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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Why zero sharings are used to mask secret value to the masked value appears to be a random value?
Some interpretations say "By masking a secret value with a uniformly random zero sharing, the masked value appears to be a random value drawn from a uniform distribution. This randomness helps ...
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Reference implementation of Shamir's Secret Sharing
Is there an implementation of Shamir's Secret Sharing that can be regarded as a "canonical" (or "reference" or "standard") implementation, so that I can test other ...
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Garbled circuit and secret sharing
Recently, I was reading the paper One Hot Garbling published on CCS 2021. I noticed a sentence in it:
In this work, we forgo the standard GC notation of garbled labels in
favor of garbled sharings of ...
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Can one side of communication generate the shared secret?
Here is an example of what's on my mind:
$A\rightarrow B: Pub_{KeyA}+Sig_{TA}(Pub_{KeyA})$
$B\rightarrow A: Sig_B(Enc(Key)_{Pub_{KeyA}})+Pub_{KeyB}+Sig_{TA}(Pub_{KeyB})$
$Sig_{TA}$ is Trusted ...
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Question about Secure Multi-Party Computation
I am doing research about Non-interactive Secure Multi-party Computation and encounter a dilemma that I am not quite sure if it is possible and wonder if there are better thoughts that could help.
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Solving Shamir secret sharing schemes
I have been working through the introduction to cryptography with coding theory book and have just come across Shamir secret sharing questions. However I just don't quite think I'm understanding it ...
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Symmetry shares
I’m sorry if this is already answered, however, regarding symmetric key components to create a symmetric key using xor
(So eg comp1 xor comp2 xor comp3 = key)
If in the case of an AES KEY, which goes ...
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Multi party authentication or encryption
I rent a room in a building. There are also 9 others who rent other rooms in this building. Just like everyone else who rents a room I only have one key of this building.
With my key I can open the ...
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SMCQL practical examples
I am looking for some practical examples on how to use SMCQL on some typical SQL queries. The paper seems to be oriented more towards theory. Can somebody point me to some examples to understand it ...
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What is the flaw of secret sharing?
What is the flaw of secret sharing? It seems that there is no mention in the literature of the defects of secret sharing, such as the defects of homomorphic encryption may be less efficient computing, ...
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Conditional Boolean circuits
I have two questions I couldn't find straightforward answers to after many searches.
(1) We can perform 2-party MPC over arbitrary functions using Garbled Circuit. To do that, we first need to convert ...
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Constructing a straight line from two points not working in integer modulo group
I have a pair of coordinates of which all values belong to $Z_{p}$ where $p$ is a prime. I want to construct a straight line that goes through those two coordinates. Then I want to generate two more ...
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Is there a scheme for voting on decrypting a message with a variable voter count?
I am wondering if there might be a scheme for the following scenario: Let's suppose a government wants a truly democratic intelligence agency. For this the government publishes all intelligence ...
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MPC Protocol with Additions and Multiplications for FREE
Imagine an MPC protocol where both multiplications and additions come for free (2 round). The protocol works over arithmetic circuits, and the security setup is as relaxed as possible:
Semi-Honest.
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Using additive secret sharing to share the secret key of BFV scheme among $N$ participants
I want to share the secret key of the BFV scheme among N users using the additive secret-sharing protocol (n-out-of-n threshold secret-sharing). Can anyone please help me to adapt the two algorithms ...
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How can I use additive secret sharing to share the secret key of BFV scheme among $N$ participants?
I want to share the secret key of the BFV scheme among N users using the additive secret-sharing protocol (n-out-of-n threshold secret-sharing). Can anyone please help me to adapt the two algorithms ...
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Binary Secret Sharing vs Garbled Circuits
In Privacy-preserving machine learning, GC is usually used for privacy operation such as ReLU(x) where sign(x) needs to know. However, binary secret sharing also supports such computation via ...
