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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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117 views

Having access to multiple servers, would additional usage of “Secret Sharing” for password storage enhance security?

I am currently learning about secret sharing and I’ve started wondering why larger companies that have access to whole server networks (like – for example – Google, Facebook, etc.) don't use “Secret ...
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685 views

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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208 views

What is the difference between any secret sharing scheme and arithmetic secret sharing scheme

It looks like that only difference between two of them the variables. But it does not make sense for me and I could not find exact definition of arithmetic secret sharing scheme. I mean what exactly ...
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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 ...
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69 views

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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81 views

Tampering with Shamir's subshares

Suppose a set of Shamir's redistributable-secret-sharing participants issue a redistribution of subshares. I envision this as a series of points on a line (2 of N, is planar, easy to think about). ...
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69 views

Is it safe to derive secret from alice's private key and alice's public key?

I'm using secp256k1; in normal scenario alice.privateKey and bob.publicKey (or vice versa) is used to derive the same ...
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3answers
204 views

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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414 views

Shamir Secret Sharing Modular Reduction

Say players use Shamir's secret sharing to share a value $k$ such that each player now holds $k_i$, a share of $k$. How can they securely compute $k \bmod m$ for some $m$. Of course they can ...
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156 views

Secure multi-party computation for digital signature

Is there any practical algorithm that will allow to use public key cryptography (RSA or ECC) in the following way There are N parties. Up to M are malicious adversaries (were trusted, but got taken ...
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77 views

Creating a share of a random shared secret [duplicate]

I am interested to know if there is a solution to the following scenario: Assuming we have $n$ party members, is there a scheme that at the end of it, every party member $i$, holds a shamir's ...
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197 views

Secret Sharing Scheme, with joining players, no central entity

I am facing the the following problem: Lets assume i have a secret, $S$, I want to share it to $N$ players so that $K$ of them can cooperate in order to obtain the secret ($K$,$N$ scheme). Is there a ...
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258 views

Secure multiparty sum computation corruption bound

In Section 3.4 of the book Secure Multiparty Computation and Secret Sharing, it is claimed that for a secure multiparty computation problem with $n$ parties, the optimal corruption bound (concerning ...
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124 views

Are Lagrange Multipliers necessary for Shamir's secret sharing?

What is the implication of not using the Lagrange multipliers in Shamir's secret sharing? I mean each update will be $Poly(x_i) \bmod p$ where $p$ is a prime number instead of the original one that ...
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99 views

Is there an algorithm to derive a 1-of-N shared secret from a set of N private keys?

This is different from Shamir's Secret Sharing in that we are starting with the keys and deriving a shared secret, rather than the other way around. Let me be more precise: We are given keys $k_1, \...
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131 views

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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151 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 ...
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196 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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250 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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Impact of a non-uniform distribution in a secret sharing scheme

When it comes to the secret sharing schemes, it seems that the random numbers need to be drawn uniformly. Is there any difference between the random numbers from uniform distribution and the non-...
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1answer
55 views

Secure scheme to share symmetric key using asymmetric keys and certificates with N parties

I need to distribute symmetric AES key into number of end points which will use it to decrypt data. The AES key will be the same on all end points, it is not possible to generate unique on every end ...
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1answer
210 views

Determining the secret using the Blakley's scheme?

I am solving a example with Blakley's scheme problem. The issue that I am having is using the row operation to determine the secret $x_{0}$. So what I have so far is: Given three planes: $z = 7x + ...
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219 views

What is proactive secret sharing scheme?

In some papers, they just wrote that proactive secret sharing scheme is a secret sharing scheme which its shares are periodically updated. Does it have formal definition ?
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330 views

Dividing a secret into multiple nodes in a blockchain kind of system with time-release?

I would like to have these features and want to ask if it is theoretically possible: a) There is custom software running on nodes in a blockchain style b) A secret is kept in the blockchain that ...
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1answer
69 views

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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Can you update a (k,n) scheme to a (k+t, n+t) scheme (assuming old keys can be deleted)?

