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 ...

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Shamir Secret Sharing: Why cannot we recover polynomial's root if we have $t-1$ shares?

Imagine we have $t-1$ shares in $(t,n)$ shamir secret sharing. So at least $t$ shares are needed. Question: Why cannot we use $t-1$ shares to find a root of the polynomial and then recover the ...
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64 views

What is this encryption system called?

Let's say you want to break down a message, for simplicity it is just a bit $0$ or $1$, $m$ into two messages $(m_1, m_2)$ as follows: If $m =0$, then $(m_1, m_2) = (0, 0)$ with probability $1/2$ and ...
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84 views

Secret Sharing Encryption

Suppose Alice shares a secret block cipher key, $K_{AB}$ with Bob, and a different secret block cipher key, $K_{AC}$ with Charlie. Describe a method for Alice to encrypt an m block message such that ...
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88 views

Any reason to use Shamir given faster XOR threshold secret sharing algos?

TL;DR: Is the Kurihara algorithm really what it purports to be (dramatically faster but equally secure replacement for Shamir Secret Sharing)? ...
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29 views

Public key of a split key without calculating private key

I am searching for a secret splitting scheme where the private key doesn't exist, since each party chooses their own secrets. The other parties should however still be able to calculate the public ...
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315 views

Terminology: differences between the terms “pre-master secret”, “master secret”, “private key”, and “shared secret”?

Both crypto.SE and security.SE have excellent Q&As about how TLS generates session keys (I have linked some at the bottom). In reading these threads I'm having troubles with terminology since the ...
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70 views

Explanation of part of a visual cryptography algorithm

I have been working on a project involving visual cryptography and I am stuck with the following problem. My question is related to this paper, AN IMPROVED VISUAL CRYPTOGRAPHY SCHEME FOR SECRET ...
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1answer
33 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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53 views

Shamir secret sharing with field 2^8

I want to split a message using Shamir's Secret Sharing by splitting each byte of it so the field I'm using is $2^8$. Assume $(2,2)$ scheme, i.e., splitting it into $2$ shares and both of them are ...
3
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1answer
115 views

Image sharing without data overhead

The idea is to share $n$ images among $n$ persons so that all images can be reconstructed by someone in possession of all shares. However, there must not be any data overhead (which means the shares ...
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1answer
60 views

How are onetimepads distributed?

OTP encryption is unbreakable as it seems. I have read some stuff (wiki, blogpost, etc.) but i would not find any information how they are used. If i wanted to create a messenger service, how would i ...
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102 views

Choosing finite field size in Shamir's Secret Sharing Scheme

The Wikipedia article on Shamir's Secret Sharing says to that to have information theoretical security the splitting algorithm should be evaluated using finite field arithmetic on the field ...
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103 views

Benefit of using random key in Shamir's Secret Sharing

I am implementing Shamir's Secret Sharing, and I find that in (t,n)-threshold scheme, the shares are just using 1,2,3...,n as the key to form the shares ...
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31 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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1answer
52 views

Using hashed password as shared secrets. Good or bad idea?

I built a system that allowed users to generate an unlimited number of email addresses. Instead of storing each one in a db, I created addresses dynamically and made the address an hmac signed ...
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51 views

Problem in understanding Blakley's Secret Sharing Scheme

I need to implement Blakley's Secret Sharing Scheme. I have read below mentioned two research papers but still unable to understand how to implement it. Safeguarding cryptographic keys Two Matrices ...
2
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1answer
63 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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1answer
126 views

Verifiable, Distributed Secret Santa Assignments

My family was planning a secret santa and I thought about how I might write a little web app to dole out these secret assignments. But the downsides to this approach are obvious: there's no way for ...
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402 views

Is splitting AES ecrypted data safe?

Say I have a key, an iv and an AES/GCM/NoPadding encoded string and I want to split this information between three people such that only jointly can they reveal the ...
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87 views

Does the transposition cipher have a network application?

So I'm reading a chapter in my networking book and it talks about substitution and transposition ciphers (Transposition Cipher Wikipedia). I know that most network security uses public key or ...
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1answer
165 views

Roots of polynomial in Shamir secret sharing

I need to know whether one can obtain any roots of the polynomial in Shamir secret sharing if he possesses less than threshold shares. For instance in (t,n) if he has t-1 shares can he obtain any ...
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1answer
74 views

Checking the share membership in secret sharing schemes

I was thinking of this since yesterday. Imagine, a secret is split into its respective shares (using any secret sharing scheme) with threshold $t$ and total $n$. Can we find out given any random ...
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72 views

How to distribute symmetric key between $n$ entities?

If there are $n$ servers for broadcasting a symmetric key in such a manner that following holds: No server alone can find the key $K$ alone. Any two servers can pass $k_i$ and $k_j$ such that ...
5
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1answer
100 views

$(k, n)$ threshold secret sharing to $(k+k', n + n')$ without reissuing all shares

Given a $(k,n)$ threshold secret sharing used to back up a secret (meaning that the dealer has access to the secret at all times), is it possible to update it to a $(k+k', n+n')$ threshold secret ...
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1answer
121 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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240 views

Elliptic Curve Crypto, is a distributed signing method possible using Shamir's Secret Sharing?

