"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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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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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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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 $...
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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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Shadowed identity in cryptography

I was trying to implement zero knowledge protocol for authentication based on the paper "A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory". ...
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Why Victor must not know which tunnel Peggy chooses?

In the classic description of Zero Knowledge Proof of Knowledge, Victor must wait outside the entrance to the cave while Peggy goes to the fork and choose a side. It's only once Peggy has entered a ...
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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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889 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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Can I construct a zero-knowledge proof that I solved a Project Euler problem?

Is there a practical method, and if so what is the method, to reveal that I have the following type of answer but conceal the answer itself? The answer is, let's say, the solution to a Project Euler ...
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381 views

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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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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How to forge Schnorr signatures if you can guess the challenge

Underlying the Schnorr signature is an identification protocol: let $G$ be a cyclic group where discrete log is "hard" and choose $g$ as a generator of $G$. Now have Alice pick a random (secret) ...
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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 ...
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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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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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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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283 views

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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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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281 views

Proving the possession of signature in zero-knowledge

Does anybody know an efficient mechanism to prove the possession of a digital signature (e.g. RSA) on a certain attribute (message) in zero-knowledge? That is, without revealing the actual signature (...
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574 views

Zero knowledge proof of possession of key

Suppose Alice has at some point in time produced ciphertext $C$ from message $M$ with key $k$. Suppose Alice has then passed $C$ to Bob, and also made a commitment to her key $k$ (thanks to ...
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863 views

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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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. Zero-knowledge-...
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Zero-knowledge proof system which is not proof of knowledge?

I have learned that a zero-knowledge (ZK) proof system can be constructed by making use of the three-color problem. In this particular case, the proof system also happens to be proof of knowledge (POK)...
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Proof of correct construction of a private key in distributed cryptography

In an exponential ElGamal encryption scheme where the key generation is done in a distributed way among $n$ trustees we have that each trustee $i$ (where $1 \leq i \leq n$): Selects a private key ...
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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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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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Is there a practical zero-knowledge proof for this special discrete log equation?

We have a multiplicative cyclic group $G$ with generators $g$ and $h$, as in El Gamal. Assume $G$ is a subgroup of $(\mathbb{Z}/n\mathbb{Z})^*$. There are two parties, Alice and Bob: Alice knows: ...
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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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Can I prove set membership and uniqueness without revealing the element?

Assuming a publicly known set $\Psi$ with $N$ unique elements. I have a set $\Sigma=\{\sigma_1,\sigma_2,...,\sigma_m\}$ where $m\leqslant N$. I would like to publicly prove that all the elements in $...
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273 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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Homomorphism and Zero Knowledge in FIPS 140-2 compliant systems

I am analyzing a system that needs to be at least level 3 FIPS 140-2 compliant. The system may leverage from homomorphic and Zero Knowledge constructs, but, as far as I can see, the algorithms ...
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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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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 ...
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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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How to prove membership of a list without disclosing the list members?

I'm designing a messaging system where the sender A sends a message m with a signature s to n Receivers. A Receiver Ri should then be able to prove to a Verifier V that he is one of the receivers of ...
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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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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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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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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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How to construct a zero-knowledge proof of a number of the form $n=p^a q^b$

Let $n = p^a$$q^b$ where p and q are distinct primes and a and b are positive integers. How to construct a zero knowledge proof that n is of such form? This is actually a homework problem with a ...
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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 $\varphi(...
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State of the art in zero knowledge proof compilers?

What is the current state of the art zero knowledge proof compiler ? I need one that can minimally handle double exponentiation by a known value E.g. $$Pok\{(\alpha):h=g^{\alpha^b}\} $$ where b, ...
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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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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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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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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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Zero-knowledge proof using quadratic residue: why two options?

In the zero knowledge proof using QR, why do we even bother with the server sending us $b = 0$ back? As I understand it, the server selects $b = 0$ or $b = 1$. If $b = 0$, then the client (Alice) ...
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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 ...