"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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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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Question about proof of knowledge defintion?

I am just reading the "soundness"-definition for proofs of knowledge by Bellare / Goldreich. A proof of knowledge is a proof between a prover $P$ and a verifier $V$. $P$ convinces $V$ to know a secret ...
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225 views

Zero-knowledge proof that a group element is a quadratic residue?

In a paper it says: "To convince a verifier that a group element is a quadratic residue, the prover executes the following proof with the verifier": $PK \left\{ (\alpha) : y = \pm g^\alpha \right\}$ ...
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Zero-Knowledge Challenge-Responce Protocol

Good day to everyone. I am trying to implement an e voting system (just for reference -it is not important though-it is described at the Internet Voting Protocol Based on Improved Implicit Security ...
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308 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 ...
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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 ...
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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) ...
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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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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 ...
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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. ...
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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 ...
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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 : $$ ...
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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 ...
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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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1answer
455 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. ...
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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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697 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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1answer
187 views

Zero Knowledge auth schemes with weak secret

In Zero Knowledge auth schemes the public DH factor of each peer is encrypted with a potentially weak pre-shared secret and the resulting ciphertexts are exchanged over an insecure channel. Why is no ...
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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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289 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 ...
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1answer
285 views

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 ...