Note: A distributed signature scheme exists for RSA: Practical Threshold Signatures, Victor Shoup. Is it possible to adapt such scheme for ECC? A centralized signing machine is vulnerable to ...
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197 views

Secure Secret sharing

I'm trying to come up with a new way to do oblivious transfer that is faster and requires less computation than existing methods. The basis of my method is shamir secret sharing. Below is an example ...
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90 views

(n,n) Shamir secret sharing [duplicate]

In (n,n) Shamir secret sharing if n shareholders do not have the public values (X values) can they still obtain the secret with only Y values?
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1answer
64 views

Send a symmetric key generated by one user to other users (more than two) using a server

I am developing a software in which I am using AES for encrypting messages shared in a group. The key is generated by one user, the admin of the group and needs to be shared with other members. How ...
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455 views

Shamir's secret sharing scheme - type of channels

For information theoretic security in Shamir's [m,m] secret sharing scheme, do i need both authentic and confidential channels? Another related query is ;is it true that if the channels are only ...
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1answer
116 views

Encrypt HDD with keyfile and password and allow backing up the keyfile with secret sharing

I want to: Encrypt my whole HDD with a keyfile and a password (meaning that both are required to decrypt it), Be able to back up pieces of the keyfile in several distant locations using Secret ...
5
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1answer
105 views

Back up an information as $n$ pieces and require exactly $n-1$ to recover it

Let $X\in \Bbb F_2^p$ be some information. How do I create $Y_1,\dots,Y_n \in \Bbb F_2^q$ so that having less than $n-1$ of the $Y_i$s gives you no information on $X$ but having $n-1$ of them allows ...
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102 views

Numeric combination of passwords

Pls I need explanation on How i can design a Cryptography that use multiple passwords or passphrase to open a safe(Lock). For example, if i need five people to unlock a secured device whereby all the ...
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280 views

Diffusion in Shamir's secret sharing scheme

The popular command line utility ssss implements the classic Shamir's secret sharing scheme over the generic field $GF(2^q)$ with $8 \le q \le 1024$. When $q>=64$, the constant coefficient ($c_0$) ...
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Is anyone aware of Du atallah multiplicative secret sharing scheme for dot products for > 2 party scenario?

I am working on Du Atallah's multiplicative secret sharing scheme for more than 2 party scenario. Is anyone aware of its multiparty version (more than 2 parties). The paper for 2 party can be found ...
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106 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, ...
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1answer
70 views

Secret Sharing 1 Required

Devise a scheme so that a message M can be shared among X, Y and Z in such a say that the only way of recovering the message is when X is present with either Y or Z. When X isn't present or each is ...
3
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1answer
354 views

Can I use Shamir's secret sharing scheme for multiplicative homomorphism for secure multiparty computation?

I would like to perform a dot product operation among $m$ parties using Shamir's $(m,m)$ secret sharing that is used for Secure Multiparty Computation. I am aware that Shamir's $(m,m)$ scheme is ...
3
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1answer
149 views

Does Runge phenomenon affect Shamir's secret sharing scheme?

Lagrange interpolation seems to be affected by the so-called Runge phenomenon when one tries to interpolate polynomials of high degree from a set of equidistant points. Lagrange interpolation is ...
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211 views

Do deterministic secret sharing schemes exist?

Are there algorithms for secure secret sharing such that the algorithm depends solely on the value being secured, relying on no randomness in its calculations. If there aren't, is such an algorithm ...
3
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142 views

Secret sharing - no dealer, modifiable, verifiable

I need to find a secret sharing scheme with these properties: The scheme is set up by all participants, ie no single entity called the dealer The parameters of secret sharing need to be ...
10
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1answer
420 views

Shared secret: Generating Random Permutation

-- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ...
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77 views

How do you distribute secret shares without knowing who to first distribute them to?

Figure 1 on page 1249 of the “Multiparty Computation Secure Against Continual Memory Leakage” paper shows $m$ committees are elected in step 1 and then later in step 3 are each given a secret share. ...
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659 views

Coefficients in Shamir's Secret Sharing Scheme

Sorry if this is a stupid question, but: in Shamir's scheme, we construct a polynomial and make our secret $S$ the zero-th coefficient $a_0$. What, if anything, necessitates this - in other words, can ...
3
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1answer
228 views

How can Shamir's method for secret sharing work in the GF(256)?

I have been reading about Shamir's secret sharing, and maybe i completely misunderstand something, but the field is meant to be a prime. However, when i look at the implementations of this algorithm, ...
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1answer
155 views

Secure function evaluation

Consider 3 parties, Alice, Bob and Charlie. Suppose each party has a bit as input, i.e. Alice, Bob and Charlie hold $a, b, c \in \{0, 1\}$ respectively. Show how construct a scheme with which ...
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133 views

How does secret sharing solve the partial exposure problem?

I have been trying to understand how secret sharing methods like Shamir's secret sharing solve the problem of a share revealing information about the secret. I guess there are some random numbers ...
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1answer
77 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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260 views

Is multiplicative secret sharing secure?

I suggested mulitiplicative secret sharing in an answer to another question, but noted that I wasn't sure if it was even secure and was hoping someone would comment on the security. Since no one did, ...
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1answer
97 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.