"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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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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Changing SRP-6a message order

In SRP-6a, the public key $B$ of the server is normally sent after receiving the public key of the client $A$. Is it okay to send $B$ and $s$ after the client sends its username $I$, but before the ...
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55 views

Usage of Zero-knowledge proofs for NP-complete languages

It is well known that if OWFs/PRGs exist, then there is a zero knowledge proof for any NP-complete language, say G3C (graph coloring in 3 colors). The zero-knowledge notion maintains that any ...
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How does the simulator of the special-honest verifier zero-knowledge property works?

I’m a bit confused about what the simulator of the special-honest verifier zero-knowledge property of a $\Sigma$-protocol is supposed/allowed to do and how to prove that it is indeed efficient (i.e. ...
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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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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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61 views

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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Prove that certain amount of data was stored

I'm looking for a way to prove that a certain amount of data was stored, through some easily verifiable piece of information. Similarly to how proof-of-work can prove through a hash that a certain ...
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87 views

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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64 views

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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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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Zero knowledge proof protocol example?

Alice is color blind. She never knows if her gloves are matched. Her brother Bob always teases her saying her gloves are mismatched and she should go change them. Alice wants to know if ...
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81 views

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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318 views

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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What is a Non-Interactive Zero Knowledge Proof?

I understand the concept of a Zero Knowledge Proof thanks to the easy to understand analogy of Alibaba's cave. However, this seems to require interaction between the verifier and the other party. I ...
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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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55 views

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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41 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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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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48 views

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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272 views

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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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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Non-interactive proof that an element is in a subgroup

I am just reading the DAA paper (http://eprint.iacr.org/2004/205.pdf, Appendix A). A party $\mathcal{I}$ generates two group elements $g' \in \mathrm{QR}_n$ and $h = g'^r \bmod n$ with $r \in_R \left| ...
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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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62 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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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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70 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 [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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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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62 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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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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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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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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115 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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54 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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245 views

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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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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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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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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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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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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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 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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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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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 ...