"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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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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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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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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In interactive proofs, do we assume that the prover can always solve the problem?

I'm having a difficult time understanding a concept from interactive proofs: A trivial interactive proof for the graph isomorphism problem is having the prover just send a permutation that shows an ...
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How to prove secret value in Pedersen commitment is equal to secret value in Fujisaki commitment?

We have Pedersen commitment C to the secret value x, and Fujisake commitment C' to the secret value x. How can we make a zero-knowledge proof of equality for x value in the commitments?
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How to use “proof of knowledge” to verify the result of modular exponentiation

I am thinking about regarding proof of knowledge as the inverse of result verification in server aided computing. For example, a user asks the server to compute $R=x^y \bmod z$. Normally, the user ...
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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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Zero Knowledge Example using discrete log

I've been exploring Zero Knowledge Proofs and while the classic cave example by Jean-Jacques Quisquater makes sense, I find the discrete log example problematic. Since the Verifier is given p, g and ...
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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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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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Is it possible to find out whether a number is greater than another number without knowing the numbers?

Is it possible to construct a zero knowledge proof that one encrypted number is larger (or not) than another encrypted number without releasing the values of either numbers?
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What is adaptive zero-knowledge?

In this paper on pg. 1241 the authors discuss bullet point on Adaptive Zero-Knowledge : I am new to Zero-Knowledge and I am having trouble understanding what they are saying. I think they are ...
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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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241 views

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-proof for discrete log that is not honest-verifier

Take a cyclic group of prime order. The Schnorr-protocol for proving knowledge of the discrete logarithm of some group element is honest-verifier zero-knowledge, meaning that if the verifier chooses ...
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Explanation of the Fiat-Shamir heuristic

The Wikipedia page on the topic (http://en.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic) is completely useless as it only explains what it is and not how it works. I looked at the original paper ...
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163 views

Chess Grandmaster Problem and “Valid” Attacks on Zero-Knowledge Proofs of Identity

A long question here, but I really want to motivate why I'm confused. Consider the following attack on the Schnorr Identification Scheme. Alice chooses a random $k$, computes $\gamma = \alpha^k ...
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69 views

How to prove NIZK proof of knowledge?

Assuming we have an El-Gamal pk tuple $(G,q,g,g^s)$. Someone, knows only the first three parameters. In round $i$, I send him $X_i=(g^s)^{t_i}$ (the $t_i$ values are chosen randomly for each round), ...
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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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Why is the definition of Special-honest verifier zero-knowledge probabilistic?

Let $P$ be a prover willing to prove to a verifier $V$ that he knows a witness $w$ satisfying $(x,w) \in R$ for some relation $R$ and some common input $x$. As found in the literature, $P$ can use a ...
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128 views

Simulation Based Proof: How the Corrupted Party's Input is Given To Simulator

Imagine we have a 3-party protocol, including client $A$,client $B$ and a server. In this protocol client $B$ encrypts its input under its public key and sends it to the server. The server performs ...
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Simulator in Private Outsourced Computation over Outsourced Datasets

Please, consider two honest parties $A$ and $B$ outsourced their private data to a malicious server $S$. So the parties store their data in the server. Then at a later point in time they want to ask ...
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Is this an example of a zero knowlege proof?

My Math Structures professor mentioned the strange concept of a zero knowledge proof to me after class one day, and I decided to do some reading about it. After reading the relatively famous "How to ...
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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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Soundness idea of basic zero knowledge prood

I am having a hard time figuring out the soundness proof of the bellow zero knowledge protocol. As it is a typical proof, I would love to deeply understand it. zero knowledge argument that $h \in ...
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Non-Interactive Zero-Knowledge-Proof for discret Logarithm?

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 ...
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Is succinct verification of an arbitrary data transformation theoretically possible? Is it feasible? How?

