# Questions tagged [zero-knowledge-proofs]

Zero-knowledge proofs are 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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### Proving knowledge of a preimage of a hash without disclosing it?

We consider a public hash function $H$, assumed collision-resistant and preimage-resistant (for both first and second preimage), similar in construction to SHA-1 or SHA-256. Alice discloses a value $h$...
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### Is a hash a zero-knowledge proof?

I’m trying to wrap my head around zero knowledge proofs, but I’m having trouble understanding it. In my current understanding, zero-knowledge proofs prove to the recipient that the sender has a ...
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### Zero knowledge proof for sign of message value

I am using ElGamal encryption to encrypt an integer message $m$ as, $E[m]$ = ($g^x$, $g^m.h^x$) Can I write a zero-knowledge proof to prove to a verifier that $m > 0$ ? I can create the bit ...
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### Is Using Digital Signatures to prove identity a zero knowledge proof?

Suppose Alice publishes a book with a public key in it, and later wants to prove that she wrote the book. She could sign challenge messages with her private key, and others could verify those signed ...
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### Range proof for elements in Vector Pedersen commitment

If I construct a vector pedersen commitment $c = a_1G_1 + a_2G_2 + ... + a_nG_n$ with an arbitrary scalar vector $(a_1, a_2, ..., a_n)$ and group elements $(G_1, G_2, ..., G_n)$, is it possible to ...
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### Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
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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 Bob ...
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### Perfect zero knowledge for the Schnorr protocol?

Can somebody explain (or point to a reference) why the Schnorr protocol cannot be proved zero knowledge?
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### Proof of non-membership on a Merkle tree?

Assume a user $U$ and a server $S$. $U$ uploads its data and wants later to perform an authenticity check. It also sends a Merkle tree to the server. Let’s say we would like $U$ to ask for a specific ...
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### 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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### zk-SNARKs vs. Zk-STARKs vs. Bulletproofs: definitions

I have become quite familiar with Bulletproofs the last few months. Bulletproofs is the name given to a zero-knowledge proof system for arithmetic circuits, by Benedikt Bünz et al. It is a specific ...
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### How to verify a number encrypted with an unknown key

Alice and Bob are going to follow the protocol below. Are there any crypto-constructions to help Bob verify the correctness of the answer he gets?: Alice encrypts a set of numbers using some ...
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### Practical consequences of a honest-verifier zero-knowledge of the Schnorr protocol

Schnorr protocol is known to be honest-verifier zero-knowledge and not perfectly zero-knowledge. What are the practical consequences of this fact? Does it mean a dishonest verifier can do something ...
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### What is difference between Zero Knowledge proof and Zero Knowledge Proof of Knowledge?

In a zero knowledge proof, a prover interactively proves to a verifier that an NP statement is true. If the language is an NP complete language and if the prover runs in poly time, the only way a ...
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### 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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### Is there a public key semantically secure cryptosystem for which one can prove in zero knowledge the equivalence of two plaintexts?

If Alice encrypts two messages $a$ and $b$, such that $x=E(a)$, $y=E(b)$. Can Alice prove (without revealing $a$, $b$ or the private key) that $a = b$? Obviously the proof must not be too long and it ...
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### Finding out the greater number under zero-knowledge conditions?

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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### Using two elliptic curves to do a range proof

Suppose Alice holds a secret value $a$ to which she has publicly committed to using two elliptic curves of distinct order. The curves are $g$ and $g'$ of orders $q$ and $q'$ (with $q < q'$) and ...
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### Why is a common reference string needed in zero knowledge proofs?

Can we have a non-trivial language without a CRS? Why?
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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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### 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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### 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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### What is a "rewinding argument"?

I've been reading a bit about cryptographic protocols and I keep seeing the phrase "rewinding argument". I've been unable to find a good source that would explain what is meant by this. It seems like ...
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### Can we prove possession of an AES-256 key without showing it?

Imagine this situation: Alice has an AES256GCM key $K$, a plaintext $X$, and $Y$ which is the ciphertext of $X$ encrypted by $K$ Bob has $X$ and $Y$ Alice and Bob can communicate with each other Bob ...
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### What are zk-STARK's?

