# 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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### 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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### 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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### 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 ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Does “identity-based dynamic threshold signature” exist and could such scheme contain a “Signature Combination” algorithm?

I came across [1] and I'm very puzzled by this paper. They use a building block which they call "identity-based dynamic threshold (IBDT) signature", citing paper [2]. First of all [2] does use this ...
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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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### Negative exponents in Shoup's threshold RSA?

I'm trying to implement threshold RSA operations, starting with decryption based on Peeters, R., Nikova, S., & Preneel, B. (2008). Practical RSA Threshold Decryption for Things That Think. ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...