"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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Is there any zero-knowledge technique to verify proof of knowledge of shared secret key?

Generally, to verify knowledge/key generated between two interacting parties in an authentication protocol uses Hash, MAC, Digital Signatures or encryption (based on random challenge). But I would ...
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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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437 views

What is an example of a secure sigma proof?

I want to implement Threshold Elgamal as described in section 6.3.1 and in the decryption phase each party must broadcast a sigma proof to show that it actually has a valid secret share of the secret ...
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150 views

Hamiltonian Path Zero Knowledge Proof using Commitments to a Series of Edges

Commonly, Zero Knowledge Proofs based on the Hamiltonian Path or Cycle problems are given as follows: The Prover has a graph $G$, for which he knows a Hamiltonian Path (or Cycle). $G$ is also known ...
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Zero-knowledge proof for the product of additive Paillier ciphers

Suppose that Alice received the cipher values: $E(x_1), E(x_2), ..., E(x_n)$ that are encrypted using Paillier cryptosystem by $n$ entities with Bob's public key. Alice computes $E(\sum x_i)$ from ...
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Proof that a hash matches an encrypted file

Assume that Alice has a file $F$ which she is going to send, in encrypted form to Bob. Alice possesses $F$ and an encryption key $K$. She sends to Bob the encryption of $F$ using $K$, $E(F,K)$ as ...
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76 views

Zero knowledge proof of shared secret

Alice holds a secret $a \in X$. Bob holds a secret $b \in X$. Is there a protocol that lets them compute $f(a, b) = \begin{cases} 1 & \textrm{if } a = b \\ 0 & \textrm{else} \end{cases}$ If ...
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Additively homomorphic cryptosystem with non-interactive zero-knowledge proof of non-negativity

I need a cryptosystem that is additively homomorphic. Paillier preferably, but not neccessarily. Also, for every ciphertext the private key holder must be able to prove non-interactively that the ...
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60 views

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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120 views

Zero-Knowledge Proof of a polynomial

I have two secret values $L_1$, $L_2$, and two Pedersen commitments $C_1 = C(L_1)$, $C_2=C(L_2)$. The commitments $C_1$, $C_2$ are public. Given a challenge $c$, I want to output $d = c*L_1+L_2$ and ...
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34 views

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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Simulation-based proofs and universal composability proofs

I recently read Ran Canetti's famous UC paper but I'm still trying to wrap my head around the concepts. I think this answer has me confused a bit, particularly where it says The stand-alone ...
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68 views

Consequence of a change on the Guillou-Quisquater Protocol

In the Guillou-Quisquater Protocol, the prover convinces the verifier that he knows an $e$-th root of an element $y \in \mathbb{Z}^*_n$ ($p, q, e$ are primes, $n = pq$ and $e$ is coprime with ...
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1answer
17 views

With ECDSA is there a way for the verifier to calculate any properties of $k$?

With ECDSA, given $(r,s)$ and $m$, is there a way for a verifier to calculate any (boolean) properties of $k$, without knowing $k$ or the private key $D_A$? (I understand that $k$ should be random, ...
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Salary Negotiation Problem

Imagine Alice is applying for a new job. Alice has an idea of the minimum salary that she is willing to accept—let's call this value A. Bob, the hiring manager for ...
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77 views

How to prove knowledge of discrete logarithm in a product?

Definitions Suppose I have two large safe primes $p$ and $q$, and a composite number $N=pq$. I have $G$, a large cyclic subgroup of $\mathbb{Z}^{*}_{N}$; $g$ and $h$ are generators of $G$. I commit ...
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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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1answer
51 views

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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Zero-Knowledge Proof of Subgraph Isomorphism

I'm trying to find a Zero-Knowledge proof of subgraph isomorphism in the following scenario: Alice and Bob both know about graphs G1 and ...
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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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31 views

Zero knowledge proof of bilinear equation

Suppose A and B have pre-shared a secret key $r$. Is there a way for A to prove that $p=[e(a,b)e(g^{c_i},b)]^r$ has been correctly computed with this $r$ but without knowing or revealing either a,b or ...
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2answers
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On the fly signatures and zero-knowledge

I am reading some articles which explain on the fly signatures (also called online/offine signatures). The principle is that a few operations do not depend of the message we want to sign, so these ...
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72 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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91 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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1answer
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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36 views

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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183 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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51 views

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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193 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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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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62 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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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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43 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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1answer
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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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285 views

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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149 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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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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31 views

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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1answer
93 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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69 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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1answer
94 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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174 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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92 views

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 ...