someone in possession of all shares. However, there must not be any data overhead (which means the shares ...
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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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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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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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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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1answer
776 views

Shamir Secret Sharing - Threshold decryption implementation

I'm implementing Shamir secret sharing in C using OpenSSL. I've split up the private key and I'm ready to start decrypting the original message using some of the shares. I set $n = 5$ (5 shares ...
2
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1answer
32 views

Does pseudorandom secret sharing require a central dealer?

I'm trying to figure out whether pseudorandom secret sharing (as described in this paper) requires a central dealer, i.e. one party who doles out keys to the other players and thus who would be able ...
2
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1answer
119 views

Secure MultiParty Computation with secret inputs for secret outputs

I want to know if it’s possible to use a SMPC (Secure Multi-Party Computation) to have $N$ entities compute the outcome of a known mathematical operation with two or more secret inputs, where each ...
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96 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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244 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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62 views

Feldman's VSSS: Showing the Correctness of shares that are Consistent

This is something with which I am struggling to get my head around. In Feldman's VSSS, I am aware that the Dealer broadcasts exponentials $a_{1},...,a_{t-1}$ of the secret $K$ and the coefficients ...
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77 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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103 views

Educational videos for security topics [closed]

Is there anything like the famous "sorting out sorting" video in cryptography/security. I am looking for some nice videos that explaines SSL, SET, IPSec, PGP, S/MIME ....
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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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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. ...