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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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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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101 views

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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52 views

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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26 views

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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58 views

Interpolate $(x_i,y'_i)=[(1,5),(2,1),(3,4)]$ with $\prod_{i=1}^n y'{_i}^\left(\prod_{\genfrac{}{}{0}{1}{j\not=i}{j=1}}^n\frac{x_j}{x_j-x_i}\right)$

I have three points $(x_i,y_i) = [(1, 9), (2, 20), (3, 37)]$ from a polynomial $3x^2 + 2x + 4 \pmod{11}$ where the secret $s=4$ And I would like to compute the constant $c=9$ to the power of the ...
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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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65 views

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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39 views

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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35 views

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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62 views

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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42 views

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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81 views

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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113 views

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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105 views

$t$-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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1answer
67 views

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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28 views

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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24 views

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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58 views

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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194 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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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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1answer
73 views

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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68 views

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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28 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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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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241 views

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 ...
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65 views

Can I prove my app uses randomness right way?

We are developing an iOS app which employs Shamir Secret Sharing algorithm. We made all possible steps users can trust us. We can't remember their secrets nor we can save encoded fragments. But they ...
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74 views

Combining multiple cryptographic keys to generate an encryption key

We have a system that has several SecretKeys (for example, one for a user, and one for us). We want to encrypt data in a way that requires all of those keys to be available in order to decrypt. I ...
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83 views

How to reversely compute from hash [closed]

What are practical methodologies to derive the following ciphertext: 1bd0d370b262d748b21c40cc7e5746642b4c06079a224c65e443e429289753c2
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How to perform homomorphic multiplication using Shamirs secret sharing

Shamir's secret sharing (SSS) support additive homomorphism. The problem with it while dealing with multiplication is it will increase the polynomial degree and as a result number of shares required ...
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1answer
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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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47 views

Conditional $k,n$ secret sharing

I would like to know if there is a way to place a condition on $k$-out-of-$n$ secret sharing such that out of $k$ participants who can pool their shares to reconstruct a secret, one of them should ...
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Additive homomorphic secret sharing

I am new to cryptography esp, homomorphic encryption. I would like to know if the following is possible using something similiar to additive homomorphic secret sharing. Please apologize me if its too ...
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102 views

Generating a safe prime and its primitive root

I am trying to write a program for Verifiable Secret Sharing, where I want to generate large prime (512 bit) and to find its primitive root. Giving such a large prime, I have to generate a safe ...
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81 views

Interpolation in the Exponent (Shamir Shared PRF)

Trying to implement the Diffie-Hellman distributed PRF mentioned by Cachin : https://cachin.com/cc/papers/abba.pdf. It makes sense to me... just use the same Lagrange coefficient I'm using to combine ...
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135 views

A problem in secret sharing and mixed operators over $\mathbb{Z}$

Recently, I studied an article in which it was written that having $(A-B)\oplus C$ and $B\oplus C$, we cannot find $A$. The authors used this result to build a secret sharing scheme, but they did not ...
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What SMPC protocols make use only of additive secret sharing?

In Appendix G of the Hawk paper, where it talks about financially fair SFE, it mentions that it's possible to run a SMPC protocol where, at the end, each party has a share of their own output y, and a ...
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1answer
69 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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57 views

How to express access structure (access tree, linear secret sharing, etc.)

What are the differences and similarities between access trees (binary decision diagrams) and linear secret sharing in the use of attribute-based encryption schemes for access control?
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49 views

Shamir's Secret Sharing - Impersonating the Dealer

I understand that Shamir's Secret sharing has nothing to do with the methods that are used to share and later recover a key. That means then, the secret is only as secure as the methods used in ...
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What would be the best way to distribute shares created from a secret sharing scheme for an application?

I built application A that uses a secret key to encrypt and decrypt sensitive data. I also implemented Shamir's Secret Sharing Scheme to shard the secret with minimum points = 3. I want the ...
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Shamir's Secret Sharing Computation time

Hello for my thesis I am making research about SSS computational time. Based on (K,N) threshold scheme Where K is the minimum number of shares to rebuild the secret and N is the number of shares ...