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Gap in Shamir's Secret Sharing Scheme security proof
I'm trying to understand the security proof of Shamir's Secret Sharing method, as I want to adapt the polynomial creation a bit, and I've found the proofs I had available to be surprisingly vague or ...
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Shamir's secret sharing homomorphism for different degree polynomials
The $(t,n)$ Shamir’s polynomial based secret sharing scheme is $(+,+)$-homomorphic in which the addition of two polynomials secrets equals the Lagrange’s interpolation of the sum-of-shares for the ...
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Can I use Additive Secret Sharing without Finite Fields without introducing an exploitable bias?
As far as I know Additive Secret Sharing uses a finite field to generate its shares.
The gist of the scheme is that the shares $A_{shares}$ = {$A_1, A_2, ..., A_n$} of a value $A$ on a finite field $N$...
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Shamir Secret Sharing over an unsecure channel for a protocol design
Let's suppose that we have two parties, $A$ and $B$ that are using a Shamir Secret Sharing scheme with $k=3$. $A$ holds the points $[x_1, f(x_1)]$ and $[x_2, f(x_2)]$ while $B$ holds $[x_3, f(x_3)]$ ...
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Additive vs Linear Secret Sharing
I'm a beginner in the cryptography domain. Can anyone help me understand Additive Secret Sharing and Linear Secret Sharing? Are there any sources or references to understand their difference and how ...
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Multiple input AND/OR gate evaluation
In MPC, AND and XOR gates are two mostly used gates. However, most of the solutions (Garbled Circuit or Boolean Secret Sharing) considered these gates having 2 input wires and 1 output wire.
I am ...
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How to share a function securely?
I was reading a paper on Function Secret Sharing, and in that the author made use of the idea of GGM-style tree to propose a scheme based on pseudorandom generator.
Here I became interested in how to ...
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Solving colluding problem in Shamir's secret sharing
Can setting random indexes (and hiding them from the parties) in Shamir's secret sharing solve the colluding problem?
Here, Colluding problem is defined as if the threshold number of fraud parties ...
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Colluding problem in Shamir's secret sharing
Is there any standard solution to the colluding problem in Shamir's secret sharing i.e. How should I prevent my k friends from colluding and recovering my secret?
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Shamir secret sharing, recovery of keys which have 0 bytes in front of them?
From what I know SSS creates a polynomial with a0 = secret key and interpolates it on recovery using k coeffs. if a0 is a number,...
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Encrypt clients files and shares
I have to encrypt data (files) of client on server side and only the client can read theses files (admin can't see name and content of file).
To resolve this, I have the idea to just use something ...
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Increase encryption key length in Shamir secret sharing
Can Shamir's secret sharing work on any size of key?
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How to compute $\frac{1 + a_1 \times \dots \times a_n}{b_1 \times \dots \times b_n}$ where $a_i$ and $b_i$ are secret?
How can $n$ peers compute
$$\frac{1 + a_1 \times \dots \times a_n}{b_1 \times \dots \times b_n}$$
such that the pair of values $a_i$ and $b_i$ remains secret to the $i$-th peer?
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How to select the top two highest (or smallest) value in Two/Three Party Computation?
I want to select the top two secret-shared values from a vector of secret-shared values among 2/3 parties.
Formally, given secret-shared (assume using additive/replicated secret sharing) vector $<V&...
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What issues does the following Distributed Shamir Secret Sharing scheme have?
What (obvious) security issues does the following "onion" Distributed Shamir Secret Sharing scheme on a blockchain for the purpose of e-voting have?
The blockchain in this context, is an ...
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On a public e-voting, how do I keep the votes from being disclosed prematurely without a trustee?
I am trying1 to build a Proof Of Concept of a e-voting scheme on a blockchain. Before the elaboration, the question:
On a public e-voting, how do I keep the votes from being disclosed prematurely ...
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How is sum of two share of (2,n) shamir scheme equal to the secret?
I am refering to Privacy Aware Incentive Mechanism to Collect
Mobile Data While Preventing Duplication https://ieeexplore.ieee.org/document/7357616.