Given input string S, and transformation (i.e. computer program) T, is it possible to provide a succinct proof that another binary string S' is identical to the output T(S)? By "succinct", I ...
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difference between soundness in ZKPoK and special soundness for sigma proofs

What is the difference between soundness in ZKPoK and special soundness for sigma proofs?
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Committing Bilinear equation in Groth-Sahai framework

Groth-Sahai framework enables us to commit to QE, MSME, PP equations. Now, is the equation below committable in GS framework? A bilinear map $e: G_1 \times G_2 \rightarrow G_T$. $g_1 \in G_1$ and ...
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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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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 ...
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Several questions about Paillier cryptosystem

I have several questions concerning the original Paillier cryptosystem as described in Paillier, Pascal (1999). "Public-Key Cryptosystems Based on Composite Degree Residuosity Classes". EUROCRYPT. ...
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Zero Knowledge Argument for Subset Sum

What is the currently most efficient (interactive) zero knowledge proof/argument for the subset sum problem? The most recent relevant paper I have found is Efficient Modular NIZK Arguments from Shift ...
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How to prove that a commitment hides the decryption of an ElGamal ciphertext?

I've decided to remove a previous unanswered question of mine and break it down into smaller pieces so it's not such a loaded question. For this question I need to prove that I've committed to a ...
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Proposed unidirectional authentication scheme

I've been looking around for a way to authenticate a client to the server and deliver a message, but in a unidirectional fashion - that is, the client sends messages to the server, but the server ...
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Proving that a plaintext is the Paillier decryption of a certain ciphertext [duplicate]

Assume that Alice received 100 ciphertexts encrypted with additive homomorphic encryption, say Paillier, using the same public key that belongs to Bob. Alice added all of them, and wants to know the ...
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What does Set Membership actually prove?

While going through this paper, I came across the idea of Set Membership proofs. The proof allows a prover to prove that a value is contained in some set. The point where I am confused is, all the ...
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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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Any functioning system for interactive proof?

My problem is to outsource an array of data and ask the prover to sort the data. I am wonder if there is any working system out there that support interactive proof for the above computation? Or if ...
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267 views

Sigma-protocol for 3SAT problem

I have some questions from previous years exams, I hope you could help me with them. :) Let $g,h$ denote generators of a group $G$ of large prime order $n$ such that $\log_g h$ is unknown to anyone. ...
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Transforming simplest protocol into a Sigma-protocol

I have some questions from previous years exams, I hope you could help me with them. :) Suppose that a protocol satisfies the properties of a $\Sigma$-protocol, except that it is only (plain) ...
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Is this a valid real-time authentication scheme?

The scenario in Alice/Bob/Cindy terms: Alice approaches someone she doesn't know, but thinks is Bob, and asks for some secret information. Bob doesn't know and doesn't trust Alice, but Alice says she ...
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Simulation based proofs: Simple examples

I am aware that,(in theory) in order to proof that a scheme is secure using simulation based proof we replace an adversary in real world with a simulator in ideal world. Then we try to show that their ...
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Simulation Based Proof: What Can / Can not Simulator Do?

I have seen some examples in "Foundation of cryptography" and "Efficient two party computation", in which simulator can do some things that in the real world model the parties cannot do, for instance: ...
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145 views

Zero knowledge / proof of knowledge sudoku solution

I recently started a coursera course "cryptography 1" provided by Stanford university. In one point when explaining zero proof knowledge the instructor mentions the following: Almost any puzzle ...
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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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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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Simplified Fiat-Shamir example generates wrong output

I am trying to implement the Fiat-Shamir identification protocol, however the end results always fail to match. I am using algorithm's description from here. Preparation: Select 2 prime integers ...
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Can a zero knowledge proof (or MAC) be generated from human-typable input?

Edit: My goal is to create a voting scheme that doesn't require a lot of crypto infrastructure to be deployed on the client side. Smartcards, and tokens are impractical for these purposes. I ...
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Common reference string in NIZK

I want to ask that does the common reference string in NIZK have to be random? Or can it be anything?