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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Is an implementation of blinded encryption/decryption mechanism exists?

I want to use 2 semi trusted servers, to decrypt a secret for a user but I don't want those servers to have access to the plain text. Those server need to be able to "partially" decrypt and let the ...
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How to backup a secret encrypted by multi parties without revealing the secret?

I'm searching for a way to backup a secret that only the end user knows the information with 2 trusted hosts. But trusted hosts shouldn't have access to secret at any time. First basic version : ...
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Example of a Two-party GMW Protocol

I have been looking for a concrete example of GMW protocol for two parties. I was trying with the following example for computing $XOR$ of two parties: A's secret bit is $a = 0$, B's secret bit is $b ...
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How modern messengers encryption keys can't be hacked [closed]

I dont know is this question more like reverse-engineering or cryptographic. Why governments are hunting for encryptions keys? Aren't they delievering by the network the same as the encypted messages? ...
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Faster alternative to shamirs secret sharing algorithm

I recently discovered shamirs secret sharing scheme. Pretty interesting stuff. I noticed that a common case is to split a secret which is used to encrypt/decrypt something else. For example Vault is ...
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Encrypting text with AES and MPC

I'm thinking of implementing text encryption and decryption in my program using AES using key sharing thanks to MPC (the point is that the key should never be provided in full), however, all public ...
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Secret sharing in different groups; Rounding down of elements

I have the following problem: A secret $x \in \mathbb{Z}_q$ is secret shared (additive secret sharing) between $n$ parties, now is it possible to compute the secret shares of $y = \lfloor x \rfloor ...
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Publicly verifiable secret sharing scheme

In https://www.win.tue.nl/~berry/papers/crypto99.pdf, Schoenmakers proposes a publicly verifiable secret sharing scheme, that uses a non-interactive DLEQ proof to allow any participant to verify the ...
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Difference between group key agreement, group key sharing, group key distribution and group key establishement

I am currently doing a survey on group key, and throughout my readings, I stumbled on these different terms: Group Key agreement, Group key Sharing, Group key distribution, and Group key establishment....
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Understanding a variant of Shamir's cryptosystem with authorization levels

I am having problems understanding this implementation of Shamir's secret sharing with confidentially levels (in this case 3). I will give the context and then my problem to make it more clear. ...
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ElGamal Threshold Cryptosystem

Suppose we have a threshold ElGamal cryptosystem $(t, n)$ over an Elliptic Curve $E_p$, $p$ being a large prime, with the following parameters: $G$ is a generator point of $E_p$ with order $q$ A ...
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Secret sharing scheme verifiability

This secret sharing scheme takes place in the polynomial ring over a finite field $F_p[x]$, $p$ being a large prime, in the following simplified way: The dealer chooses a private polynomial $f(x)$. ...
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PCI - Limit Key Injection Capabiltiy 3DES + DUKPT

Current Context: I'm using a Triple DES with a DUKPT Key Management Approach. I have two organization which have access to the BDK Key: Orgzanization 1 which acts as the Secure Decryption ...
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$X_ {i_1}, . . . , X_{ i_ k} $ are IID random variables or not?

In this paper secret sharing is to distribute information (the secret) over a set of participants such that the secret can only be reconstructed if certain authorized combinations of participants join ...
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In a shamir secret sharing scheme, why can't the secret be a middle coefficient and only the first or the last?

In the shamir secret sharing scheme, the Secret s is set as the constant in the equation $ y_p = s+ \sum_{i=0}^{i = t-1} a_i * x_p^i$ s can only be the constant term or the last coefficient or the ...
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Example of the $Ω$−partite

Consider the following definition from section 2.2 of this research paper We write $\mathcal{P}(𝑃)$ for the power set of the set $𝑃$. An $𝑟-$partition $Ω=\{𝑃_1,\cdots,𝑃_𝑟\}$ of a set $𝑃$ ...
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Encrypt data. Create 5 keys. Just 3 keys are needed for decryption

I would like to encrypt some data and create 5 keys. These keys are stored in different places. If I want to decrypt the data I just need 3 of these 5 keys. Is there a way to do this?
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Distributed group signature scheme

Since there is only one group manager in group signature scheme, are there any scheme that have n group managers who pubilish the member private key or member credential together(or like threshold ...
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Which flaws does the following 2 out of 3 threshold secret sharing algorithm have?

Let's say the secret is an ordered set of two 8-bit integers — $\{a, b\}$. First, we generate additional entropy, another ordered set of random 8-bit integers — $\{c, d\}$. \begin{gather} a \oplus c ...
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Literature question on secure multiparty computation

Consider $N$ players and assume that a private channel between each pair of players is available. Player $i \in \{ 1, \ldots,N\}$ holds a secret $S_i$, which is a sequence of $B$ random bits. The ...
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How is Shamir's Secret Sharing better than this simple 2-password technique?

I'm looking for a solution to protect a message, such that both password1 (usually given to trusted person #1) and password2 (...
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Secret Sharing between $x$ parties

So for an unknown number of parties $x$, I make $x-1$ random $n$-bit strings represented by {$r_1, r_2,...,r_{x-1}$}. Where $s$ is the complete string split up between $x$ parties (yes?). I then ...
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Shamir Secret Sharing - How to reconstruction secret? Example

I try implement Shamir Secret Sharing. In this video: https://www.youtube.com/watch?v=j7Ngtl1cCpY is example. But for another three share holders is can't reconstruction secrete. For example: a) a(...
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Do I need verifiable shares?

