"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 framework for c programs - how to prove correct C program execution with private inputs

I am looking for a zk framework that could be used for proving correct execution of programs written in C (or any other high level language) such as: I know x s.t. SHA-256(x) = y (y is public, x is ...
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Constructing set membership proof for private set

Is it possible to construct a set membership proof to show $\delta \in \Psi$ where $\delta$ is publicly known and $\Psi$ should stay only known to the prover? It seems rather impossible but I would ...
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Non-interactive zero-knowledge proof for discrete logarithm without random oracle

Is there any non-interactive zero-knowledge proof for discrete logarithm without random oracle over the group $\mathbb Z_p$?
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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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39 views

Commitment scheme to share money

I have such problem: party $X$ has an amount of money $M$, which it needs to share with $n$ other parties. Every week the amount of money is different. Let say not, that I am a party A, which is one ...
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Role of trusted party in the Ideal model in Malicious case

Imagine there is a protocol supporting outosurced multi party computation. There are three parties involved in the protocol: client $A$, client $B$ and a server. Client $A$ and $B$ send their private ...
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The non-interactive proof of verifiable computation: Pinocchio

I am reading the Pinocchio paper. The paper says, in paragraph "polynomial asymptotics" of section 4.2.1, a worker, in order to include $h(s)$ into the proof, has to interpolate $p(x)$, and then ...
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Mutual verification of shared secret

Is it possible to develop a scheme where two parties, unsure if they have the same secret, can verify that the other does or does not share the same secret, without one party being able to cheat and ...
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3answers
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Why aren't zero-knowledge proofs used for authentication in practice?

I read on Wikipedia that zero-knowledge proofs are not used for authentication in practice. Instead (I think) the server is entrusted with seeing a password in plaintext form, which it should then add ...
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57 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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49 views

arithmetic calculation problem to quadratic arithmetic program

I am reading the Pinocchio paper (verifiable computation): http://research.microsoft.com/pubs/180286/pinocchio.pdf The paper is rather hard for me. I am considering this calculation problem: ...
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Figure 2 in the Verifiable Computation - Pinocchio

I am reading the Pinocchio paper (verifiable computation): http://research.microsoft.com/pubs/180286/pinocchio.pdf The paper is rather hard for me. For the Figure 2, I guess $v_1(x)$ should be ...
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62 views

Verification of Pinocchio (verifiable computation)

I am reading the Pinocchio paper. The calculated result $y$ is a part of the verification input, but it seems to me, the verification procedure does not utilize the result $y$. Can anyone can help me ...
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Proving that a plaintext is the Paillier decryption of a certain ciphertext

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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59 views

Zero knowledge proof relation + number is binary

I want to develop a ZKPK for the following problem: $$Y=g_0^{r_Y} \prod_{i=1}^n g_i^{s_i}$$ and $$Z=h_0^{r_Z} \prod_{i=1}^n h_i^{s_i}$$ I want to proof knowledge of $r_Y,r_Z$ and $s_i$ which I have ...
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47 views

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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2answers
78 views

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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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?
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Zero knowledge of two factor

Here I overconfident in myself state that I can show, that n has two factors. This is not completely true, can possibly show $n$ is composite - prover generates RSA key with modulo $n$, and gives $e$ ...
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67 views

Blum primes [x=3(mod 4)] zero knowledge proof?

Lets say we have 2 primes, $p \equiv q \equiv 3 \pmod{4}$, and we make $n=p \times q$ public. I can, without revealing factors, show that $n$ has two prime factors. How can i zero knowledge prove ...
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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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99 views

Zero Knowledge Non Interactive Proof with random oracle

I am trying to write an assay about Non Interactive Zero-Knowledge proofs and would like to take the simple discrete logarithm problem example fallowing the Feige-Fiat-Shamir heuristics. I understand ...
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53 views

Why is it a quadratic equation?

In Groth-Sahai NIZK proof system, they have defined something called Quadratic Equation in $\mathbb{Z}_n$ as shown below. But, my idea of quadratic equation was a second order polynomial equation in a ...
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Hiding and Binding key in Groth-Sahai NIZK proof system

In context of Groth-Sahai NIZK proof system, I have a couple of doubts on Hiding and Binding keys. In case of hiding keys (highlighted in red), how is it ensured that $\tau(A) \subseteq \langle ...
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How does multi platform encrypted cloud storage work?

I'm really interested in end-to-end encrypted cloud storage and couldn't find out how following scenario could work: A user of a cloud provider which provides zero-knowledge-authentication (like for ...
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Simplifying the zero-knowledge proof example? [duplicate]

There is this http://en.wikipedia.org/wiki/Zero-knowledge_proof#Abstract_example. Now I'm curious about this. Why is it not possible for Victor to stand at the entrance and watch Peggy take one path ...
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Is there a way to “shorten” a Merkle chain?

If I have a Merkle chain of 3 items, is it possible to create a zero knowledge proof of the existance of a correct chain between hash 1 and hash 3? Editing to clarify (Thanks Ricky), what I mean my a ...
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81 views

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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1answer
155 views

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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169 views

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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2answers
530 views

What are SNARKs?

What does it mean and what is it used for, I have been hearing this term a lot lately. From the context I've heard it talked about it seems to be connected with zero knowledge?
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Isn't Groth-Sahai proof system applicable beyond Bilinear groups?

Classical paper by Groth-Sahai on NIZK proof system is titled as "Efficient Non-interactive Proof Systems for Bilinear Groups". To my understanding, only (Pairing Product Equation) PPE are defined ...
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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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Correctness vs Completeness

What is the conceptual difference between the definition of correctness and completeness in verifiable cryptographic protocols? They justify that if a statement is correct then the verification should ...
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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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Group Dependent Language

The text below has been taken from the below paper Groth-Sahai Paper. The relevant part is highlighted in red. What does this group-dependent language mean in this context? From the definition of a ...
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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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70 views

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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Calculating cost of variables and equation in Groth-Sahai (DLIN) proof system

In Groth-Sahai proof system under DLIN assumption [Page 29], they have provided a few number denoting the cost of each variable and equation. Can anyone please explain how did they calculated 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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Groth-Sahai proofs and hardness assumptions

I am learning Groth-Sahai NIZK proof system for Bilinear groups. While going through the literature, I am getting confused on how the proof system is related to Subspace Decision, SXDH or DLIN ...
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understanding the proof of knowledge

Recently I've been reading the paper “A New Family of Implicitly Authenticated Diffie-Hellman Protocols”. It's very hard for me to go further. Especially when it comes to the proof of knowledge. ...
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61 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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Fiat–Shamir: why do r and s have to be smaller than n?

I have a question regarding the Fiat–Shamir identification protocol. In this source (pdf) for example it says on pages 9 and 10 that the random commitment $r$ and the private key $s$ have to be ...
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70 views

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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1answer
49 views

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 ...