The zk-STARK is a proof zero-knowledge proof system that, in contrast to the zk-SNARK, no longer relies on a trusted setup where the "toxic waste" parameters are initialized. What are, in layman's ...
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### Proof that lottery does not know outcome of draw

Could a variable participant lottery system cryptographically prove that they have zero knowledge of the outcome of a draw? Participants do not choose numbers in this lottery and winning numbers are ...
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### Examples of protocols that are insecure when run concurrently

I was reading Canetti00 Universally Composable security paper. The first page of introduction says that there are some MPC protocols and Zero knowledge protocols that are insecure under concurrent ...
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### Prove I know a value $v$ in a Pedersen Commitment without revealing it

Given a Pedersen Commitment: $P = aG + vH$ Where $G$ and $H$ are points in some group. $a$ is a blinding value/mask and $v$ is the value I wish to commit to. Is there a way to prove I know $v$ ...
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### Minimizing exchanges for ZK proof of a message with given SHA-256

Consider the problem of proving knowledge of a message $m$ which has a certain public SHA-256 hash $h$, without disclosing $m$ or usable information about it, while minimizing the information exchange ...
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### Why is the Pedersen commitment perfectly hiding?

I learned today about the Pedersen commitment scheme. A quick reminder (I know there are some variants of this scheme, so I will present the one I learned about): Public parameters - 2 primes $p,q$...
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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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### Why does SRP-6a use k = H(N, g) instead of the k = 3 in SRP-6?

I've been reading up on the Secure Remote Pasword protocol (SRP). There are a couple different versions of the protocol (the original published version being designated SRP-3, with two subsequent ...
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### ZKP: Prove that >18 while hiding age

I am relatively new to cryptography, but I've been programming for a while. Here's a story that sets well the problem I'm trying to solve: Alice has a digital passport that's signed with her ...
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### Security of zero knowledge proof protocols

When designing a protocol based on zero knowledge proofs, be it based on the discrete log problem, or on a Hamiltonian cycle in a graph, or something else, I assume there are security considerations, ...
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### Commutative homomorphic encryption for zero-knowledge transfers

I am trying to design a scheme that would allow the following: Alice has a number $a$ which she wants to keep secret Bob has a number $b$ which he wants to keep secret Alice can "transfer" a number ...
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### zero-knowledge proof of disjunctive statements (OR proofs)

I know there are standard ways to prove disjunctive statements about discrete logs, e.g. OR proof. But are there similar approaches for other class of language? For example, how can one go about ...
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### How to compute a challenge c using Fiat Shamir?

I have a prover and verifier. They are engaged in a zero-knowledge proof protocol. A verifier sends a challenge $c$ to the prover so he can compute a proof using the value $c$. How to use Fiat Shamir ...
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### Zero-knowledge transfer of value protocol inspired by EC El Gamal

This is a follow up on the question I asked here. I designed a scheme that allows the following: Alice has a value $a$ which she wants to keep secret Bob has a value $b$ which he wants to keep secret ...
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### Problem with Fiat-shamir on poly-round interactive protocol?

I have read in many places that Fiat Shamir technique is used to convert constant round interactive protocols to non-interactive arguments. What would be the problem in applying Fiat Shamir to poly-...
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### Zero knowledge RSA public key

Suppose Bob has $k>1$ RSA public keys $(e_i, n_i)$ without any knowledge of their corresponding private keys. Alice also has all the public keys, but also has a private key for only one of them, ...
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### Can we use non-adaptive zero-knowledge proof in group signatures

Group Signature schemes are used to provide anonymity of the signers. During signature generation, signers provide a NIZK proof to prove that they are certified group members. Verifiers check whether ...
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### Information sharing using interactive zero-knowledge system

I am trying to build a system that would allow information sharing in a kind of zero-knowledge way. Here is the set up: Let's say there is a trusted third party that has Alice's sensitive info M (e.g....
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### How do I explain zero knowledge proof to my 7 year old cousin? [duplicate]

How do I explain zero knowledge proof to my 7 year old cousin?
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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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### 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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### converting to rank one constraint system

I was reading Vitalik Buterin's post on ZK-snarks and I need some clarification on some points . since there aren't that many posts and articles regarding the subject , I had no choice other than ...
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### Zero Knowledge Password Proof

I'm working on implementing a cryptographic system and I'm trying to understand the Zero Knowledge Password Proof concept. So here's some background: To generate a secret key I am: Doing an ECDH key ...
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### 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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### Cryptographically safe lookup of value in a set

I'm looking for an elegant solution to the might-seem-trivial problem of looking up for specific value in a known set of values without disclosing what value we look for. Let me describe it in a ...
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