I'm using Shamir's secret sharing in a 2:3 system. Thus a secret Key is split in 3 subkeys (KeyS:KeyC:KeyT) I've 3 entities at ...
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How can we evaluate a polynomials in a group instead of a field? (verifiable secret sharing on elliptic curves)

I am trying to understand how we can have cryptographic schemes that builds on both secret sharing, which is build on top of a finite field, and bilinear maps, which are built on top of elliptic curve ...
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Key derivation scheme with shared secrets?

I want to derive a list of sub-keys derived[t] from a master key mk by a key derivation function ...
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How to create a generator for a $Q_3$ access structure?

I'm reading about access structures used for multiparty-computation from https://eprint.iacr.org/2004/245 and https://eprint.iacr.org/2000/037. My understand is that to actually use the access ...
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What does non-collusion assumption mean in server-aided protocol based on secret sharing?

Suppose $m$ clients split their own input into $n$ shares using additive secret sharing scheme (mod something). Then, each of the clients sends each share to each of $n$ external servers. After ...
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EC threshold private key's multiplicative inverse and derived-key sharing

I have two devices, and each has a private key xPriv-i. Each device computes the corresponding EC public key xPub-i, shares it, and the linear combination of the keys is the "real" public key xPub. ...
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Why does using infinite fields leak secrets in Shamirs Secret Sharing Scheme? [duplicate]

There is a similar question here, but the answers as I understand them basically say (1) you can leak the parity of the secret and (2) you can run into over/underflow issues as well as floating point ...
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How to go about distributed private/public key pair generation?

I'm trying to implement a protocol in which two parties generate a private/public keypair, where both know the public key, but each party has only one part of the private key and cannot derive the ...
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Asymetric encryption, multiple recipients, traitor must share private key

Is there an Asymetric encryption scheme, or public key encryption, where multiple recipients are able to access the data but in order for one of the recipients to leak the key to the data they would ...
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What is the motivation of multipartite secret sharing?

In this thesis chapter 3.1 A multipartite secret sharing scheme is a scheme in which the set of participants is divided into several parts and all participants in the same part play an ...
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Question about publication “Efficient (k,n) Threshold Secret Sharing Schemes Secure Against Cheating from n − 1 Cheaters”

In the paper on section "4 Proposed Scheme", I suppose that the scheme does not protect if an adversary has access to the $k - 1$ original shares, am I correct? If the adversary has $k - 1$ of both ...
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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 sharing with one smaller share [duplicate]

Given a t-out-of-n shared secret scheme with the message space characterized by binary string of length l, why if one share is smaller than l the scheme is insecure?
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Shamir Secret Sharing: Using $a_0 \ldots a_k$ to store secret? [duplicate]

Let's assume I have a truly random secret $s$ that is 256 bits long, and I want to use SSS with e.g. $(k=4,n=8)$. The normal approach is to set $a_0=s$ and choose $a_1 \ldots a_{k-1}$ randomly, ...
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Explain the meaning of “$E_i = g^{F_i} g^{G_i}$ is uniformly distributed in $G_q$”?

In this paper[1] Qiong et al.’s CRT-based VSS} {Dealer Phase} To share a secret $ d \epsilon Z_{m_0} $ among a group of $n$ users with verifiable shares, the dealer does the following: <...
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Is my analysis regarding $M_3$ and $M_4$ correct?

In this paper authors gave the following equations for $M_3$ and $M_4$ in section $3.2$ of Share distribution phase: Shares Distribution To distribute $n$ shares of a secret $K$ among the set of ...
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How can one prove correctness of shared secrets in secret sharing schemes?

Assume we are in a centralized secret sharing setting, where one party generates the shares, and distributes them to other parties. How can the distributor who creates the shares prove to the parties ...
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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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MPC and Secret Sharing in not Fully-Connected Network

I have an interest in applications of MPC and Secret Sharing. My point of view is from fields of distributed computing and Game Theory. I want to generalize some results to arbitrary network ...
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Does lagrange interpolation work with points in an elliptic curve?

Defining the lagrange interpolation for $x=0$ as $\mathcal{L} = \sum_{i=1}^{t+1} y_{i} \cdot l_{i}$ with $l_{i}$ as the lagrange basis polynomials. Does this hold if we apply the elliptic curve ...
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Secret sharing - Size of the share

I'm having some hard time understanding why the size of the share must be at least as large as the secret itself, why is this restriction imposed? What would happen if the share is smaller?
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When Shamir secret sharing used in one time pad scheme

In the following, all operations are defined over a finite field of prime order. Please note that what I'm explaining below is a part of a bigger protocol, however, to keep things simple I just ...
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Split TOTP/HOTP secret and generate pin without trusted dealer

Many site use time-based one time password (totp) as second factor auth method, such as aws. So we can split the totp secret and distribute each part to different party to achieve threshold login ( ...
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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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Shamir's secret sharing for vectors

How would we go about building a scheme for Shamir secret sharing for vectors? I have already tried to use a vector of secrets and random distribution of the secrets to $n$ parties and then use $t$ of ...
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Cheating in (2,6)-Shamir Sharing Scheme

We consider a $(2, 6)$ Shamir secret sharing scheme over $Z_{11}$. Four players $A,B,C,D$ cooperate to find the secret, but one of them is cheating (so the share he claims to have might not be an ...
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How can I calculate the feasibility of brute-forcing missing secret shares against the secret checksum?

Secret sharing has the problem of player cheating, where a forged share $s'_i$ can be sent to generate a fake secret $m'$ during reconstruction (and the cheaters can even collude to generate the real ...

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