# 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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### Cryptographic Operations and Security

sign((M’, TAlice, sign(( encrypt(( encrypt(M, KpbBob), M’), K), TBob), KsBob)), KsAlice) Can you tell me six security-related facts ...
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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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### 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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### 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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### 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 ...
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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 $p'$ ...