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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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Mathematics behind the paper “how to leak a secret” for ring signature

I'm reading the paper "How to Leak a Secret" (Rivest, Shamir, Tauman; 2001). On page 8/14, in chapter 3.4, the authors present the following "combining function": $$C_{k,v}(y_1, y_2,\ldots,y_r) = ...
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secret sharing scheme difference

confused about differences between 5 out of 5 threshold secret sharing scheme and 4 out of 5 threshold secret sharing scheme. how would the share and reconstruction schemes be different assuming both ...
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PCI DSS requirement 3.5.3

3.5.3 Store secret and private keys used to encrypt/decrypt cardholder data in one (or more) of the following forms at all times: ............ As at least two full-length key components or key shares, ...
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Shamir Secret Sharing and Diffie-Hellman procedure

Alice needs to share an already generated numeric secret $s$ with Bob and she doe not want the world to see it. The problem is that she has never contacted Bob before. I thought Alice and Bob could ...
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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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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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Pairing-based cryptography VS ZK-proofs: what's more efficient for threshold systems?

In some papers (e.g. 1, 2) the authors approve that pairings are more efficient than classic zk-proofs (e.g. proof of discrete logarithm knowledge) for the described applications (threshold encryption,...
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Difference between Asmuth-Bloom and Shamir's Secret Sharing

Both Asmuth and Shamir are threshold based secret sharing schemes and perfectly secure. In which point of view Asmuth bloom secret sharing scheme is better than Shamir secret sharing scheme. Could ...
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Secret sharing over reals - Difficulty with Computer implementation

I asked a question recently regarding the paper "Secret Sharing Over Infinite Domains" - B. Chor and E. Kushilevitz which describes a secret sharing scheme for real numbers in the interval $[0,1]$. I ...
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Change a secret key in an embedded device

There is a device that uses a secret key Sk to encrypt data. Assume this Sk is compromised. Could the following scheme be considered safe, in case we want to change the compromised Sk: We store some ...
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Under what conditions is broadcast possible? (Cryptographically, and in the model of Maurer 2006)

In this paper, Ueli Maurer uses a very cool model to generalize a number of results about broadcast, secret sharing and secure multiparty computation. Rather than talking about an adversary being ...
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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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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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Secret sharing over reals - constructing a (k,n) threshold scheme

After following a discussion that Shamir's Secret Sharing scheme cannot be used to share a real number as secret, I came across the paper "Secret Sharing Over Infinite Domains" - B. Chor and E. ...
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Multi-secret sharing (Packed secret sharing) - Some questions

In the publication - "Communication complexity of secure computation", I have encountered a small problem - on page 5 of the literature under the heading "Theorem 1" they have described a $(c,d; k,n)$ ...
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Shamir Secret Sharing Scheme - leak of information

After going through some literature, I've convinced myself that to recover the exact secret using Shamirs Secret Sharing scheme, we must have S(the secret converted into a number) < p (choice of ...
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Shamir Secret Sharing Scheme - some doubts not answered earlier

my first question on here. I've gone through some examples of Shamirs Secret Sharing Scheme, but I have 2 rather pressing doubts - i. Why do we choose the co-efficients of the polynomial from the ...
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Private Key Sharding - How is it Secure in a Distributed Network?

In a Distributed Network in order for a private key not to be compromised sharding will have to take place off the network, correct? If so: Why is it when a Distributed Network shards private keys ...
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How to perform Shamir Secret Sharing with a Tabula Recta?

In this post, a couple comments suggested that a tabula recta could be used to perform Shamir Secret Sharing. I'm specifically interested in this statement: you could just have a table of all 100 ...
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Is recursive secret sharing of practical value?

This paper describes recursive secret sharing. In one of their illustrations, a binary secret of length L, along with 3 other binary secrets of lengths shorter ...
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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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How does one construct a 27x27 tabula recta for 2-of-3 secret sharing?

In the answer to this post at security.stackexchange, someone describes how, using pencil and paper, one can do 2-of-3 secret sharing with a tabula recta. But I don't understand how he created his ...
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Why every access structure is a multipartite access structure?

The set of authorized subsets of participants is called an access structure. In a multipartite access structure, the set of participants is divided into several parts and all participants in the ...
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Combining secret keys into a single shared key

Let's say there are $n$ participants each with their own secret key $x_i$. Is it possible for them somehow to build a shared key which is an arithmetic sum of all their secret keys ($x_0 + x_1 + ... + ...
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Adding new participants to a multiparty signature scheme

I'm looking for a signature scheme that allows a group of N parties, without the help of a trusted dealer, to: Jointly create a group public key $P$ Produce a valid signatures for an arbitrary ...
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What's the functional difference between fountain codes and polynomial secret sharing?

