# Tagged Questions

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 ...

76 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 ...
300 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 ...
53 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 ...
111 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 ...
61 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 ...
53 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 ...
87 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 ...
84 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 ...
173 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 ...
179 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 ...
84 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?
51 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 ...
370 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 ...
87 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 ...
97 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 ...
94 views

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 ...
198 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 ($c_0$) ...
43 views

### 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 ...
80 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, ...
58 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 ...
197 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 ...
136 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 ...
154 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 ...
105 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 ...
349 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 ...
71 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. ...
317 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 ...
163 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, ...
136 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 ...
116 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 ...
67 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 ...
172 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, ...
86 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.
191 views

### How to Distribute the Shares using Secret Sharing for arbitrary Monotone Access Structures

Consider 4 people, $A$,$B$,$C$,$D$, & a secret $s\in\{0,1\}^k$. Construct a scheme which enables the following subsets of people to retrieve the secret $\{A,B\}$, $\{A,C\}$, $\{B,C,D\}$. I know ...
275 views

### XOR secret sharing scheme

I was wondering how we can get a secret sharing of $a+b$ from the sharing of secrets $a$ and $b$ themselves by using an XOR secret sharing scheme, where $a_1,...,a_n$ and $b_1,...,b_n$ are the shares ...
66 views

### Safety when disclosing hashes of secrets used to calculate other secrets

In my application, I am generating a big random number and publishing a SHA256 hash of it. After the hash it published (but not the secret), anyone can submit any number, and the system will calculate ...
109 views

### Is there way to combine secrets first and later split them?

Shamir's Secret Sharing allows a secret to be split into multiple shares so that it can be reconstructed later. Is there a way to do the reverse? Can we combine a few secrets first and later split ...
94 views

### post-quantum threshold secret sharing

I am looking for a references for post-quantum threshold secret sharing schemes. I am especially interested in knowing whether any one based on one-way compressor functions or cryptographic hashes ...
143 views

### Shamir's Secret Share Over the Reals

What about using Shamir's secret share over the real numbers leaks information? I know there is a problem with random number generation, and someone suggested it leaks the parity of the polynomial, ...
215 views

### Shamir's Secret Share [duplicate]

I'm not quite sure the benefits of working over a prime modulus in Shamir's secret share- but doesn't limiting the numbers you pull from make the secret easier to guess? Instead of being over the real ...
51 views

### Algorithm for sharing secret information with redundant keys [duplicate]

I have an information that I would like to encrypt and give it to someone else. I would like to encrypt it using N separate passwords (say 5) and give each password to some other persons. However the ...
195 views

### Shamir's secret sharing with passwords

I'm trying to design an extension to Shamir's Secret Sharing that would allow the participant to specify a password instead of remembering/storing a large integer or binary data. So far, I have two ...
164 views

### General-purpose non-interactive multi-party computation protocol

Most of general purpose multi-party computation protocols are highly interactive. Especially the ones with Shamir's secret scheme, as there is a degree reduction step in multiplication that needs the ...
550 views

### Lagrange Interpolation for finite field GF(2^8), for Secret Reconstruction

I'm using Lagrange's Interpolation technique to reconstruct the secret from a set of point pairs (x,y). Since I only need the secret, not the whole polynomial, I have simplified the reconstruction ...
226 views

### Secret sharing scheme with possibility to change the secret

Here's a scenario I want to handle with a secret sharing scheme: Alice wants to share the secret $S$ with Bob, Charlie and Dave. Alice generates private shares based on $S$ for Bob, Charlie and ...
687 views

### Why does Shamir's Secret Sharing Scheme need a finite field?

I read ampersand's question "Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme", where he asked why Shamir's Secret Sharing Scheme uses arithmetic in a ...
167 views

### What's efficient MPC protocol for determining if sum's bigger than y?

My secure multi-party computation (MPC) in need is simply to determine if a sum of two private variable is bigger than a given value $y$, as $f(x_0, x_1) = [(x_0 + x_1) > y]$ in which the value ...
127 views

### Size of Parameters in Polynomial Key-Splitting Algorithm

I've seen the elegant way of splitting a key among different people so that only a certain number need to be present to re-compute the key, yet nobody has enough information to re-compute the key on ...