"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.

learn more… | top users | synonyms

2
votes
2answers
86 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 ...
2
votes
1answer
68 views

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 ...
2
votes
2answers
586 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?
2
votes
1answer
236 views

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: $b$. ...
2
votes
2answers
117 views

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 ...
2
votes
2answers
361 views

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 ...
2
votes
1answer
74 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 ...
2
votes
1answer
90 views

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 ...
2
votes
1answer
307 views

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 ...
2
votes
1answer
454 views

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. ...
2
votes
0answers
30 views

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 ...
2
votes
0answers
90 views

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 ...
2
votes
0answers
83 views

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 ...
2
votes
0answers
76 views

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: ...
2
votes
0answers
70 views

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 ...
2
votes
0answers
190 views

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) ...
2
votes
0answers
104 views

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 ...
1
vote
1answer
59 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 ...
1
vote
2answers
114 views

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 ...
1
vote
1answer
126 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 ...
1
vote
1answer
236 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 ...
1
vote
1answer
310 views

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 ...
1
vote
2answers
104 views

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 ...
1
vote
1answer
55 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?
1
vote
1answer
165 views

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 ...
1
vote
1answer
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 ...
1
vote
1answer
145 views

Homomorphic crypto allowing anonymous yes/no votes?

I'd need a crypto system allowing online yes/no votes but without revealing who voted what. Is a "partial" homomorphic crypto system what I'm after? Would, for example, Damgard-Jurik work in my case? ...
1
vote
1answer
192 views

Non-interactive Zero-knowledge proof signature validation without public key

I'm looking for a method for a scenario with following requirements: At least 3 people (A,B,C,...) are in a Network where they can broadcast messages to everyone but not communicate with a specific ...
1
vote
2answers
37 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 ...
1
vote
1answer
73 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 ...
1
vote
1answer
48 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?
1
vote
1answer
58 views

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 ...
1
vote
1answer
52 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 ...
1
vote
1answer
207 views

How to prove that a ciphertext is encrypting multiplication of two values?

Zero-knowledge proofs with soundness, completness and zero-knowledge enable a prover to convince a verifier that a witness validates successfully a predicate without giving any information about the ...
1
vote
1answer
342 views

How can I prove in zero knowldege that an ElGamal shuffle is correct for a special setting? [closed]

In a special ElGamal encryption scheme, every user has an ElGamal encryption key-pair using the same cyclic group $G$ and generator $g$. The system has a special function : $$ ...
1
vote
1answer
108 views

Is secure remote snap possible?

Scenario: We have a central server $S$. We have a number of peripheral servers $P_i$ We have some individuals $U_j$ A given individual may be "known" to one or more peripheral servers. Each ...
1
vote
0answers
52 views

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 $\mathbb Z_p$?
1
vote
0answers
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 ...
1
vote
1answer
34 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 ...
1
vote
1answer
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 ...
1
vote
0answers
36 views

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 $e$ ...
1
vote
0answers
105 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 ...
1
vote
0answers
56 views

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 ...
1
vote
0answers
86 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 ...
1
vote
0answers
185 views

What would make it impossible to deny that decryption of a package has taken place?

I'm part of a team designing a system where a user have to be able to read a certain package, if he has preformed an action or series of actions that makes it legal for him to do so. The tricky part ...
1
vote
0answers
162 views

SRP6a client server exchanged message order

In SRP6a, the public key of server is send after receiving the public key of client A. Its that okay that B send along together with s right after client send the username, and then later on client ...
1
vote
0answers
184 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. ...
1
vote
1answer
288 views

ZKIP for Paillier public key correctness

I'm using the Paillier cryptosystem in a protocol similar to mental poker. In the beginning of the protocol, each player generates a Paillier public key $(n,g)$. Later in the protocol, a player may ...
0
votes
1answer
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 ...
0
votes
1answer
43 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: ...