"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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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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364 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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76 views

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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66 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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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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49 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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411 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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48 views

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: $(c_1*...
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210 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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34 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 $(r_6-...
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121 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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76 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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142 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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100 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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94 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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178 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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64 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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326 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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187 views

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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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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103 views

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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179 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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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. 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 ...
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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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200 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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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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246 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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What is the sign bit for in Feige-Fiat-Shamir?

The Feige-Fiat-Shamir identity scheme is based on a ZKP assuming that square roots are "hard" modulo an integer of unknown factorization. The "parallel version" of this protocol includes a "sign bit" ...
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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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78 views

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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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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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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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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75 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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886 views

How realistic is a dictionary attack on a secure remote password protocol (SRP) verifier?

I'm deploying a secure remote password protocol implementation and I'm wondering what the consequences are when the client generated verifier gets leaked to an attacker. I've read Thomas Wu's paper ...
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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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63 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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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 ...