They claim to split secret $X$ into $X_s=\{x_0,\...
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Is there three-party protocol for Secure Equality Test (a.k.a Socialist Millionaire problem)?
Secure Equality Test is an important building block in Secure Multi-Party Computation (MPC) with respect to Secure Comparison, also known as Socialist millionaire problem.
A similar question was ...
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Looking for multi-party key exchange/shared secret algorithm with specific requirements
I'm looking for the ability to create a SINGLE CONSTANT shared secret amongst two or more users (a group) AND if a new user is added to such a secured group the new user should also be able to learn ...
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Why are binary extension fields preferred for Shamir secret sharing?
It is known that Shamir's secret sharing works over any finite field but I don't get it why binary extension fields are preferred?
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Correcting threshold in multi-party computation
I am currently reading the paper Graceful Degradation in Multi-Party
Computation. The paper mentioned something about correct structure, denoted C = {C1, . . . , Cl}.
On page 10 the paper reads:
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A question about masking input then share
I am confused about a simple input-sharing schema.
The schema: a party that holds an input x, and generates a random variable r.
That party secret share r as [r], then distribute it to other parties.
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"shared" variant of 1-out-of-N oblivious transfer
In the traditional 1-out-of-n OT, we suppose Alice has an array $A=\{x_1,{\cdots},x_n\}$ and ...
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Giving a continuous fractional (e.g. irrational) part of a secret to someone
In secret sharing schemes, we usually give rational fractional parts of a secret out. E.g. Alice gets 4/10ths of the secret, Bob gets 7/10ths, Charlie gets 5/10ths, David gets 1/10th, etc., and you ...
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Public-key/asymmetric encryption where you can only leak the decrypted message by leaking your password
A bunch of friends are using public-key encryption to send encrypted messages to each other using an open public forum. I.e. each friend has a public key (which you can use to encrypt messages for ...
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What are the uses of shared cipher texts and signatures?
In Distributed Key Generation(DKG), why is there a need to actually create a master secret which can then derive into a single public and private keypair(for signatures) and a secret key(encryption)?
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Tools/libraries to protect private keys using shamir secret sharing / multi-party computation?
here is the scenario. I want to use the concept of shamir secret sharing (or other multi-party computation methods) to store my private key in the public-key encryption. For example, I use RSA to ...
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Problem with Shamir secret sharing degree reduction in multiplication gate
The process of Shamir secret sharing degree reduction in multiplication gate is explained in
the following link
Now, based on the secret sharing that done by a degree one polynomial, we must be able ...
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Question about round complexity of secure multiple party computation based on secret sharing
I am reading Fast and Secure Three-party Computation:
The Garbled Circuit Approach
And in the introduction section it said that:
the round complexity of these protocols is proportional to the
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How could this scheme work?
When we use a secret sharing scheme we usually want to reconstruct the polynomial function $p(x)\in\mathbb{Z}_q[X]$ with the Lagrange interpolation method and then compute $s=p(0)=a_0$. However, the ...
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How can I use a secret sharing scheme when the secret is not a number but a statement?
I want to use a secret sharing scheme, where every player $i\in N$ has to share a pair of secrets $(l_i,\nu_{l_i})$, where $l_i$ is a unique code (positive integer) for every player, but $\nu_{l_i}$ ...
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Is it secure to do Shamir key split on a key in blocks and recombine?
Yesterday I made a PR to a python crypto library to support key sizes larger than 16 bytes for Shamir secret sharing scheme.
Currently it supports 16 bytes, as follows:
$$
K = \{ 0, 1 \}^{128}
$$
$$
...
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What could $a_0=s$ in Shamir's secret sharing scheme represent?
What could $a_0=s$ in Shamir's secret sharing scheme represent?
As we already know in a $k$ out of $n$ secret sharing scheme, a secret is split in $n$ parts however only $k=t$ parts (of a polynomial ...
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