# Tagged Questions

Threshold cryptography is the art of chopping a secret into little bits, so that the secret can only be learned by possessing more than a threshold number of those bits.

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### 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 ...
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### An electronic voting system

This semester I am taking the course Cryptography. I will have a presentation about the topic "Voting Scheme". I am preparing myself by reading from the book “Cryptography : an Introduction” by N....
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### Terminology for secret sharing

To my understanding, there are two "approaches" to t out of n threshold encryption. In both of them, n shares are given to different shareholders, and at least t of them must agree to "proceed". "...
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### 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 ...
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### Does Ed25519 support cryptographic threshold signatures?

This is a loaded question so I'll list the concerns, not all of which need to be satisfied. Does there exist a threshold-signature scheme for Ed25519 that... Does not require a trusted dealer to ...
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### Why $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ for RSA crypto?

For RSA cryptography, we know that the modulo $n$ is a product of two big prime numbers(say $p$ and $q$). However, in some documents I see an extension of $p=2p'+1$ and $q=2q'+1$ with $q'$ and $p'$ ...
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### Threshold cryptosystem with a required share

I am trying to find an implementation or variant of a (k, n) threshold cryptosystem (as described here Shamir's Secret Sharing) where we can fix at least one of the k key parts, i.e., instead of ANY k ...
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### NIZK Proof of knowledge N of M discrete logarithms (threshold)

It is well known how to produce a NIZK that curvepoints $aG$ and $aP$ have the same discrete logarithm $a$ with respect to the curvepoints they are multiplied by. There is also a way to prove that a ...
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### Shamir's Secret Sharing vs. Asmuth-Bloom scheme

I need to make use of a secret sharing scheme and I don't really know how to decide which one to use, Shamir's or Asmuth-Bloom (using CRT). The complexity for recovering the secret seems to be linear ...
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### Asmuth-Bloom's threshold secret sharing scheme

I was learning Asmuth-Bloom's threshold secret sharing scheme. I was working out an example as given in this Wikipedia article. As per the example, the secret,d is 2, the number of shares, n is 4 and ...
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### 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)? https://scholar.google.com/scholar?q=kurihara+secret+...
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### Is Shoup's Practical Threshold Signatures considered secure?

I am planning to use threshold cryptography in a Java application. So far, I have only found ThresSig and a ECDSA implementation used in TwoFactorBtcWallet. However, ThresSig is based on a 15-years ...
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### Recombination thresholds in degree reduction of multiplied Shamir shares

Shamir's secret sharing can be considered multiplicatively homomorphic, if one is aware of the fact that multiplying two shares of a (n,t)-threshold shared secret yields a share of the same secret, ...
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### 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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### Problem with applying threshold scheme

For a report on threshold signature schemes, I have to explain a threshold signature scheme and give a simple example with numbers. A threshold signature scheme is a scheme in which a network of n ...
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### 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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### Does threshold crypto (m-of-n) guarantee that m peers discover the plain text?

In a threshold cryptosystem, is there any guarantee that all $m$ peers participating in retrieving a plain-text will all retrieve it? If not, is it possible to provide such a guarantee? For instance ...
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### Time efficiency of Bitcoin Multi-signature Vs. threshold signature

I read this paper (Securing Bitcoin wallets via a new DSA/ECDSA threshold signature scheme) that illustrated that threshold signature is the best solution to avoid single point of failure but I think ...
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### What is the difference between a one-shot MPC protocol and a unbounded invocation of multiple MPC protocols?

In this paper on pg. 1236, under the section "Security Against Continual Leakage", the authors say: "We further remark that the weaker security notion previously achieved cannot be extended ...
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### CP-ABE for threshold cryptography

I would like to know if there is any research work using CP-ABE for threshold cryptography? I want to know also if applying CP-ABE for threshold cryptography would overcome other techniques.
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### Reducing key shares in Damgård-Dupont threshold RSA

I'm working on understanding and implementing Damgård, I., & Dupont, K. (2005). Efficient Threshold RSA Signatures with General Moduli and No Extra Assumptions. Public Key Cryptography-PKC ...
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### Distributed Asymmetric Key Decryption with threshold

Threshold decryption of public key encryption schemes allows the decryption key to be distributed among trustees. Then, to decrypt the cipher text it requires at least threshold t trustees to run the ...
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### Secure Multiparty Sum in malicious model using threshold encryption

Suppose $n$ actors each hold a plaintext $p_i$. We wish to find $\sum p_i$, without leaking any information about individual $p_i$. Any actor (or any link in the network) could be controlled by an ...
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### Is normal to take wrong values of the polynomial for given x while applying Horner's rule

I want to evaluate the polynomial $a_0+a_1x+a_2x^2+...a_nx^n$ using Horner's evaluation due to i want to speed up my performance of application written in Java. The problem is that sometimes it gives ...