# Tagged Questions

"Zero Knowledge Proof" is an interactive method for one party to prove to another that a statement is true, without revealing anything other than the veracity of the statement.

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### Fiat-Shamir security problem question

I am trying to understand the Fiat-Shamir identification protocol, but have a problem with understanding how this protocol is supposed to be save, even if you repeat it several times. I am using ...
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### server aid secure equality test

The scenario is like this: $P_1$ has $m_1$, $P_2$ has $m_2$, they want to compare whether $m_1=m_2$ via the server $S$. After the protocol, only $S$ knows the result, and there is no interaction ...
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### Is there an oblivious decryption scheme?

Alice has $K$; Bob has $E(K, m)$; Is there such a scheme that enables Alice decrypts $E(K, m)$ without knowing $m$, and Bob gets $m$ ?
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### Hamiltonicity proof of knowledge

I'm learning the POK notion and definitions and as a self exercise I wante to prove the statement that the Hamiltonicity protocol is a POK system with knowledge error $1/2$. So the question will be ...
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### How to prove identity without revealing identity

Let us say Alice publishes a book under the name of Claire. The book becomes wildly popular and now Bob comes along, claiming to be Claire, to reap all the success. How does Alice prove that she wrote ...
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### Proving the possession of signature in zero-knowledge

Does anybody know an efficient mechanism to prove the possession of a digital signature (e.g. RSA) on a certain attribute (message) in zero-knowledge? That is, without revealing the actual signature ...
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### Are ZKPPs possible with server-side hashed passwords?

A basic ZKPP (Zero Knowledge Password Proof) is based on the server being able to challenge the client, and the client can then prove it knows the password (in such a way that is verifiable to the ...
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### Zero-knowledge proof of a product

I have non-negative integers $x,y,z$. I'm going to give you commitments $C(x),C(y),C(z)$ to them. Then, I would like to prove in zero knowledge that $xy=z$. I can choose the commitment scheme to ...
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### Can I prove set membership and uniqueness without revealing the element?

Assuming a publicly known set $\Psi$ with $N$ unique elements. I have a set $\Sigma=\{\sigma_1,\sigma_2,...,\sigma_m\}$ where $m\leqslant N$. I would like to publicly prove that all the elements in ...
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### Burn after read algorythm. Software verification on compromised environment. Software smart card

Please help me pick right design of software… I have to design client-server software, where the server should verify that the client runs software from specific source code. It has to be verifiable ...
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### Is there a simple zero knowledge proof of $x$ for $b=x^x\pmod p$?

We have a multiplicative cyclic group $G$ which is a subgroup of $(\mathbb{Z}/n\mathbb{Z})∗$. There are two parties, Alice and Bob: If: Alice knows: $b$ and $x$ such that $x^x = b$; Bob knows: $b$. ...
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### Reliability of a single-pass deniable authentication protocol?

I look for one-pass deniable authentication protocol with a short message payload for my project and find a solution: ...
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### Zero-knowledge proof for committing a choice?

Let's say there are 100 choices (which are publicly known), each represented as a different string, and today you have to choose one of them. You need not reveal what that choice is right now, though. ...
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### Generating shared secret random permutation

There are three blind card game players. Each player does not trust any other, even prejudicing other two players may not be blind, or there may be others in the room, peeking at their cards. In ...
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### Rock-paper-scissors over network, how to protect from cheating server?

I'm trying to design cryptographic protocol to play Rock-Paper-Scissors with two parties, neither trusting each other, nor trusting server they use for communication, so game is 'provably fair'. So ...
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### When would one prefer a proof of knowledge instead of a zero-knowledge proof?

I've just realized I find it hard to distinguish between these two terms (proof of knowledge, and zero-knowledge proof), specially where only the latter seems to be used in many cryptographic ...
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### Zero knowledge proof of possession of key

Suppose Alice has at some point in time produced ciphertext $C$ from message $M$ with key $k$. Suppose Alice has then passed $C$ to Bob, and also made a commitment to her key $k$ (thanks to ...
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### Proof of correct construction of a private key in distributed cryptography

In an exponential ElGamal encryption scheme where the key generation is done in a distributed way among $n$ trustees we have that each trustee $i$ (where $1 \leq i \leq n$): Selects a private key ...
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### Feedback requested on a method of posting a message without revealing the author

So I was thinking about variations on the Dining Cryptographers problem - In some cases, it's useful to be able to post a message without revealing the source, but with the additional constraint of ...
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### Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
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### Perfect zero knowledge for the Schnorr protocol?

Can somebody explain (or point to a reference) why the Schnorr protocol cannot be proved zero knowledge?
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### Could this be a valid variation of the Schnorr protocol?

The Schnorr protocol is a 3-steps proof of knowledge of a discrete logarithm, whose interactive version works as follows. Let $p$ and $q$ be two public primes, such that $q \mid (p-1)$, and let $G$ ...
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### Alice's forgetful banking

Alice has a bank account number, but has forgotten which bank it is for. There are 4 banks, run by Bob, Carlos, David, and Eve. She could find out by going to all of the banks and asking if they have ...
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### Zero-knowledge proof using quadratic residue: why two options?

In the zero knowledge proof using QR, why do we even bother with the server sending us $b = 0$ back? As I understand it, the server selects $b = 0$ or $b = 1$. If $b = 0$, then the client (Alice) ...
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### How do zero knowledge protocol with vertex-3-coloring work?

I'm currently not sure if I understood how the zero knowledge protocol with vertex-3-coloring works. I'll describe what I think I've understood and I'll write my questions in bold. ...
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### Question about proof of knowledge defintion?

I am just reading the "soundness"-definition for proofs of knowledge by Bellare / Goldreich. A proof of knowledge is a proof between a prover $P$ and a verifier $V$. $P$ convinces $V$ to know a secret ...
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### How can two UProve token holders prove to a 3rd party that they aren't the same user?

Suppose I have two users who are issued two different UProve IDs. The Issuer has guaranteed that one UProve token bearer will never have more than one UProve token ID. How can I use UProve to ...
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### State of the art in zero knowledge proof compilers?

What is the current state of the art zero knowledge proof compiler ? I need one that can minimally handle double exponentiation by a known value E.g. $$Pok\{(\alpha):h=g^{\alpha^b}\}$$ where b, ...
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### How to verify a number encrypted with an unknown key

Alice and Bob are going to follow the protocol below. Are there any crypto-constructions to help Bob verify the correctness of the answer he gets?: Alice encrypts a set of numbers using some ...
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### Zero-knowledge proof that a group element is a quadratic residue?

In a paper it says: "To convince a verifier that a group element is a quadratic residue, the prover executes the following proof with the verifier": $PK \left\{ (\alpha) : y = \pm g^\alpha \right\}$ ...
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### Zero-Knowledge Challenge-Responce Protocol

Good day to everyone. I am trying to implement an e voting system (just for reference -it is not important though-it is described at the Internet Voting Protocol Based on Improved Implicit Security ...
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### Questions about proof of correct encryption in the Paillier cryptosystem

In the Paillier cryptosystem [1] the encryption of $m \in \mathbb{Z}_N$ with randomness $r \in \mathbb{Z}_n^*$ is $c = g^m r^n \bmod{n^2}$. A proof of correct encryption could look like presented in ...
In a Non-Interactive $Zero-Knowledge-Proof$, the challenge is chosen by the Prover. I am trying to find a Non-Interactive Zero-Knowledge-Proof based on the following problem: DISCRETE LOGARITHM ...