I know that $(k,n)$ can increased to $(k+t,n-s)$ one, by generating a random polynomial $p(x)$ of degree $k+t$ with constant term $0$, and then ordering each agent $a$ to add $p(a_x)$ (where $a_x$ is ...
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193 views

Recombination thresholds in degree reduction of multiplied Shamir shares

Shamir's secret sharing can be considered multiplicatively homomorphic, if one is aware of the fact that multiplying two shares of a (n,t)-threshold shared secret yields a share of the same secret, ...
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111 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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166 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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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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1answer
64 views

Share secret non-interactively in a verifiable way

In an application, I need to share a secret (random number) with a Group of known receivers over a public channel (a Blockchain) but each receiver needs to be able to check that the others received ...
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112 views

Reference for additive secret sharing

Regarding the secret sharing schemes, I am wondering if there are any academic references for the Additive Secret Sharing and its variations. Is there any textbook or article which has specifically ...
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Adding new share (Shamir Secret Shares ) [duplicate]

I am using this https://github.com/gburca/ssss-js Shamir implementation. I generated 4 shares from secret (threshold of 2). I am wondering if I can recreate (interpolate) original polynomial from ...
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68 views

Differential privacy and Shamir's scheme

I have been unable to find any proofs (for my own reference) that demonstrate that Shamir's secret sharing scheme does (or does not) satisfy the definition of $\textbf{differential privacy}$ as ...
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62 views

Asmuth-Bloom Secret Sharing $m_0$ public?

i am trying to figure out how Asmuth-Bloom secret sharing works and followed the example on wikipedia and replaced it with own numbers. Namely, i used: $S=3$ $k=3$ $n=4$ $m_0 = 13, m_1=45, m_2=46, ...
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What is difference between Unipartite Secret Construction, Bipartite Secret Construction and Multipartite Secret Construction

In this paper authors extend Asmuth–Bloom and Kaya schemes to bipartite access structures and further investigate how SSSs realizing multipartite access structures can be conducted with the CRT. The ...
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Verifiable secret sharing - Benaloh scheme; some doubts not answered earlier

I reviewed the paper "Secret sharing homomorphisms: keeping shares of a secret secret" by J.C. Benaloh yesterday and I had some difficulty understanding his version of verifiable secret sharing to ...
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35 views

Threshold signature without revealing id of signers to the recombiner

I want a threshold signature t out of n algorithm where set of t signers are not known before hand and want to remain anonymous after signing. How is recombination possible if id of signer is not ...
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Are there any information-theoretically secure verifiable secret sharing protocols with t=n?

Disregarding matters such as efficiency and round complexity, can verifiable secret sharing be done in a way such that the secret cannot be decoded unless you have all n shares, and that this ...
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1answer
157 views

Baek and Zheng’s Threshold Cryptosystem - limit on threshold?

I have just completed an implementation of Simple and Efficient Threshold Cryptosystem from the Gap Diffie-Hellman Group by Baek and Zheng and am hitting a problem with high values of the threshold. ...
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Ecash - Probability of catching a user using secret splitting who duplicates the coin

For detecting double spending, secret splitting is used. If a user duplicates the coin, then there will be two different transaction items in transaction list. What is the probability of catching a ...
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124 views

How does threshold decryption with secretly shared exponents actually work?

Imagine the case where you have a sufficiently large finite field (or any multiplicative field for that matter) $\mathbb{Z}_{p}$ where p is some large prime. Now, I have a number $g \in \mathbb{Z}_{p}...
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Can you explain “k out of n” from the VCS paper by Naor and Shamir

I am new to visual cryptography. I’ve just read the paper “Visual Cryptography” by Moni Naor and Adi Shamir and I'm stuck on the chapter about the “$k$ out of $n$” construction. I am aware that, on ...
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153 views

Signing integers and UUIDs and restoring them from a third party server without tampering

I'm educating myself about cryptography. I know this is a long one, but please, bear with me. :) Now I have a scenario in my mind and I'd like to ask if what I've thought is sound (enough), what more ...
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277 views

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, i....
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641 views

Distributed Shamir's secret sharing

Wikipedia on its page for Shamir's secret sharing scheme provides a python implementation that applies the idea. This algorithm will generate a (k, n) threshold scheme so for example we could split a ...
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Is this a good way of splitting a private key into a 2 of 3 scheme?

Basically the idea is to split a key into three parts ($key_a, key_b, key_c$) of which any 2 of the 3 parts can be used to recreate the original key $key_a$: a random number smaller then our original ...
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Formal Proof of Shamir's Secret Sharing Scheme Security

Shamir's Secret Sharing scheme is perfectly secure. Could you please suggest where I can read a formal proof of Shamir's Secret Sharing scheme being perfectly secure?
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Security of Shamir secret sharing with regards to the threshold

Consider Shamir Secret Sharing Scheme (SSSS). This is completely unfounded, but my intuition tells me that the threshold k we set (AKA the number of shares required ...
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1answer
122 views

What is definition of adversary ? And what they do?

Currently I am writing my last assignment about secret sharing. But I don't get clearly about adversary. I know this seems so basic understanding in secret sharing. But I couldn't get references that ...