# 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 secret....

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### 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 ...
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### How do you find a cheater in Shamir Secret Sharing?

If there are 4 people involved, and every two of them should be able to know the secret (the polynomial is just a line) and you are given f(x) and x for each of those people, and you know one of them ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Requiring a “supervisor” key pair and a “user” key pair to decrypt multiple-recipient messages

I've been toying with some encryption scenarios recently. One of the hard ones I came across is a multi-party system. So we have Bob -- The person who sends the message (and knows it's recipients) ...
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### Is this a sensible cryptographic protocol intending to reduce the impact of compromised security?

I'm in the process of designing a cryptographic protocol which will reduce the impact an attacker will have if they gained root access to a server storing data. The basic crux of it is that keys ...
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### Understanding Feldman's VSS with a simple example

I'm trying to understand Feldman's VSS Scheme. The basic idea of that scheme is that one uses Shamir secret sharing to share a secret and commitments of the coefficients of the polynomial to allow the ...
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### Implementing secret reconstruction in Shamir's Secret Sharing

I am trying to implement Shamir's secret sharing in C++. I have got the generation of shares working. However, I am very confused with the reconstruction of shares. I get the part on how three users ...
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### Addition with Shamir secret sharing

When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$. I believe this would be the correct solution (correct me if I'm wrong): Each party ...
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### How to generate a random polynomial of degree $m$?

I am trying to do a homework in which implement a variation of this paper and I don't know how to generate a polynomial of degree $m-1$. This polynomial is used to generate the $y_0$ and $y_1$ values. ...
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### Does zero-padding the secret in Shamir's sharing scheme increase security?

When performed in binary Galois fields $GF_{2^n}$, Shamir's threshold secret sharing scheme produces shares that are each the same bit-size as the secret. Though the scheme is "perfectly secure" in ...
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### Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme

Shamir's original paper (PDF, 197kb) describing a threshold secret sharing scheme states: To make this claim more precise, we use modular arithmetic instead of real arithmetic. The set of ...
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### Is there a secret sharing scheme which allows delegation/re-sharing without reconstructing the original secret?

EDIT: Ilmari Karonen's answer below well not exactly what I want, gives a very good idea of what I am trying to accomplish. Are there any known secret sharing schemes that allow new parties to be ...
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### Shamir Secret Sharing - Threshold decryption implementation

I'm implementing Shamir secret sharing in C using OpenSSL. I've split up the private key and I'm ready to start decrypting the original message using some of the shares. I set $n = 5$ (5 shares ...
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### Security considerations for partially shared password databases

Programs like KeyPass and 1Password store password database files encrypted by a single password. If someone knows the protecting password ("Vault Key"), they can read the entire database ("secrets"). ...
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### RS Erasure Coding and Shamir's Secret Sharing

So I was trying to understand the basic difference between erasure coding and secret sharing, and I found this paper (that you can find here or here). For what I understand, it states that Shamir's ...
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### Can I pre-define the points in Shamir's Secret Sharing algorithm

With Shamir's secret sharing is it possible to pre-define the points returned by the algorithm? For simplicity if I have (k, n) where k=2, and n=4, and I have the points X,Y,Z, and Q. Can I create ...
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### Relation between Threshold Cryptosystem and Secure Multiparty Computation ?

Is there any relation between secure multiparty computation and threshold cryptosystem ?
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### Trying to find an algorithm to share portions of a key with multiple people

Sorry if this question's a bit basic, but I don't know of any way to ask it concisely enough for a search... What I'm looking for is a proven means of doing the following: Create x number of ...
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### K out of N encryption

A friend just showed me how to combine padlocks to achieve a lock that opens when k out of n people turn their keys. I was ...
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