Fountain codes, as I understand it, allow for the reconstruction of a set of data (e.g. a 64-bit word), by sending (without corruption or failure) chunks of data generated using a probabilistic ...
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Multiparty key exchange for end-to-end encryption

I need to make end-to-end encrypted messaging between 2 and more parties without trusting a server. Each party has it's secret and private keys. The obvious solution is to make ECDH between all of ...
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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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Preserving location privacy

What are cryptographic techniques that could be used so that if I wanna to enable a server to send message to certain nodes in a network with preserving the privacy location for them ??
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Question regarding reconstruction vector in LSSS

Suppose we have a policy $A \wedge ( D \vee (B \wedge C))$ with attributes ${\{A,B,C,D}\}$. The set of subsets of attributes which satisfy this policy is ${\{{\{A,D}\},{\{A,B,C}\},{\{A,B,D}\},{\{A,C,D}...
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Reconstruction vector in Linear secret sharing schemes

Suppose we have a policy $A \wedge ( D \vee (B \wedge C))$ with attributes ${\{A,B,C,D}\}$. The set of subsets of attributes which satisfy this policy is ${\{{\{A,D}\},{\{A,B,C}\},{\{A,B,D}\},{\{A,C,D}...
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Eliptic curve verifiable secret sharing

I am implementing the following the algorithm instructions as shown in 1 (section IV, B). When trying to verify the share given the commits, $a_jG$ verifier $i$ checks whether $f(i)G=\sum_{j=0}^{t} (...
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Reverse Shamir's Secret Sharing Algorithm?

Shamir's Secret Sharing algorithm works by breaking a single secret to multiple parts. While it is trivial to implement the reverse in a $n$-out-of-$n$ scheme, how would one implement an $m$-out-of-$n$...
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AES encryption using MPC SPDZ protocol

I'm reading the article about SPDZ protocol for secure multiparty computation (and also improvements for offline phase like MASCOT). However I'm thinking about practical application of SPDZ for AES ...
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$t$-out-of-$n$ Secret Sharing over $\Bbb Z_2$?

Is it possible to construct a $t$-out-of-$n$ secret sharing scheme over $\Bbb Z_2$? Shamir Secret Sharing allows for an arbitrary threshold $t$ and an arbitrary number of participants $n$, but ...
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Number of possible access structure with $n$ person

I want to count number of possible access structures in closed form(if possible) as a variable of $n$,the number of share holder. I have tried in several ways. Still no good progress. It is very hard ...
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Can I share a secret among more than two keys in ECC? [duplicate]

Sharing a secret in ECC is easy. Alice calculates $S = aB$ and Bob calculates $S=bA$. They will both arrive at the same secret because $aB=bA=abG$. This does not seem to be easily generalizable to ...
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Multiparty secret generation protocol

The goal is to create a secret S on a trusted server by having users A, B and C each send a private seed to the server, in such a way that any 2 of them can later recover S by resubmitting their ...
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Threshold signature scheme with combiner outside the group

Assume we have a (t,n) threshold signature scheme in which the secret key is shared between the n group users. If at least t users sign a certain message . Can we build the scheme in such away ...
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Minimal size of share in Shamir's Sharing Scheme

Why does the combined shared key in Adi Shamir's Sharing Scheme have to be smaller or equal than each secret share?
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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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Anti-collusion cryptography/schemes for multi party authentication

Due to the fact that 95+%, if I remember correctly, of security breaches are done by insiders (due to malicious intent or incompetence), I made a (experimental) server that uses Shamir Secret Sharing ...
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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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Optimized Random-OT Security in Standard Model

I was going through the paper - " Efficient Oblivious Transfer and Extensions for Faster Secure Computation" by Asharov et al. where the authors propose an optimized OT protocol along with a Random-OT ...
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Can Secure Multi-party Computation be used to reconstruct secret shares?

When using Shamir's Secret Sharing is it possible to use Secure Multi-Party Computation to reconstruct the original secret without revealing one's secret share? When searching I have found results ...
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A method for creating distributed public key for ECDSA, what are the risk factors?

There is quite a bit of literature on distributed ECC signing without a trusted dealer. Published works are mostly overly complicated, so I am proposing this simple technique which I am sure if it is ...
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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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Can we use Shamir secret sharing conversely?

Suppose $n$ users choose random numbers $r_1,r_2,\dots, r_n$, can we reconstruct a secret using $t$ of them with Shamir's technique?
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Does adding a random number to my data make it secure?

Say I have some real valued data that i want to keep secure. Now I have to pass on some modified version of the data to a second party for some computation, but i do not wish to reveal my data to the ...